TPTP Problem File: SEV652+1.p

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%------------------------------------------------------------------------------
% File     : SEV652+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Mapiter MapFold M1
% Version  : [Kal26] axioms : Especial.
% English  :

% Refs     : [CK18]  Czajka L. & Kaliszyk (2018), Hammer for Coq: Automatio
%          : [Kal26] Kalizyk (2026), Email to G. Sutcliffe
% Source   : [Kal26]
% Names    : Mapiter.MapFold.M1.p [Kal26]

% Status   : Unknown
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    : 2903 (1194 unt;   0 def)
%            Number of atoms       : 9344 (3042 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 6592 ( 151   ~; 781   |;1636   &)
%                                         (1043 <=>;2981  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  539 ( 538 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1683 (1683 usr;1047 con; 0-22 aty)
%            Number of variables   : 9054 (8439   !; 615   ?)
% SPC      : FOF_UNK_RFO_SEQ

% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
%            with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
    p(c_24True) ).

fof('_HAMMER_COQ_FALSE',axiom,
    ~ p(c_24False) ).

fof('_HAMMER_COQ_TYPE_TYPE',axiom,
    cType___24t(cType) ).

fof('$_case_Coq.Init.Datatypes.bool$11350',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411350___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411350___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$11355',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411355___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411355___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$117232',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117232___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
            | ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117232___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$117243',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( cType___24t(Vv__CANONICAL__0)
           => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
             => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
                & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2etrue
                    & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
                  | ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2efalse
                    & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) )
          | ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$117248',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117248___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
          | ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117248___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$117253',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117253___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117253___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$7052',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_247052___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_247052___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88547',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488547___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0),c_24__let__var__8__m__88537__88540___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488547___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,c_24__let__var__8__m__88537__88540___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5),cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88569',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488569___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488569___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88575',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
       => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488575___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) )
          | ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488575___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88579',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
       => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488579___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
          | ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488579___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88626',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488626___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488626___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$88639',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__5)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__5)
                 => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
                        & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
                        & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$118689',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118689___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__118690] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118690)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118690)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118689___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__118690)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$118711',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__118712] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118712)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118712)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__118712)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.option$88776',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ( ? [Vvar__1___24Anonymous__88779] :
                ( t(Vvar__1___24Anonymous__88779,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88779)
                & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2488776___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88779) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__case__Coq_2eInit_2eDatatypes_2eoption_2488776___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.prod$11121',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__2)
       => ( c_24__type__9974___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
         => ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
           => ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => ? [Vvar__2___24Anonymous__11126] :
                  ( t(Vvar__2___24Anonymous__11126,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__11127] :
                      ( t(Vvar__3___24Anonymous__11127,Vv__CANONICAL__2)
                      & happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__11126,Vvar__3___24Anonymous__11127)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411121___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
                      <=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__11126)),Vvar__3___24Anonymous__11127)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$118706',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
     => ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__118707] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118707)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__118707)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__118707) )
        | ? [Vvar__0___24Anonymous__118708] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118708)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__118708)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__118708) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$121121',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__121122] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121122)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121122)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__121137__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__121122)) )
        | ? [Vvar__0___24Anonymous__121129] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121129)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121129)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121129) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_$_let_var_6_p_1156_1159',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1155] : c_24__let__var__6__p__1156__1159___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1155) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1155) ).

fof('$_def_$_let_var_6_p_1158_1160',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1157] : c_24__let__var__6__p__1158__1160___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1157) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1157) ).

fof('$_def_$_let_var_8_m_88537_88540',axiom,
    ! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__88535] : c_24__let__var__8__m__88537__88540___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__88535) = cIntMap_2eMap_2eMapPut1___24a6(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27,Vvar__0___24Anonymous__88535) ).

fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__117363] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__117363)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__117363)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__117364] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__117364)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__117364)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__117367] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__117367)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__117367)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__117364,Vvar__0___24Anonymous__117367) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.Even',axiom,
    ! [V0__n] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V0__n)
    <=> ? [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
          & V0__n = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__m) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
    <=> ? [V2__z] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
          & V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V0__n,V1__m)
    <=> ? [V2__p] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
          & cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = V1__m ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    ! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__113374___24a1(V0__A)) ).

fof('$_def_Coq.Bool.Bool.Is_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24True) ) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24False) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.eqb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.leb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & ( cCoq_2eBool_2eBool_2eleb___24a2(V0__b1,V1__b2)
          <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & ( cCoq_2eBool_2eBool_2eleb___24a2(V0__b1,V1__b2)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
    cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).

fof('$_def_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eleft___24a3(c_24__prop__11175,c_24__prop__11176,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue)) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V0__b) = cCoq_2eInit_2eSpecif_2eright___24a3(c_24__prop__11177,c_24__prop__11178,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse)) ) ) ) ).

fof('$_def_Coq.Bool.Zerob.zerob',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__105613] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__105613)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__105613)
            & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    ! [V0__i,V1__t] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__102424] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__102424)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__102424) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    ! [V1__i,V2__m] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
     => ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
          & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__102472] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__102472)
            & ? [Vvar__1___24Anonymous__102473] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__102473)
                & ? [Vvar__2___24Anonymous__102474] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__102474)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
                     => ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__102472,Vvar__1___24Anonymous__102473,Vvar__2___24Anonymous__102474)
                        & ( ? [Vvar__0___24Anonymous__102487] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102487)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102487)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__102487,Vvar__2___24Anonymous__102474) )
                          | ? [Vvar__0___24Anonymous__102488] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102488)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102488)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__102488,Vvar__0___24Anonymous__102472) )
                          | ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__102473 ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__102450] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__102450)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__102450) ) ).

fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
    ! [V0__r] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
     => ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
        | ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
        | ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
          & cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).

fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
    ( p(cCoq_2eInit_2eDatatypes_2eIDProp)
  <=> ! [V0__A] :
        ( cProp___24t(V0__A)
       => ( p(V0__A)
         => p(V0__A) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.andb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_def_Coq.Init.Datatypes.app',axiom,
    ! [V0__A,V2__l,V3__m] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
          | ? [Vvar__1___24Anonymous__83007] :
              ( t(Vvar__1___24Anonymous__83007,V0__A)
              & ? [Vvar__2___24Anonymous__83008] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__83008)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__83007,Vvar__2___24Anonymous__83008)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__83007,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__83008,V3__m)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.fst',axiom,
    ! [V0__A,V1__B,V2__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
         => ? [Vvar__2___24Anonymous__69] :
              ( t(Vvar__2___24Anonymous__69,V0__A)
              & ? [Vvar__3___24Anonymous__70] :
                  ( t(Vvar__3___24Anonymous__70,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__69,Vvar__3___24Anonymous__70)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__69 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.is_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2eis__true___24a1(V0__b)
    <=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_def_Coq.Init.Datatypes.length',axiom,
    ! [V0__A,V2__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
          | ? [Vvar__1___24Anonymous__82997] :
              ( t(Vvar__1___24Anonymous__82997,V0__A)
              & ? [Vvar__2___24Anonymous__82998] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__82998)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__82997,Vvar__2___24Anonymous__82998)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__82998)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__117257___24t(V0__P,V0__P)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
       => ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
            & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
          | ? [Vvar__0___24Anonymous__117255] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__117255)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__117255)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__117255),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__117255)) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.negb',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('$_def_Coq.Init.Datatypes.orb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).

fof('$_def_Coq.Init.Datatypes.prod_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( c_24__type__82901___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
           => ? [Vvar__2___24Anonymous__82894] :
                ( t(Vvar__2___24Anonymous__82894,V0__A)
                & ? [Vvar__3___24Anonymous__82895] :
                    ( t(Vvar__3___24Anonymous__82895,V1__B)
                    & V4__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__82894,Vvar__3___24Anonymous__82895)
                    & cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V0__A,V1__B,V2__P,V3__f,V4__p) = happ(happ(V3__f,Vvar__2___24Anonymous__82894),Vvar__3___24Anonymous__82895) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.snd',axiom,
    ! [V0__A,V1__B,V2__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
         => ? [Vvar__2___24Anonymous__81] :
              ( t(Vvar__2___24Anonymous__81,V0__A)
              & ? [Vvar__3___24Anonymous__82] :
                  ( t(Vvar__3___24Anonymous__82,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__81,Vvar__3___24Anonymous__82)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__82 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.xorb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.add',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__88979] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__88979)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__88979)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__88979,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.compare',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__104026] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104026)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104026)
                  & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__104027] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104027)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104027)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__104030] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104030)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104030)
                      & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__104027,Vvar__0___24Anonymous__104030) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.div2',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__113391] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113391)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113391)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113391)
                & ( ( Vvar__0___24Anonymous__113391 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__113394] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113394)
                      & Vvar__0___24Anonymous__113391 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113394)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__113394)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.double',axiom,
    ! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).

fof('$_def_Coq.Init.Nat.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__104011] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104011)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104011)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__104012] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104012)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104012)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__104015] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104015)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104015)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__104012,Vvar__0___24Anonymous__104015) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.even',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__104035] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104035)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104035)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104035)
                & ( ( Vvar__0___24Anonymous__104035 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__104038] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104038)
                      & Vvar__0___24Anonymous__104035 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104038)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__104038) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.gcd',axiom,
    ! [V1__a,V2__b] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
     => ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
        | ? [Vvar__0___24Anonymous__118421] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__118421)
            & V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118421)
            & cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118421)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__118421)) ) ) ) ).

fof('$_def_Coq.Init.Nat.max',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__113358] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113358)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113358)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__113361] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113361)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113361)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__113358,Vvar__0___24Anonymous__113361)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.min',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__113364] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113364)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113364)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__113367] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113367)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113367)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__113364,Vvar__0___24Anonymous__113367)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.mul',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__104002] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104002)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104002)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__104002,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.pow',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
     => ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
        | ? [Vvar__0___24Anonymous__111269] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__111269)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__111269)
            & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__111269)) ) ) ) ).

fof('$_def_Coq.Init.Nat.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
        | ? [Vvar__0___24Anonymous__117182] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__117182)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__117182)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__117182 ) ) ) ).

fof('$_def_Coq.Init.Nat.sqrt',axiom,
    ! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_def_Coq.Init.Nat.sub',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
        | ? [Vvar__0___24Anonymous__104005] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104005)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104005)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__104008] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104008)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104008)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__104005,Vvar__0___24Anonymous__104008) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.testbit',axiom,
    ! [V1__a,V2__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
     => ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
        | ? [Vvar__0___24Anonymous__104042] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104042)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104042)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__104042) ) ) ) ).

fof('$_def_Coq.Init.Peano.ge',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).

fof('$_def_Coq.Init.Peano.gt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).

fof('$_def_Coq.Init.Peano.lt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).

fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
    ! [V0__A,V1__P,V2__e] :
      ( cType___24t(V0__A)
     => ( c_24__type__113590___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
         => ? [Vvar__2__x__113584] :
              ( t(Vvar__2__x__113584,V0__A)
              & p(happ(V1__P,Vvar__2__x__113584))
              & V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__113584)
              & cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__113584 ) ) ) ) ).

fof('$_def_Coq.Init.Specif.projT1',axiom,
    ! [V0__A,V1__P,V2__x] :
      ( cType___24t(V0__A)
     => ( c_24__type__113770___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
         => ? [Vvar__2__x__113764] :
              ( t(Vvar__2__x__113764,V0__A)
              & ? [Vvar__3___24Anonymous__113765] :
                  ( t(Vvar__3___24Anonymous__113765,happ(V1__P,Vvar__2__x__113764))
                  & V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__113764,Vvar__3___24Anonymous__113765)
                  & cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__113764 ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sigT_rect',axiom,
    ! [V0__A,V1__P,V2__P,V3__f,V4__s] :
      ( cType___24t(V0__A)
     => ( c_24__type__111596___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__111604___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__111588] :
                ( t(Vvar__2__x__111588,V0__A)
                & ? [Vvar__3___24Anonymous__111589] :
                    ( t(Vvar__3___24Anonymous__111589,happ(V1__P,Vvar__2__x__111588))
                    & V4__s = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__111588,Vvar__3___24Anonymous__111589)
                    & cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(happ(V3__f,Vvar__2__x__111588),Vvar__3___24Anonymous__111589) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sig_rec',axiom,
    ! [V0__A,V1__P,V2__P] : cCoq_2eInit_2eSpecif_2esig__rec___24a3(V0__A,V1__P,V2__P) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V0__A,V1__P,V2__P) ).

fof('$_def_Coq.Init.Specif.sig_rect',axiom,
    ! [V0__A,V1__P,V2__P,V3__f,V4__s] :
      ( cType___24t(V0__A)
     => ( c_24__type__111509___24t(V0__A,V1__P,V2__P,V1__P)
       => ( c_24__type__111517___24t(V0__A,V1__P,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
           => ? [Vvar__2__x__111501] :
                ( t(Vvar__2__x__111501,V0__A)
                & p(happ(V1__P,Vvar__2__x__111501))
                & V4__s = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__111501)
                & cCoq_2eInit_2eSpecif_2esig__rect___24a5(V0__A,V1__P,V2__P,V3__f,V4__s) = happ(V3__f,Vvar__2__x__111501) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sumbool_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__f,V5__s] :
      ( cProp___24t(V0__A)
     => ( cProp___24t(V1__B)
       => ( c_24__type__111659___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
           => ( ( p(V0__A)
                & V5__s = cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V3__f )
              | ( p(V1__B)
                & V5__s = cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V4__f ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Specif.sumor_rec',axiom,
    ! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumor__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumor__rect___24a3(V0__A,V1__B,V2__P) ).

fof('$_def_Coq.Init.Specif.sumor_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__f,V5__s] :
      ( cType___24t(V0__A)
     => ( cProp___24t(V1__B)
       => ( c_24__type__98601___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
           => ( ? [Vvar__2___24Anonymous__98592] :
                  ( t(Vvar__2___24Anonymous__98592,V0__A)
                  & V5__s = cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,Vvar__2___24Anonymous__98592)
                  & cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = happ(V3__f,Vvar__2___24Anonymous__98592) )
              | ( p(V1__B)
                & V5__s = cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B)
                & cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V0__A,V1__B,V2__P,V3__f,V4__f,V5__s) = V4__f ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Wf.well_founded',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
    <=> ! [V2__a] :
          ( t(V2__a,V0__A)
         => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).

fof('$_def_Coq.Lists.List.In',axiom,
    ! [V0__A,V2__a,V3__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
            <=> p(c_24False) ) )
          | ? [Vvar__1___24Anonymous__88083] :
              ( t(Vvar__1___24Anonymous__88083,V0__A)
              & ? [Vvar__2___24Anonymous__88084] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__88084)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__88083,Vvar__2___24Anonymous__88084)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__88083 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__88084) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.fold_left',axiom,
    ! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
              & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
            | ? [Vvar__1___24Anonymous__118275] :
                ( t(Vvar__1___24Anonymous__118275,V1__B)
                & ? [Vvar__2___24Anonymous__118276] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__118276)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__118275,Vvar__2___24Anonymous__118276)
                    & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__118276,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__118275)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.fold_right',axiom,
    ! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
         => ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
              & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
            | ? [Vvar__1___24Anonymous__88149] :
                ( t(Vvar__1___24Anonymous__88149,V1__B)
                & ? [Vvar__2___24Anonymous__88150] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__88150)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__88149,Vvar__2___24Anonymous__88150)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__88149),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__88150)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.hd',axiom,
    ! [V0__A,V1__default,V2__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
          | ? [Vvar__1___24Anonymous__92] :
              ( t(Vvar__1___24Anonymous__92,V0__A)
              & ? [Vvar__2___24Anonymous__93] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__93)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__92,Vvar__2___24Anonymous__93)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__92 ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.map',axiom,
    ! [V0__A,V1__B,V2__f,V4__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
              & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
            | ? [Vvar__1___24Anonymous__88126] :
                ( t(Vvar__1___24Anonymous__88126,V0__A)
                & ? [Vvar__2___24Anonymous__88127] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__88127)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__88126,Vvar__2___24Anonymous__88127)
                    & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__88126),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__88127)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.nth',axiom,
    ! [V0__A,V2__n,V3__l,V4__default] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
       => ( ( cType___24t(V0__A)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
             => ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                & ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                    & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
                  | ? [Vvar__1___24Anonymous__6931] :
                      ( t(Vvar__1___24Anonymous__6931,V0__A)
                      & ? [Vvar__2___24Anonymous__6932] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6932)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6931,Vvar__2___24Anonymous__6932)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__6931 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__6934] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6934)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6934)
                    & ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                        & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
                      | ? [Vvar__1___24Anonymous__6941] :
                          ( t(Vvar__1___24Anonymous__6941,V0__A)
                          & ? [Vvar__2___24Anonymous__6942] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6942)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6941,Vvar__2___24Anonymous__6942)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__6934,Vvar__2___24Anonymous__6942,V4__default) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.tl',axiom,
    ! [V0__A,V1__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
       => ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__103] :
              ( t(Vvar__1___24Anonymous__103,V0__A)
              & ? [Vvar__2___24Anonymous__104] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__104)
                  & V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__103,Vvar__2___24Anonymous__104)
                  & cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__104 ) ) ) ) ) ).

fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
    ! [V0__A,V1__B,V2__eqB,V3__f] :
      ( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
    <=> ! [V4__x] :
          ( t(V4__x,V0__A)
         => ! [V5__y] :
              ( t(V5__y,V0__A)
             => ! [V6__z] :
                  ( t(V6__z,V1__B)
                 => p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).

fof('$_def_Coq.Logic.Decidable.decidable',axiom,
    ! [V0__P] :
      ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
    <=> ( p(V0__P)
        | ~ p(V0__P) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
    ! [V0__U,V1__P,V2__p,V3__x] :
      ( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
    <=> ! [V4__y] :
          ( t(V4__y,happ(V1__P,V2__p))
         => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
           => V3__x = V4__y ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
    ! [V0__U,V1__p,V2__Q,V3__x] :
      ( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x)
    <=> ( V1__p = V1__p
       => V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
    ! [V0__U] :
      ( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K_____24a1(V0__U)
    <=> ! [V1__x] :
          ( t(V1__x,V0__U)
         => ! [V2__P] :
              ( c_24__type__117399___24t(V0__U,V1__x,V2__P)
             => cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P) ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
    ! [V0__U,V1__x,V2__P] :
      ( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
    <=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
       => ( V1__x = V1__x
         => p(V2__P) ) ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    ! [V0__U,V1__x,V2__y] :
      ( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
    <=> ( V1__x = V2__y
       => c_24Proof = c_24Proof ) ) ).

fof('$_def_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
    ! [V0__U,V1__x] :
      ( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__U,V1__x)
    <=> ( V1__x = V1__x
       => c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.b2n',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.discr',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V0__n) = cCoq_2eInit_2eSpecif_2einright___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__102335),c_24__prop__102336,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0)) )
        | ? [Vvar__0___24Anonymous__102332] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102332)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102332)
            & cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V0__n) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__102338___24a1(Vvar__0___24Anonymous__102332)),c_24__prop__102339___24a1(Vvar__0___24Anonymous__102332),cCoq_2eInit_2eSpecif_2eexist___24a4(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__102338___24a1(Vvar__0___24Anonymous__102332),Vvar__0___24Anonymous__102332,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102332)))) ) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
    ! [V0__p,V1__q] :
      ( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
    <=> ? [V2__r] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
          & V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.NArith.BinNat.N.le',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
    <=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.NArith.BinNat.N.le_alt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V0__n,V1__m)
    <=> ? [V2__p] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
          & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = V1__m ) ) ).

fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
    <=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
    ! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__120981___24a1(V0__A)) ).

fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__102310] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102310)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102310)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__102313] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102313)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102313)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__102310,Vvar__0___24Anonymous__102313)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
            & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__105624] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105624)
                  & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105624)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__105625] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105625)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105625)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__105628] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105628)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105628)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__105625,Vvar__0___24Anonymous__105628) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.div',axiom,
    ! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).

fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__11199] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11199)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11199)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11199)
                & ( ? [Vvar__0___24Anonymous__11203] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11203)
                      & Vvar__0___24Anonymous__11199 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11203)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11203) )
                  | ? [Vvar__0___24Anonymous__11204] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11204)
                      & Vvar__0___24Anonymous__11199 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11204)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11204) )
                  | ( Vvar__0___24Anonymous__11199 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__11189] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11189)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11189)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11189)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
     => ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
         => ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
            & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__11191] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11191)
                  & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11191)
                  & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__11192] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11192)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
             => ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11192)
                & ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__11195] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11195)
                      & V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11195)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__11192,Vvar__0___24Anonymous__11195) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__116009] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116009)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__116009)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__116012] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116012)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__116012)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__116009,Vvar__0___24Anonymous__116012) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__102327] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102327)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102327)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__102330] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102330)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102330)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__102327,Vvar__0___24Anonymous__102330) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
    ! [V0__n,V1__n_27] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
    ! [V0__n,V1__n_27] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
    ! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).

fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__102315] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102315)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102315)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__102318] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102318)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102318)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__102315,Vvar__0___24Anonymous__102318)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
    ! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).

fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__120977] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__120977)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__120977)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__120977)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.pow',axiom,
    ! [V0__n,V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
     => ( ( V1__p = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__120966] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120966)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120966)
                & ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__120969] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120969)
                      & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120969)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__120969,Vvar__0___24Anonymous__120966)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__120964] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120964)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__120964)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__120964) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__105614] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105614)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105614)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__105619] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105619)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105614)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105619)
                         => ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105619)
                            & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__105614,Vvar__0___24Anonymous__105619) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
                                & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                              | ? [Vvar__0___24Anonymous__105622] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105622)
                                  & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__105614,Vvar__0___24Anonymous__105619) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__105622)
                                  & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105622) )
                              | ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__105614,Vvar__0___24Anonymous__105619) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
                                & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__111343] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111343)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111343)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__111343)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__11186] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11186)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11186)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11186)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
    ! [V0__a,V1__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__105633] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105633)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105633)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__105633,V1__n) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__105635] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105635)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105635)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__105635) ) ) ) ).

fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    ! [V0__c,V1__c_27] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
     => ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
        | ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
        | ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
          & cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__102348] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102348)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102348)
                & ( ? [Vvar__0___24Anonymous__102352] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102352)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102352)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__102347__1__add__carry___24a2(Vvar__0___24Anonymous__102348,Vvar__0___24Anonymous__102352)) )
                  | ? [Vvar__0___24Anonymous__102353] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102353)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102353)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__102348,Vvar__0___24Anonymous__102353)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102348)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__102354] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102354)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102354)
                & ( ? [Vvar__0___24Anonymous__102358] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102358)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102358)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__102354,Vvar__0___24Anonymous__102358)) )
                  | ? [Vvar__0___24Anonymous__102359] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102359)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102359)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__102354,Vvar__0___24Anonymous__102359)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102354) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__102360] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102360)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102360)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102360)) )
              | ? [Vvar__0___24Anonymous__102361] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102361)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102361)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102361) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.divide',axiom,
    ! [V0__p,V1__q] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2edivide___24a2(V0__p,V1__q)
    <=> ? [V2__r] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__r)
          & V1__q = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V2__r,V0__p) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__105659] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105659)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105659)
                & ( ? [Vvar__0___24Anonymous__105663] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105663)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105663)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__105659,Vvar__0___24Anonymous__105663) )
                  | ? [Vvar__0___24Anonymous__105664] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105664)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105664)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__105665] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105665)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105665)
                & ( ? [Vvar__0___24Anonymous__105669] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105669)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105669)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__105670] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105670)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105670)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__105665,Vvar__0___24Anonymous__105670) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
         => ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__105671] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105671)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105671)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ? [Vvar__0___24Anonymous__105672] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105672)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105672)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
    ! [V0__A,V1__f,V3__x,V4__n] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
       => ( ? [Vvar__0___24Anonymous__105646] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105646)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105646)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__105646),Vvar__0___24Anonymous__105646)) )
          | ? [Vvar__0___24Anonymous__105647] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105647)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105647)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__105647),Vvar__0___24Anonymous__105647) )
          | ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    ! [V0__A,V1__op,V3__p,V4__a] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
       => ( ? [Vvar__0___24Anonymous__121065] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121065)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121065)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__121065,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__121066] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121066)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121066)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__121066,happ(happ(V1__op,V4__a),V4__a)) )
          | ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
    ! [V0__p,V1__p_27] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
    ! [V0__p,V1__p_27] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
    ! [V1__x,V2__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__11211] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11211)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11211)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11211,V2__y))) )
        | ? [Vvar__0___24Anonymous__11212] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11212)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11212)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11212,V2__y)) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__116406] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__116406)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__116406)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__116406)
                & ( ( Vvar__0___24Anonymous__116406 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
                  | ? [Vvar__0___24Anonymous__116409] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__116409)
                      & Vvar__0___24Anonymous__116406 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__116409)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__116406)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__121082] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121082)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121082)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__121082)) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
    ! [V1__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__11208] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11208)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11208)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11208)) )
        | ? [Vvar__0___24Anonymous__11209] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11209)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__11209)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__11209)) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__121031] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121031)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121031)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__121031)) )
        | ? [Vvar__0___24Anonymous__121032] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121032)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121032)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__121032)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
          | ? [Vvar__0___24Anonymous__102385] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102385)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__102385)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__102385 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
    ! [V1__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__105643] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105643)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105643)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__105643)) )
        | ? [Vvar__0___24Anonymous__105644] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105644)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105644)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105644) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__121035] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121035)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121035)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__121048___24a1(Vvar__0___24Anonymous__121035) )
        | ? [Vvar__0___24Anonymous__121039] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121039)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121039)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__121055___24a1(Vvar__0___24Anonymous__121039) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__121059 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__104059] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__104059)
          & ? [Vvar__1__Qden__104060] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__104060)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104059,Vvar__1__Qden__104060)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__104060 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__104054] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__104054)
          & ? [Vvar__1__Qden__104055] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__104055)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104054,Vvar__1__Qden__104055)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__104054 ) ) ) ).

fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
    ! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).

fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
        | ? [Vvar__0___24Anonymous__104078] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104078)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__104078)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__104078) )
        | ? [Vvar__0___24Anonymous__104079] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104079)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__104079)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__104079)) ) ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
    <=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
        | V0__r1 = V1__r2 ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
    ! [V0__r1,V1__r2] :
      ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
    <=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
        | V0__r1 = V1__r2 ) ) ).

fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
    ! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).

fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
    ! [V0__A,V1__R] :
      ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__A)
         => ! [V3__y] :
              ( t(V3__y,V0__A)
             => ( p(happ(happ(V1__R,V2__x),V3__y))
               => ( p(happ(happ(V1__R,V3__y),V2__x))
                 => V2__x = V3__y ) ) ) ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__161___24a1(V0__A) ).

fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).

fof('$_def_Coq.Sets.Relations_1.Antisymmetric',axiom,
    ! [V0__U,V1__R] :
      ( cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V0__U,V1__R)
    <=> ! [V2__x] :
          ( t(V2__x,V0__U)
         => ! [V3__y] :
              ( t(V3__y,V0__U)
             => ( p(happ(happ(V1__R,V2__x),V3__y))
               => ( p(happ(happ(V1__R,V3__y),V2__x))
                 => V2__x = V3__y ) ) ) ) ) ).

fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
    ! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__161___24a1(V0__U) ).

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [Vvar__121004] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__121004)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__121004) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [Vvar__116350] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__116350)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__116350) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [Vvar__120955] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__120955)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__120955) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [Vvar__121160] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__121160)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__121160) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq = c_3d___24a1(cCoq_2eStrings_2eString_2estring) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__121161] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__121161)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__121161) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
    cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__121222] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__121222)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__121222) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.Bezout',axiom,
    ! [V0__n,V1__m,V2__p] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p)
    <=> ? [V3__a] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__a)
          & ? [V4__b] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__b)
              & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__a,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__b,V1__m)) = V2__p ) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.Even',axiom,
    ! [V0__a] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eEven___24a1(V0__a)
    <=> ? [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
          & V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__b) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
    <=> ? [V2__z] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
          & V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
    ! [V0__x,V1__y] :
      ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).

fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
    ! [V0__x,V1__y] :
      ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
    <=> V0__x != V1__y ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__105763] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105763)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105763)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105763) )
        | ? [Vvar__0___24Anonymous__105764] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105764)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105764)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105764) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__121185] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121185)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121185)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__121185) )
        | ? [Vvar__0___24Anonymous__121186] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121186)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121186)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__121186) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__121181] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121181)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121181)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__121181) )
        | ? [Vvar__0___24Anonymous__121182] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121182)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121182)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__121182) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.add',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V1__y )
        | ? [Vvar__0___24Anonymous__11234] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11234)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11234)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__11238] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11238)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11238)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__11234,Vvar__0___24Anonymous__11238)) )
                  | ? [Vvar__0___24Anonymous__11239] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11239)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11239)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__11234,Vvar__0___24Anonymous__11239) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__11240] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11240)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11240)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__11244] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11244)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11244)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__11244,Vvar__0___24Anonymous__11240) )
                  | ? [Vvar__0___24Anonymous__11245] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11245)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11245)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__11240,Vvar__0___24Anonymous__11245)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.compare',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
            & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__11265] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11265)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11265)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__11266] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11266)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11266)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__11267] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11267)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11267)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__11271] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11271)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11271)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__11267,Vvar__0___24Anonymous__11271) )
                  | ? [Vvar__0___24Anonymous__11272] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11272)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11272)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__11273] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11273)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11273)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__11277] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11277)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11277)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__11278] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11278)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11278)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__11273,Vvar__0___24Anonymous__11278)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__11288] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__11288)
            & ? [Vvar__3___24Anonymous__11289] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__11289)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__11288,Vvar__3___24Anonymous__11289)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__11288 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__121196] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121196)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121196)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121196)
                & ( ? [Vvar__0___24Anonymous__121200] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121200)
                      & Vvar__0___24Anonymous__121196 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121200)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__121201] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121201)
                      & Vvar__0___24Anonymous__121196 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121201)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__121196 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__121202] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121202)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121202)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121202)
                & ( ? [Vvar__0___24Anonymous__121206] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121206)
                      & Vvar__0___24Anonymous__121202 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121206)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__121207] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121207)
                      & Vvar__0___24Anonymous__121202 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121207)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__121202 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.log2',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__121208] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121208)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121208)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121208)
                & ( ? [Vvar__0___24Anonymous__121212] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121212)
                      & Vvar__0___24Anonymous__121208 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121212)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__121212)) )
                  | ? [Vvar__0___24Anonymous__121213] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121213)
                      & Vvar__0___24Anonymous__121208 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121213)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__121213)) )
                  | ( Vvar__0___24Anonymous__121208 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
        | ? [Vvar__0___24Anonymous__121214] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121214)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121214)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__105773] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__105773)
            & ? [Vvar__3___24Anonymous__105774] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__105774)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__105773,Vvar__3___24Anonymous__105774)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__105774 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.mul',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__11252] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11252)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11252)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__11256] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11256)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11256)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11252,Vvar__0___24Anonymous__11256)) )
                  | ? [Vvar__0___24Anonymous__11257] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11257)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11257)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11252,Vvar__0___24Anonymous__11257)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__11258] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11258)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11258)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__11262] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11262)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11262)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11258,Vvar__0___24Anonymous__11262)) )
                  | ? [Vvar__0___24Anonymous__11263] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11263)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11263)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11258,Vvar__0___24Anonymous__11263)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__105777] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105777)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105777)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105777)
                & ( ? [Vvar__0___24Anonymous__105781] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105781)
                      & Vvar__0___24Anonymous__105777 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105781)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__105782] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105782)
                      & Vvar__0___24Anonymous__105777 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105782)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__105777 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__105783] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105783)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105783)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105783)
                & ( ? [Vvar__0___24Anonymous__105787] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105787)
                      & Vvar__0___24Anonymous__105783 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105787)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__105788] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105788)
                      & Vvar__0___24Anonymous__105783 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105788)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__105783 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__105768] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105768)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105768)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105768) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__105765] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__105765)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__105765)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__105765)) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__11247] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11247)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11247)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11247) )
        | ? [Vvar__0___24Anonymous__11248] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11248)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11248)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11248) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
     => ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__105759] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105759)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__105759)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__105759) )
        | ? [Vvar__0___24Anonymous__105760] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105760)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__105760)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
    ! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
    ! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
    ! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__121179] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121179)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121179)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__121180] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121180)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121180)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
    ! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
    ! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__121189] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121189)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121189)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__121189) )
        | ? [Vvar__0___24Anonymous__121190] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121190)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121190)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__121187] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121187)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121187)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__121187) )
        | ? [Vvar__0___24Anonymous__121188] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121188)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121188)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__121191] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121191)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__121191)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__121191 )
        | ? [Vvar__0___24Anonymous__121192] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121192)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__121192)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
          <=> p(c_24True) ) )
        | ? [Vvar__0___24Anonymous__120854] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120854)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120854)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__120854)
                & ( ? [Vvar__0___24Anonymous__120858] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120858)
                      & Vvar__0___24Anonymous__120854 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120858)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__120859] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120859)
                      & Vvar__0___24Anonymous__120854 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120859)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__120854 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__120860] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120860)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120860)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__120860)
                & ( ? [Vvar__0___24Anonymous__120864] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120864)
                      & Vvar__0___24Anonymous__120860 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120864)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__120865] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120865)
                      & Vvar__0___24Anonymous__120860 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120865)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__120860 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
          <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__115947] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115947)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115947)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__115947)
                & ( ? [Vvar__0___24Anonymous__115951] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115951)
                      & Vvar__0___24Anonymous__115947 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__115951)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__115952] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115952)
                      & Vvar__0___24Anonymous__115947 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__115952)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__115947 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__115953] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115953)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115953)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__115953)
                & ( ? [Vvar__0___24Anonymous__115957] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115957)
                      & Vvar__0___24Anonymous__115953 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__115957)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__115958] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__115958)
                      & Vvar__0___24Anonymous__115953 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__115958)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__115953 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__120867] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120867)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__120867)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__120868] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__120868)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__120868)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__120868) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.ZArith.Znat.neq',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
    <=> V0__x != V1__y ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__83034___24a1(V0__D) ).

fof('$_def_Coq.micromega.Refl.make_conj',axiom,
    ! [V1__A,V2__eval,V3__l] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
            <=> p(c_24True) ) )
          | ? [Vvar__1___24Anonymous__90423] :
              ( t(Vvar__1___24Anonymous__90423,V1__A)
              & ? [Vvar__2___24Anonymous__90424] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__90424)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__90424)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__90423,Vvar__2___24Anonymous__90424)
                        & ( ( Vvar__2___24Anonymous__90424 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
                            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                            <=> p(happ(V2__eval,Vvar__1___24Anonymous__90423)) ) )
                          | ? [Vvar__1___24Anonymous__90435] :
                              ( t(Vvar__1___24Anonymous__90435,V1__A)
                              & ? [Vvar__2___24Anonymous__90436] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__90436)
                                  & Vvar__2___24Anonymous__90424 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__90435,Vvar__2___24Anonymous__90436)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__90423))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__90424) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.Refl.make_impl',axiom,
    ! [V1__A,V2__eval,V3__l,V4__goal] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
            <=> p(V4__goal) ) )
          | ? [Vvar__1___24Anonymous__90402] :
              ( t(Vvar__1___24Anonymous__90402,V1__A)
              & ? [Vvar__2___24Anonymous__90403] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__90403)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__90402,Vvar__2___24Anonymous__90403)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__90402))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__90403,V4__goal) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
    ! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).

fof('$_def_Coq.micromega.Tauto.clause',axiom,
    ! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    ! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__118213] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118213)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118213)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__118213)
                    & ( ? [Vvar__0___24Anonymous__118217] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118217)
                          & Vvar__0___24Anonymous__118213 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__118217)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118213))) )
                      | ? [Vvar__0___24Anonymous__118218] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118218)
                          & Vvar__0___24Anonymous__118213 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__118218)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118213))) )
                      | ( Vvar__0___24Anonymous__118213 = cCoq_2eNumbers_2eBinNums_2exH
                        & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__118219] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118219)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118219)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__118219)
                    & ( ? [Vvar__0___24Anonymous__118223] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118223)
                          & Vvar__0___24Anonymous__118219 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__118223)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118219)) )
                      | ? [Vvar__0___24Anonymous__118224] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118224)
                          & Vvar__0___24Anonymous__118219 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__118224)
                          & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118219)) )
                      | ( Vvar__0___24Anonymous__118219 = cCoq_2eNumbers_2eBinNums_2exH
                        & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    ! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__118180] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118180)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__118180)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118180))) )
          | ? [Vvar__0___24Anonymous__118181] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__118181)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__118181)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__118181)) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).

fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
    ! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
       => ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
          | ? [Vvar__0___24Anonymous__103876] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103876)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__103876)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__103876) )
          | ? [Vvar__0___24Anonymous__103877] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__103877)
              & V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__103877)
              & cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__103877)) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    ! [V0__C,V1__ceqb,V3__P,V4__P_27] :
      ( cType___24t(V0__C)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
       => ( ? [Vvar__1___24Anonymous__260] :
              ( t(Vvar__1___24Anonymous__260,V0__C)
              & ( cType___24t(V0__C)
               => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                 => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__260)
                    & ( ? [Vvar__1___24Anonymous__270] :
                          ( t(Vvar__1___24Anonymous__270,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__270)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__260),Vvar__1___24Anonymous__270) )
                      | ? [Vvar__1___24Anonymous__272] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__272)
                          & ? [Vvar__2___24Anonymous__273] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__273)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__272,Vvar__2___24Anonymous__273)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__276] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__276)
                          & ? [Vvar__2___24Anonymous__277] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__277)
                              & ? [Vvar__3___24Anonymous__278] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__278)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__276,Vvar__2___24Anonymous__277,Vvar__3___24Anonymous__278)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__283] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__283)
              & ? [Vvar__2___24Anonymous__284] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__284)
                  & ( cType___24t(V0__C)
                   => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                     => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__283,Vvar__2___24Anonymous__284)
                        & ( ? [Vvar__1___24Anonymous__304] :
                              ( t(Vvar__1___24Anonymous__304,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__304)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__306] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__306)
                              & ? [Vvar__2___24Anonymous__307] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__307)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__283)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__306)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__306,Vvar__2___24Anonymous__307)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__283,Vvar__1___24Anonymous__306) = cCoq_2eInit_2eDatatypes_2eEq
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__284,Vvar__2___24Anonymous__307) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__283,Vvar__1___24Anonymous__306) = cCoq_2eInit_2eDatatypes_2eLt
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__283,Vvar__1___24Anonymous__306) = cCoq_2eInit_2eDatatypes_2eGt
                                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
                          | ? [Vvar__1___24Anonymous__312] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__312)
                              & ? [Vvar__2___24Anonymous__313] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__313)
                                  & ? [Vvar__3___24Anonymous__314] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__314)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__312,Vvar__2___24Anonymous__313,Vvar__3___24Anonymous__314)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__319] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__319)
              & ? [Vvar__2___24Anonymous__320] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__320)
                  & ? [Vvar__3___24Anonymous__321] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__321)
                      & ( cType___24t(V0__C)
                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
                         => ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__319,Vvar__2___24Anonymous__320,Vvar__3___24Anonymous__321)
                            & ( ? [Vvar__1___24Anonymous__354] :
                                  ( t(Vvar__1___24Anonymous__354,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__354)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__356] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__356)
                                  & ? [Vvar__2___24Anonymous__357] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__357)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__356,Vvar__2___24Anonymous__357)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__360] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__360)
                                  & ? [Vvar__2___24Anonymous__361] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__361)
                                      & ? [Vvar__3___24Anonymous__362] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__362)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__320)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__361)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__360,Vvar__2___24Anonymous__361,Vvar__3___24Anonymous__362)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__375___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__319)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__360)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__320,Vvar__2___24Anonymous__361) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__319,Vvar__1___24Anonymous__360) = cCoq_2eInit_2eDatatypes_2etrue
                                                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__321,Vvar__3___24Anonymous__362) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__319,Vvar__1___24Anonymous__360) = cCoq_2eInit_2eDatatypes_2efalse
                                                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
                                                    | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__320,Vvar__2___24Anonymous__361) = cCoq_2eInit_2eDatatypes_2eLt
                                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                                                    | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__320,Vvar__2___24Anonymous__361) = cCoq_2eInit_2eDatatypes_2eGt
                                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).

fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    ! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    ! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    ! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).

fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    ! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
       => ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
          | ? [Vvar__0___24Anonymous__4893] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4893)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4893)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__4893) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    ! [V0__R,V1__rmul,V3__x,V4__i] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
       => ( ? [Vvar__0___24Anonymous__1155] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1155)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1155)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__1156__1159___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1155)),c_24__let__var__6__p__1156__1159___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1155))) )
          | ? [Vvar__0___24Anonymous__1157] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1157)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1157)
              & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__1158__1160___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1157)),c_24__let__var__6__p__1158__1160___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__1157)) )
          | ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).

fof('$_def_IntMap.Fset.FSet',axiom,
    ! [Vvar__88051] :
      ( cIntMap_2eFset_2eFSet___24t(Vvar__88051)
    <=> cIntMap_2eMap_2eMap___24t(cCoq_2eInit_2eDatatypes_2eunit,Vvar__88051) ) ).

fof('$_def_IntMap.Fset.FSetDelta',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetDelta___24a2(V0__s,V1__s_27) = cIntMap_2eMap_2eMapDelta___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.FSetDiff',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetDiff___24a2(V0__s,V1__s_27) = cIntMap_2eFset_2eMapDomRestrBy___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.FSetInter',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetInter___24a2(V0__s,V1__s_27) = cIntMap_2eFset_2eMapDomRestrTo___24a4(cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.FSetUnion',axiom,
    ! [V0__s,V1__s_27] : cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27) = cIntMap_2eMap_2eMapMerge___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ).

fof('$_def_IntMap.Fset.MapDom',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM0___24a1(cCoq_2eInit_2eDatatypes_2eunit) )
          | ? [Vvar__1___24Anonymous__6917] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__6917)
              & ? [Vvar__2___24Anonymous__6918] :
                  ( t(Vvar__2___24Anonymous__6918,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__6917,Vvar__2___24Anonymous__6918)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a3(cCoq_2eInit_2eDatatypes_2eunit,Vvar__1___24Anonymous__6917,cCoq_2eInit_2eDatatypes_2ett) ) )
          | ? [Vvar__1___24Anonymous__6921] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__6921)
              & ? [Vvar__2___24Anonymous__6922] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__6922)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__6921,Vvar__2___24Anonymous__6922)
                  & cIntMap_2eFset_2eMapDom___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM2___24a3(cCoq_2eInit_2eDatatypes_2eunit,cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__1___24Anonymous__6921),cIntMap_2eFset_2eMapDom___24a2(V0__A,Vvar__2___24Anonymous__6922)) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.MapDomRestrBy',axiom,
    ! [V0__A,V1__B,V3__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
       => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__87793___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__87916] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__87916)
              & ? [Vvar__2___24Anonymous__87917] :
                  ( t(Vvar__2___24Anonymous__87917,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__87916,Vvar__2___24Anonymous__87917)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__87957___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__87916) ) )
          | ? [Vvar__1___24Anonymous__87926] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__87926)
              & ? [Vvar__2___24Anonymous__87927] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__87927)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__87926,Vvar__2___24Anonymous__87927)
                  & cIntMap_2eFset_2eMapDomRestrBy___24a3(V0__A,V1__B,V3__m) = c_24__lam__87999___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__87926,Vvar__2___24Anonymous__87927) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.MapDomRestrTo',axiom,
    ! [V0__A,V1__B,V3__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
       => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__87793___24a2(V0__A,V1__B) )
          | ? [Vvar__1___24Anonymous__87762] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__87762)
              & ? [Vvar__2___24Anonymous__87763] :
                  ( t(Vvar__2___24Anonymous__87763,V0__A)
                  & V3__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__87762,Vvar__2___24Anonymous__87763)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__87808___24a4(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__87762) ) )
          | ? [Vvar__1___24Anonymous__87772] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__87772)
              & ? [Vvar__2___24Anonymous__87773] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__87773)
                  & V3__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__87772,Vvar__2___24Anonymous__87773)
                  & cIntMap_2eFset_2eMapDomRestrTo___24a3(V0__A,V1__B,V3__m) = c_24__lam__87866___24a5(V0__A,V1__B,V3__m,Vvar__1___24Anonymous__87772,Vvar__2___24Anonymous__87773) ) ) ) ) ) ).

fof('$_def_IntMap.Fset.in_FSet',axiom,
    cIntMap_2eFset_2ein__FSet = cIntMap_2eFset_2ein__dom___24a1(cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_def_IntMap.Fset.in_dom',axiom,
    ! [V0__A,V1__a,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2ead___24t(V1__a)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
         => ( ? [Vvar__1___24Anonymous__6903] :
                ( t(Vvar__1___24Anonymous__6903,V0__A)
                & cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__6903)
                & cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
            | ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V2__m,V1__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
              & cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapCard',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
          | ? [Vvar__1___24Anonymous__88809] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88809)
              & ? [Vvar__2___24Anonymous__88810] :
                  ( t(Vvar__2___24Anonymous__88810,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__88809,Vvar__2___24Anonymous__88810)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) )
          | ? [Vvar__1___24Anonymous__88813] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__88813)
              & ? [Vvar__2___24Anonymous__88814] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__88814)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__88813,Vvar__2___24Anonymous__88814)
                  & cIntMap_2eMap_2eMapCard___24a2(V0__A,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__1___24Anonymous__88813),cIntMap_2eMap_2eMapCard___24a2(V0__A,Vvar__2___24Anonymous__88814)) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapDelta',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__7292___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__7262] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7262)
              & ? [Vvar__2___24Anonymous__7263] :
                  ( t(Vvar__2___24Anonymous__7263,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7262,Vvar__2___24Anonymous__7263)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__7304___24a3(V0__A,Vvar__1___24Anonymous__7262,Vvar__2___24Anonymous__7263) ) )
          | ? [Vvar__1___24Anonymous__7272] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7272)
              & ? [Vvar__2___24Anonymous__7273] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7273)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7272,Vvar__2___24Anonymous__7273)
                  & cIntMap_2eMap_2eMapDelta___24a2(V0__A,V2__m) = c_24__lam__7354___24a4(V0__A,V2__m,Vvar__1___24Anonymous__7272,Vvar__2___24Anonymous__7273) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapEmptyp',axiom,
    ! [V0__A,V1__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
       => ( ( V1__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2etrue )
          | ? [Vvar__1___24Anonymous__88957] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88957)
              & ? [Vvar__2___24Anonymous__88958] :
                  ( t(Vvar__2___24Anonymous__88958,V0__A)
                  & V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__88957,Vvar__2___24Anonymous__88958)
                  & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) )
          | ? [Vvar__1___24Anonymous__88961] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__88961)
              & ? [Vvar__2___24Anonymous__88962] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__88962)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__88961,Vvar__2___24Anonymous__88962)
                  & cIntMap_2eMap_2eMapEmptyp___24a2(V0__A,V1__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapGet',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__7001___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__6977] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__6977)
              & ? [Vvar__2___24Anonymous__6978] :
                  ( t(Vvar__2___24Anonymous__6978,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__6977,Vvar__2___24Anonymous__6978)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__7009___24a3(V0__A,Vvar__1___24Anonymous__6977,Vvar__2___24Anonymous__6978) ) )
          | ? [Vvar__1___24Anonymous__6985] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__6985)
              & ? [Vvar__2___24Anonymous__6986] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__6986)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__6985,Vvar__2___24Anonymous__6986)
                  & cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m) = c_24__lam__7036___24a3(V0__A,Vvar__1___24Anonymous__6985,Vvar__2___24Anonymous__6986) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapMerge',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__7292___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__88823] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88823)
              & ? [Vvar__2___24Anonymous__88824] :
                  ( t(Vvar__2___24Anonymous__88824,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__88823,Vvar__2___24Anonymous__88824)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__88848___24a3(V0__A,Vvar__1___24Anonymous__88823,Vvar__2___24Anonymous__88824) ) )
          | ? [Vvar__1___24Anonymous__88829] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__88829)
              & ? [Vvar__2___24Anonymous__88830] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__88830)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__88829,Vvar__2___24Anonymous__88830)
                  & cIntMap_2eMap_2eMapMerge___24a2(V0__A,V2__m) = c_24__lam__88880___24a4(V0__A,V2__m,Vvar__1___24Anonymous__88829,Vvar__2___24Anonymous__88830) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__7057] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7057)
              & ? [Vvar__2___24Anonymous__7058] :
                  ( t(Vvar__2___24Anonymous__7058,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7057,Vvar__2___24Anonymous__7058)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__7103___24a3(V0__A,Vvar__1___24Anonymous__7057,Vvar__2___24Anonymous__7058) ) )
          | ? [Vvar__1___24Anonymous__7069] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7069)
              & ? [Vvar__2___24Anonymous__7070] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7070)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7069,Vvar__2___24Anonymous__7070)
                  & cIntMap_2eMap_2eMapPut___24a2(V0__A,V2__m) = c_24__lam__7140___24a3(V0__A,Vvar__1___24Anonymous__7069,Vvar__2___24Anonymous__7070) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut1',axiom,
    ! [V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
       => ( ? [Vvar__0___24Anonymous__88533] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88533)
              & ( cType___24t(V0__A)
               => ( cIntMap_2eMap_2ead___24t(V2__a)
                 => ( V6__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__88533)
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
                        & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
                        & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__88535] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88535)
              & V6__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__88535)
              & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488547___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,Vvar__0___24Anonymous__88535) )
          | ( cType___24t(V0__A)
           => ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( V6__p = cCoq_2eNumbers_2eBinNums_2exH
                & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2etrue
                    & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y)) )
                  | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V2__a) = cCoq_2eInit_2eDatatypes_2efalse
                    & cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V3__y,V4__a_27,V5__y_27,V6__p) = cIntMap_2eMap_2eM2___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V2__a),V3__y),cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V4__a_27),V5__y_27)) ) ) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapPut_behind',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = cIntMap_2eMap_2eM1___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__88662] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88662)
              & ? [Vvar__2___24Anonymous__88663] :
                  ( t(Vvar__2___24Anonymous__88663,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__88662,Vvar__2___24Anonymous__88663)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__88712___24a4(V0__A,V2__m,Vvar__1___24Anonymous__88662,Vvar__2___24Anonymous__88663) ) )
          | ? [Vvar__1___24Anonymous__88674] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__88674)
              & ? [Vvar__2___24Anonymous__88675] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__88675)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__88674,Vvar__2___24Anonymous__88675)
                  & cIntMap_2eMap_2eMapPut__behind___24a2(V0__A,V2__m) = c_24__lam__88749___24a3(V0__A,Vvar__1___24Anonymous__88674,Vvar__2___24Anonymous__88675) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapRemove',axiom,
    ! [V0__A,V2__m] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
       => ( ( V2__m = cIntMap_2eMap_2eM0___24a1(V0__A)
            & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__7228___24a1(V0__A) )
          | ? [Vvar__1___24Anonymous__7212] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7212)
              & ? [Vvar__2___24Anonymous__7213] :
                  ( t(Vvar__2___24Anonymous__7213,V0__A)
                  & V2__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7212,Vvar__2___24Anonymous__7213)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__7236___24a3(V0__A,V2__m,Vvar__1___24Anonymous__7212) ) )
          | ? [Vvar__1___24Anonymous__7220] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7220)
              & ? [Vvar__2___24Anonymous__7221] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7221)
                  & V2__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7220,Vvar__2___24Anonymous__7221)
                  & cIntMap_2eMap_2eMapRemove___24a2(V0__A,V2__m) = c_24__lam__7244___24a3(V0__A,Vvar__1___24Anonymous__7220,Vvar__2___24Anonymous__7221) ) ) ) ) ) ).

fof('$_def_IntMap.Map.MapSingleton',axiom,
    ! [V0__A] : cIntMap_2eMap_2eMapSingleton___24a1(V0__A) = cIntMap_2eMap_2eM1___24a1(V0__A) ).

fof('$_def_IntMap.Map.Map_rec',axiom,
    ! [V0__A,V1__P] : cIntMap_2eMap_2eMap__rec___24a2(V0__A,V1__P) = cIntMap_2eMap_2eMap__rect___24a2(V0__A,V1__P) ).

fof('$_def_IntMap.Map.Map_rect',axiom,
    ! [V0__A,V1__P,V2__f,V3__f,V4__f,V6__m] :
      ( cType___24t(V0__A)
     => ( c_24__type__88334___24t(V0__A,V1__P,V1__P)
       => ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
         => ( ( V6__m = cIntMap_2eMap_2eM0___24a1(V0__A)
              & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = V2__f )
            | ? [Vvar__1___24Anonymous__88324] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88324)
                & ? [Vvar__2___24Anonymous__88325] :
                    ( t(Vvar__2___24Anonymous__88325,V0__A)
                    & V6__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__88324,Vvar__2___24Anonymous__88325)
                    & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = happ(happ(V3__f,Vvar__1___24Anonymous__88324),Vvar__2___24Anonymous__88325) ) )
            | ? [Vvar__1___24Anonymous__88328] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__88328)
                & ? [Vvar__2___24Anonymous__88329] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__88329)
                    & V6__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__88328,Vvar__2___24Anonymous__88329)
                    & cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,V6__m) = happ(happ(happ(happ(V4__f,Vvar__1___24Anonymous__88328),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__1___24Anonymous__88328)),Vvar__2___24Anonymous__88329),cIntMap_2eMap_2eMap__rect___24a6(V0__A,V1__P,V2__f,V3__f,V4__f,Vvar__2___24Anonymous__88329)) ) ) ) ) ) ) ).

fof('$_def_IntMap.Map.ad',axiom,
    ! [Vvar__109] :
      ( cIntMap_2eMap_2ead___24t(Vvar__109)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__109) ) ).

fof('$_def_IntMap.Map.eqm',axiom,
    ! [V0__A,V1__g,V2__g_27] :
      ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__g,V2__g_27)
    <=> ! [V3__a] :
          ( cIntMap_2eMap_2ead___24t(V3__a)
         => happ(V1__g,V3__a) = happ(V2__g_27,V3__a) ) ) ).

fof('$_def_IntMap.Map.makeM2',axiom,
    ! [V0__A,V1__m,V2__m_27] :
      ( cType___24t(V0__A)
     => ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
       => ( ( cType___24t(V0__A)
           => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( V1__m = cIntMap_2eMap_2eM0___24a1(V0__A)
                & ( ( V2__m_27 = cIntMap_2eMap_2eM0___24a1(V0__A)
                    & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM0___24a1(V0__A) )
                  | ? [Vvar__1___24Anonymous__7170] :
                      ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7170)
                      & ? [Vvar__2___24Anonymous__7171] :
                          ( t(Vvar__2___24Anonymous__7171,V0__A)
                          & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7170,Vvar__2___24Anonymous__7171)
                          & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vvar__1___24Anonymous__7170),Vvar__2___24Anonymous__7171) ) )
                  | ? [Vvar__1___24Anonymous__7174] :
                      ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7174)
                      & ? [Vvar__2___24Anonymous__7175] :
                          ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7175)
                          & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7174,Vvar__2___24Anonymous__7175)
                          & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__7178] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7178)
              & ? [Vvar__2___24Anonymous__7179] :
                  ( t(Vvar__2___24Anonymous__7179,V0__A)
                  & ( cType___24t(V0__A)
                   => ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
                     => ( V1__m = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7178,Vvar__2___24Anonymous__7179)
                        & ( ( V2__m_27 = cIntMap_2eMap_2eM0___24a1(V0__A)
                            & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM1___24a3(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vvar__1___24Anonymous__7178),Vvar__2___24Anonymous__7179) )
                          | ? [Vvar__1___24Anonymous__7194] :
                              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7194)
                              & ? [Vvar__2___24Anonymous__7195] :
                                  ( t(Vvar__2___24Anonymous__7195,V0__A)
                                  & V2__m_27 = cIntMap_2eMap_2eM1___24a3(V0__A,Vvar__1___24Anonymous__7194,Vvar__2___24Anonymous__7195)
                                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) )
                          | ? [Vvar__1___24Anonymous__7198] :
                              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7198)
                              & ? [Vvar__2___24Anonymous__7199] :
                                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7199)
                                  & V2__m_27 = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7198,Vvar__2___24Anonymous__7199)
                                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__7202] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__1___24Anonymous__7202)
              & ? [Vvar__2___24Anonymous__7203] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,Vvar__2___24Anonymous__7203)
                  & V1__m = cIntMap_2eMap_2eM2___24a3(V0__A,Vvar__1___24Anonymous__7202,Vvar__2___24Anonymous__7203)
                  & cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27) = cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27) ) ) ) ) ) ).

fof('$_def_IntMap.Map.newMap',axiom,
    ! [V0__A] : cIntMap_2eMap_2enewMap___24a1(V0__A) = cIntMap_2eMap_2eM0___24a1(V0__A) ).

fof('$_def_IntMap.Mapaxioms.eqmap',axiom,
    ! [V0__A,V1__m,V2__m_27] :
      ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
    <=> cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,V1__m),cIntMap_2eMap_2eMapGet___24a2(V0__A,V2__m_27)) ) ).

fof('$_def_Mapiter.MapIter.MapCollect',axiom,
    ! [V0__f,V1__m] : cMapiter_2eMapIter_2eMapCollect___24a2(V0__f,V1__m) = cMapiter_2eMapIter_2eMapCollect1___24a3(V0__f,c_24__lam__467,V1__m) ).

fof('$_def_Mapiter.MapIter.MapCollect1',axiom,
    ! [V1__f,V2__pf,V3__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V3__m)
     => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(cA)
          & cMapiter_2eMapIter_2eMapCollect1___24a3(V1__f,V2__pf,V3__m) = cIntMap_2eMap_2eM0___24a1(cB) )
        | ? [Vvar__1___24Anonymous__111457] :
            ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__111457)
            & ? [Vvar__2___24Anonymous__111458] :
                ( cA___24t(Vvar__2___24Anonymous__111458)
                & V3__m = cIntMap_2eMap_2eM1___24a3(cA,Vvar__1___24Anonymous__111457,Vvar__2___24Anonymous__111458)
                & cMapiter_2eMapIter_2eMapCollect1___24a3(V1__f,V2__pf,V3__m) = happ(happ(V1__f,happ(V2__pf,Vvar__1___24Anonymous__111457)),Vvar__2___24Anonymous__111458) ) )
        | ? [Vvar__1___24Anonymous__111461] :
            ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1___24Anonymous__111461)
            & ? [Vvar__2___24Anonymous__111462] :
                ( cIntMap_2eMap_2eMap___24t(cA,Vvar__2___24Anonymous__111462)
                & V3__m = cIntMap_2eMap_2eM2___24a3(cA,Vvar__1___24Anonymous__111461,Vvar__2___24Anonymous__111462)
                & cMapiter_2eMapIter_2eMapCollect1___24a3(V1__f,V2__pf,V3__m) = cIntMap_2eMap_2eMapMerge___24a3(cB,cMapiter_2eMapIter_2eMapCollect1___24a3(V1__f,c_24__lam__111469___24a1(V2__pf),Vvar__1___24Anonymous__111461),cMapiter_2eMapIter_2eMapCollect1___24a3(V1__f,c_24__lam__111471___24a1(V2__pf),Vvar__2___24Anonymous__111462)) ) ) ) ) ).

fof('$_def_Mapiter.MapIter.MapFoldDef.MapFold',axiom,
    ! [V0__f,V1__m] : cMapiter_2eMapIter_2eMapFoldDef_2eMapFold___24a2(V0__f,V1__m) = cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V0__f,c_24__lam__467,V1__m) ).

fof('$_def_Mapiter.MapIter.MapFoldDef.MapFold1',axiom,
    ! [V1__f,V2__pf,V3__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V3__m)
     => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(cA)
          & cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V1__f,V2__pf,V3__m) = cneutral )
        | ? [Vvar__1___24Anonymous__111904] :
            ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__111904)
            & ? [Vvar__2___24Anonymous__111905] :
                ( cA___24t(Vvar__2___24Anonymous__111905)
                & V3__m = cIntMap_2eMap_2eM1___24a3(cA,Vvar__1___24Anonymous__111904,Vvar__2___24Anonymous__111905)
                & cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V1__f,V2__pf,V3__m) = happ(happ(V1__f,happ(V2__pf,Vvar__1___24Anonymous__111904)),Vvar__2___24Anonymous__111905) ) )
        | ? [Vvar__1___24Anonymous__111908] :
            ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1___24Anonymous__111908)
            & ? [Vvar__2___24Anonymous__111909] :
                ( cIntMap_2eMap_2eMap___24t(cA,Vvar__2___24Anonymous__111909)
                & V3__m = cIntMap_2eMap_2eM2___24a3(cA,Vvar__1___24Anonymous__111908,Vvar__2___24Anonymous__111909)
                & cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V1__f,V2__pf,V3__m) = cop___24a2(cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V1__f,c_24__lam__111469___24a1(V2__pf),Vvar__1___24Anonymous__111908),cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V1__f,c_24__lam__111471___24a1(V2__pf),Vvar__2___24Anonymous__111909)) ) ) ) ) ).

fof('$_def_Mapiter.MapIter.MapSweep',axiom,
    ! [V0__f,V1__m] : cMapiter_2eMapIter_2eMapSweep___24a2(V0__f,V1__m) = cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,c_24__lam__467,V1__m) ).

fof('$_def_Mapiter.MapIter.MapSweep1',axiom,
    ! [V0__f,V2__pf,V3__m] :
      ( cIntMap_2eMap_2eMap___24t(cA,V3__m)
     => ( ( V3__m = cIntMap_2eMap_2eM0___24a1(cA)
          & cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,V2__pf,V3__m) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA)) )
        | ? [Vvar__1___24Anonymous__111852] :
            ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__111852)
            & ? [Vvar__2___24Anonymous__111853] :
                ( cA___24t(Vvar__2___24Anonymous__111853)
                & V3__m = cIntMap_2eMap_2eM1___24a3(cA,Vvar__1___24Anonymous__111852,Vvar__2___24Anonymous__111853)
                & cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,V2__pf,V3__m) = cMapiter_2eMapIter_2eMapSweep2___24a3(V0__f,happ(V2__pf,Vvar__1___24Anonymous__111852),Vvar__2___24Anonymous__111853) ) )
        | ? [Vvar__1___24Anonymous__111856] :
            ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1___24Anonymous__111856)
            & ? [Vvar__2___24Anonymous__111857] :
                ( cIntMap_2eMap_2eMap___24t(cA,Vvar__2___24Anonymous__111857)
                & ( c_24__type__4___24t(V0__f)
                 => ( c_24__type__1___24t(V2__pf)
                   => ( cIntMap_2eMap_2eMap___24t(cA,Vvar__1___24Anonymous__111856)
                     => ( V3__m = cIntMap_2eMap_2eM2___24a3(cA,Vvar__1___24Anonymous__111856,Vvar__2___24Anonymous__111857)
                        & ( ? [Vvar__1___24Anonymous__111869] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cIntMap_2eMap_2ead,cA,Vvar__1___24Anonymous__111869)
                              & cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,c_24__lam__111469___24a1(V2__pf),Vvar__1___24Anonymous__111856) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),Vvar__1___24Anonymous__111869)
                              & cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,V2__pf,V3__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),Vvar__1___24Anonymous__111869) )
                          | ( cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,c_24__lam__111469___24a1(V2__pf),Vvar__1___24Anonymous__111856) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA))
                            & cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,V2__pf,V3__m) = cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,c_24__lam__111471___24a1(V2__pf),Vvar__2___24Anonymous__111857) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Mapiter.MapIter.MapSweep2',axiom,
    ! [V0__f,V1__a0,V2__y] :
      ( c_24__type__4___24t(V0__f)
     => ( cIntMap_2eMap_2ead___24t(V1__a0)
       => ( cA___24t(V2__y)
         => ( ( happ(happ(V0__f,V1__a0),V2__y) = cCoq_2eInit_2eDatatypes_2etrue
              & cMapiter_2eMapIter_2eMapSweep2___24a3(V0__f,V1__a0,V2__y) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,cA,V1__a0,V2__y)) )
            | ( happ(happ(V0__f,V1__a0),V2__y) = cCoq_2eInit_2eDatatypes_2efalse
              & cMapiter_2eMapIter_2eMapSweep2___24a3(V0__f,V1__a0,V2__y) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA)) ) ) ) ) ) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__102705,Vvar__1___24Anonymous__102706,Vvar__0__P__102707,Vvar__1___24Anonymous__102708] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__102705) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__102707) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__102429,Vvar__1___24Anonymous__102430,Vvar__2___24Anonymous__102431] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__102429,Vvar__1___24Anonymous__102430,Vvar__2___24Anonymous__102431) ).

fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).

fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__117320,Vvar__1__Plt__117321,Vvar__2__Pgt__117322,Vvar__3___24Anonymous__117323,Vvar__0__Peq__117324,Vvar__1__Plt__117325,Vvar__2__Pgt__117326,Vvar__3___24Anonymous__117327] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__117320,Vvar__1__Plt__117321,Vvar__2__Pgt__117322) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__117324,Vvar__1__Plt__117325,Vvar__2__Pgt__117326) ).

fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
    cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).

fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__5165] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5165) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__25,Vvar__1___24Anonymous__26,Vvar__0__A__27] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__25,Vvar__1___24Anonymous__26) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__27) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__82872,Vvar__1__B__82873,Vvar__2___24Anonymous__82874,Vvar__0__A__82875,Vvar__1__B__82876,Vvar__2___24Anonymous__82877] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__82872,Vvar__1__B__82873,Vvar__2___24Anonymous__82874) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__82875,Vvar__1__B__82876,Vvar__2___24Anonymous__82877) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__520,Vvar__0__A__521,Vvar__1___24Anonymous__522,Vvar__2___24Anonymous__523] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__520) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__521,Vvar__1___24Anonymous__522,Vvar__2___24Anonymous__523) ).

fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
    cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__98560,Vvar__1__B__98561,Vvar__2___24Anonymous__98562,Vvar__0__A__98563,Vvar__1__B__98564,Vvar__2___24Anonymous__98565] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__98560,Vvar__1__B__98561,Vvar__2___24Anonymous__98562) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__98563,Vvar__1__B__98564) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__11151,Vvar__1__B__11152,Vvar__2___24Anonymous__11153,Vvar__0__A__11154,Vvar__1__B__11155,Vvar__2___24Anonymous__11156] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11151,Vvar__1__B__11152) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11154,Vvar__1__B__11155) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__5158] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5158) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__4591] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4591) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__11,Vvar__0___24Anonymous__12] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__11) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__121142,Vvar__1___24Anonymous__121143] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__121142,Vvar__1___24Anonymous__121143) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__102380] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__102380) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__118731,Vvar__1___24Anonymous__118732,Vvar__0__x__118733,Vvar__1__n__118734,Vvar__2___24Anonymous__118735] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__118731) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__118733,Vvar__1__n__118734) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__98656,Vvar__1___24Anonymous__98657] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__98656,Vvar__1___24Anonymous__98657) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__118567,Vvar__1__lt__118568,Vvar__2__eq__118569,Vvar__3__x__118570,Vvar__4__y__118571,Vvar__5___24Anonymous__118572,Vvar__0__X__118573,Vvar__1__lt__118574,Vvar__2__eq__118575,Vvar__3__x__118576,Vvar__4__y__118577,Vvar__5___24Anonymous__118578] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__118567,Vvar__1__lt__118568,Vvar__2__eq__118569,Vvar__3__x__118570,Vvar__4__y__118571) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__118573,Vvar__1__lt__118574,Vvar__2__eq__118575,Vvar__3__x__118576,Vvar__4__y__118577) ).

fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
    cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).

fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__112960,Vvar__0__n__112961,Vvar__1___24Anonymous__112962] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__112960) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__112961,Vvar__1___24Anonymous__112962) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__100951,Vvar__0__A__100952,Vvar__1__h__100953,Vvar__2__n__100954,Vvar__3___24Anonymous__100955] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__100951) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__100952,Vvar__1__h__100953,Vvar__2__n__100954,Vvar__3___24Anonymous__100955) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__106397,Vvar__1___24Anonymous__106398,Vvar__0__C__106399,Vvar__1___24Anonymous__106400] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__106397,Vvar__1___24Anonymous__106398) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__106399,Vvar__1___24Anonymous__106400) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__4629,Vvar__1___24Anonymous__4630,Vvar__0__C__4631,Vvar__1___24Anonymous__4632,Vvar__2___24Anonymous__4633] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4629,Vvar__1___24Anonymous__4630) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4631,Vvar__1___24Anonymous__4632,Vvar__2___24Anonymous__4633) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__83558,Vvar__1___24Anonymous__83559] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__83558,Vvar__1___24Anonymous__83559) ).

fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).

fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__99123,Vvar__1__TX__99124,Vvar__2__AA__99125,Vvar__3__AF__99126,Vvar__0__TA__99127,Vvar__1__TX__99128,Vvar__2__AA__99129,Vvar__3__AF__99130] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__99123,Vvar__1__TX__99124,Vvar__2__AA__99125,Vvar__3__AF__99126) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__99127,Vvar__1__TX__99128,Vvar__2__AA__99129,Vvar__3__AF__99130) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__103072,Vvar__0__C__103073] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__103072) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__103073) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__10681,Vvar__0__C__10682] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10681) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10682) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__205,Vvar__1___24Anonymous__206,Vvar__0__C__207,Vvar__1___24Anonymous__208,Vvar__2___24Anonymous__209] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__205,Vvar__1___24Anonymous__206) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__207,Vvar__1___24Anonymous__208,Vvar__2___24Anonymous__209) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__402,Vvar__1___24Anonymous__403] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__402,Vvar__1___24Anonymous__403) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__120627,Vvar__1__req__120628,Vvar__2__reqb__120629,Vvar__3___24Anonymous__120630] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__120627,Vvar__1__req__120628,Vvar__2__reqb__120629) ).

fof('$_discrim_IntMap.Map.M0$IntMap.Map.M1',axiom,
    ! [Vvar__0__A__129,Vvar__0__A__130,Vvar__1___24Anonymous__131,Vvar__2___24Anonymous__132] : cIntMap_2eMap_2eM0___24a1(Vvar__0__A__129) != cIntMap_2eMap_2eM1___24a3(Vvar__0__A__130,Vvar__1___24Anonymous__131,Vvar__2___24Anonymous__132) ).

fof('$_fix_102347_1_add_carry',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__102362] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102362)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102362)
                & ( ? [Vvar__0___24Anonymous__102366] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102366)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102366)
                      & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__102347__1__add__carry___24a2(Vvar__0___24Anonymous__102362,Vvar__0___24Anonymous__102366)) )
                  | ? [Vvar__0___24Anonymous__102367] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102367)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102367)
                      & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__102347__1__add__carry___24a2(Vvar__0___24Anonymous__102362,Vvar__0___24Anonymous__102367)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102362)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__102368] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102368)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102368)
                & ( ? [Vvar__0___24Anonymous__102372] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102372)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102372)
                      & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__102347__1__add__carry___24a2(Vvar__0___24Anonymous__102368,Vvar__0___24Anonymous__102372)) )
                  | ? [Vvar__0___24Anonymous__102373] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102373)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102373)
                      & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__102368,Vvar__0___24Anonymous__102373)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102368)) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__102374] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102374)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__102374)
                  & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102374)) )
              | ? [Vvar__0___24Anonymous__102375] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102375)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__102375)
                  & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__102375)) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & c_24__fix__102347__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

fof('$_fix_121137_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__121138] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121138)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121138)
            & c_24__fix__121137__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__121137__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__121138)) )
        | ? [Vvar__0___24Anonymous__121139] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121139)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__121139)
            & c_24__fix__121137__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__121139) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__121137__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__102713,Vvar__0__P__102714,Vvar__1___24Anonymous__102715,Vvar__1___24Anonymous__102716] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__102713) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__102714)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__102713 = Vvar__0__P__102714 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__102709,Vvar__0__P__102710,Vvar__1___24Anonymous__102711,Vvar__1___24Anonymous__102712] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__102709) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__102710)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__102709 = Vvar__0__P__102710 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__102432,Vvar__0___24Anonymous__102433,Vvar__1___24Anonymous__102434,Vvar__1___24Anonymous__102435,Vvar__2___24Anonymous__102436,Vvar__2___24Anonymous__102437] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__102432,Vvar__1___24Anonymous__102434,Vvar__2___24Anonymous__102436) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__102433,Vvar__1___24Anonymous__102435,Vvar__2___24Anonymous__102437)
     => ( Vvar__2___24Anonymous__102436 = Vvar__2___24Anonymous__102437
        & Vvar__1___24Anonymous__102434 = Vvar__1___24Anonymous__102435
        & Vvar__0___24Anonymous__102432 = Vvar__0___24Anonymous__102433 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__117328,Vvar__0__Peq__117329,Vvar__1__Plt__117330,Vvar__1__Plt__117331,Vvar__2__Pgt__117332,Vvar__2__Pgt__117333,Vvar__3___24Anonymous__117334,Vvar__3___24Anonymous__117335] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__117328,Vvar__1__Plt__117330,Vvar__2__Pgt__117332) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__117329,Vvar__1__Plt__117331,Vvar__2__Pgt__117333)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__117332 = Vvar__2__Pgt__117333
        & Vvar__1__Plt__117330 = Vvar__1__Plt__117331
        & Vvar__0__Peq__117328 = Vvar__0__Peq__117329 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__117344,Vvar__0__Peq__117345,Vvar__1__Plt__117346,Vvar__1__Plt__117347,Vvar__2__Pgt__117348,Vvar__2__Pgt__117349,Vvar__3___24Anonymous__117350,Vvar__3___24Anonymous__117351] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__117344,Vvar__1__Plt__117346,Vvar__2__Pgt__117348) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__117345,Vvar__1__Plt__117347,Vvar__2__Pgt__117349)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__117348 = Vvar__2__Pgt__117349
        & Vvar__1__Plt__117346 = Vvar__1__Plt__117347
        & Vvar__0__Peq__117344 = Vvar__0__Peq__117345 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__117336,Vvar__0__Peq__117337,Vvar__1__Plt__117338,Vvar__1__Plt__117339,Vvar__2__Pgt__117340,Vvar__2__Pgt__117341,Vvar__3___24Anonymous__117342,Vvar__3___24Anonymous__117343] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__117336,Vvar__1__Plt__117338,Vvar__2__Pgt__117340) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__117337,Vvar__1__Plt__117339,Vvar__2__Pgt__117341)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__117340 = Vvar__2__Pgt__117341
        & Vvar__1__Plt__117338 = Vvar__1__Plt__117339
        & Vvar__0__Peq__117336 = Vvar__0__Peq__117337 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__32,Vvar__0__A__33] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__32) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__33)
     => Vvar__0__A__32 = Vvar__0__A__33 ) ).

fof('$_inj_Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__5166,Vvar__0___24Anonymous__5167] :
      ( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5166) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5167)
     => Vvar__0___24Anonymous__5166 = Vvar__0___24Anonymous__5167 ) ).

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__28,Vvar__0__A__29,Vvar__1___24Anonymous__30,Vvar__1___24Anonymous__31] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__28,Vvar__1___24Anonymous__30) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__29,Vvar__1___24Anonymous__31)
     => ( Vvar__1___24Anonymous__30 = Vvar__1___24Anonymous__31
        & Vvar__0__A__28 = Vvar__0__A__29 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__526,Vvar__0__A__527,Vvar__1___24Anonymous__528,Vvar__1___24Anonymous__529,Vvar__2___24Anonymous__530,Vvar__2___24Anonymous__531] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__526,Vvar__1___24Anonymous__528,Vvar__2___24Anonymous__530) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__527,Vvar__1___24Anonymous__529,Vvar__2___24Anonymous__531)
     => ( Vvar__2___24Anonymous__530 = Vvar__2___24Anonymous__531
        & Vvar__1___24Anonymous__528 = Vvar__1___24Anonymous__529
        & Vvar__0__A__526 = Vvar__0__A__527 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__82878,Vvar__0__A__82879,Vvar__1__B__82880,Vvar__1__B__82881,Vvar__2___24Anonymous__82882,Vvar__2___24Anonymous__82883] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__82878,Vvar__1__B__82880,Vvar__2___24Anonymous__82882) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__82879,Vvar__1__B__82881,Vvar__2___24Anonymous__82883)
     => ( Vvar__2___24Anonymous__82882 = Vvar__2___24Anonymous__82883
        & Vvar__1__B__82880 = Vvar__1__B__82881
        & Vvar__0__A__82878 = Vvar__0__A__82879 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__82884,Vvar__0__A__82885,Vvar__1__B__82886,Vvar__1__B__82887,Vvar__2___24Anonymous__82888,Vvar__2___24Anonymous__82889] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__82884,Vvar__1__B__82886,Vvar__2___24Anonymous__82888) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__82885,Vvar__1__B__82887,Vvar__2___24Anonymous__82889)
     => ( Vvar__2___24Anonymous__82888 = Vvar__2___24Anonymous__82889
        & Vvar__1__B__82886 = Vvar__1__B__82887
        & Vvar__0__A__82884 = Vvar__0__A__82885 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__524,Vvar__0__A__525] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__524) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__525)
     => Vvar__0__A__524 = Vvar__0__A__525 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__49,Vvar__0__A__50,Vvar__1__B__51,Vvar__1__B__52,Vvar__2___24Anonymous__53,Vvar__2___24Anonymous__54,Vvar__3___24Anonymous__55,Vvar__3___24Anonymous__56] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__49,Vvar__1__B__51,Vvar__2___24Anonymous__53,Vvar__3___24Anonymous__55) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__50,Vvar__1__B__52,Vvar__2___24Anonymous__54,Vvar__3___24Anonymous__56)
     => ( Vvar__3___24Anonymous__55 = Vvar__3___24Anonymous__56
        & Vvar__2___24Anonymous__53 = Vvar__2___24Anonymous__54
        & Vvar__1__B__51 = Vvar__1__B__52
        & Vvar__0__A__49 = Vvar__0__A__50 ) ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__98522,Vvar__0__A__98523,Vvar__1__P__98524,Vvar__1__P__98525,Vvar__2__x__98526,Vvar__2__x__98527,Vvar__3___24Anonymous__98528,Vvar__3___24Anonymous__98529] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__98522,Vvar__1__P__98524,Vvar__2__x__98526) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__98523,Vvar__1__P__98525,Vvar__2__x__98527)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__98526 = Vvar__2__x__98527
        & Vvar__1__P__98524 = Vvar__1__P__98525
        & Vvar__0__A__98522 = Vvar__0__A__98523 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__113464,Vvar__0__A__113465,Vvar__1__P__113466,Vvar__1__P__113467,Vvar__2__Q__113468,Vvar__2__Q__113469,Vvar__3__x__113470,Vvar__3__x__113471,Vvar__4___24Anonymous__113472,Vvar__4___24Anonymous__113473,Vvar__5___24Anonymous__113474,Vvar__5___24Anonymous__113475] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113464,Vvar__1__P__113466,Vvar__2__Q__113468,Vvar__3__x__113470) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113465,Vvar__1__P__113467,Vvar__2__Q__113469,Vvar__3__x__113471)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__113470 = Vvar__3__x__113471
        & Vvar__2__Q__113468 = Vvar__2__Q__113469
        & Vvar__1__P__113466 = Vvar__1__P__113467
        & Vvar__0__A__113464 = Vvar__0__A__113465 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__111562,Vvar__0__A__111563,Vvar__1__P__111564,Vvar__1__P__111565,Vvar__2__x__111566,Vvar__2__x__111567,Vvar__3___24Anonymous__111568,Vvar__3___24Anonymous__111569] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__111562,Vvar__1__P__111564,Vvar__2__x__111566,Vvar__3___24Anonymous__111568) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__111563,Vvar__1__P__111565,Vvar__2__x__111567,Vvar__3___24Anonymous__111569)
     => ( Vvar__3___24Anonymous__111568 = Vvar__3___24Anonymous__111569
        & Vvar__2__x__111566 = Vvar__2__x__111567
        & Vvar__1__P__111564 = Vvar__1__P__111565
        & Vvar__0__A__111562 = Vvar__0__A__111563 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__113542,Vvar__0__A__113543,Vvar__1__P__113544,Vvar__1__P__113545,Vvar__2__Q__113546,Vvar__2__Q__113547,Vvar__3__x__113548,Vvar__3__x__113549,Vvar__4___24Anonymous__113550,Vvar__4___24Anonymous__113551,Vvar__5___24Anonymous__113552,Vvar__5___24Anonymous__113553] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113542,Vvar__1__P__113544,Vvar__2__Q__113546,Vvar__3__x__113548,Vvar__4___24Anonymous__113550,Vvar__5___24Anonymous__113552) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113543,Vvar__1__P__113545,Vvar__2__Q__113547,Vvar__3__x__113549,Vvar__4___24Anonymous__113551,Vvar__5___24Anonymous__113553)
     => ( Vvar__5___24Anonymous__113552 = Vvar__5___24Anonymous__113553
        & Vvar__4___24Anonymous__113550 = Vvar__4___24Anonymous__113551
        & Vvar__3__x__113548 = Vvar__3__x__113549
        & Vvar__2__Q__113546 = Vvar__2__Q__113547
        & Vvar__1__P__113544 = Vvar__1__P__113545
        & Vvar__0__A__113542 = Vvar__0__A__113543 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__98566,Vvar__0__A__98567,Vvar__1__B__98568,Vvar__1__B__98569,Vvar__2___24Anonymous__98570,Vvar__2___24Anonymous__98571] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__98566,Vvar__1__B__98568,Vvar__2___24Anonymous__98570) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__98567,Vvar__1__B__98569,Vvar__2___24Anonymous__98571)
     => ( Vvar__2___24Anonymous__98570 = Vvar__2___24Anonymous__98571
        & Vvar__1__B__98568 = Vvar__1__B__98569
        & Vvar__0__A__98566 = Vvar__0__A__98567 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__98572,Vvar__0__A__98573,Vvar__1__B__98574,Vvar__1__B__98575,Vvar__2___24Anonymous__98576,Vvar__2___24Anonymous__98577] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__98572,Vvar__1__B__98574) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__98573,Vvar__1__B__98575)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__98574 = Vvar__1__B__98575
        & Vvar__0__A__98572 = Vvar__0__A__98573 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__11157,Vvar__0__A__11158,Vvar__1__B__11159,Vvar__1__B__11160,Vvar__2___24Anonymous__11161,Vvar__2___24Anonymous__11162] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11157,Vvar__1__B__11159) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11158,Vvar__1__B__11160)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__11159 = Vvar__1__B__11160
        & Vvar__0__A__11157 = Vvar__0__A__11158 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__11163,Vvar__0__A__11164,Vvar__1__B__11165,Vvar__1__B__11166,Vvar__2___24Anonymous__11167,Vvar__2___24Anonymous__11168] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11163,Vvar__1__B__11165) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11164,Vvar__1__B__11166)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__11165 = Vvar__1__B__11166
        & Vvar__0__A__11163 = Vvar__0__A__11164 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__5159,Vvar__0___24Anonymous__5160] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5159) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5160)
     => Vvar__0___24Anonymous__5159 = Vvar__0___24Anonymous__5160 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__4594,Vvar__0___24Anonymous__4595] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4594) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4595)
     => Vvar__0___24Anonymous__4594 = Vvar__0___24Anonymous__4595 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__4592,Vvar__0___24Anonymous__4593] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4592) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4593)
     => Vvar__0___24Anonymous__4592 = Vvar__0___24Anonymous__4593 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__13,Vvar__0___24Anonymous__14] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__14)
     => Vvar__0___24Anonymous__13 = Vvar__0___24Anonymous__14 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__15,Vvar__0___24Anonymous__16] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__16)
     => Vvar__0___24Anonymous__15 = Vvar__0___24Anonymous__16 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__121144,Vvar__0__p__121145,Vvar__1___24Anonymous__121146,Vvar__1___24Anonymous__121147] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__121144,Vvar__1___24Anonymous__121146) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__121145,Vvar__1___24Anonymous__121147)
     => ( Vvar__1___24Anonymous__121146 = Vvar__1___24Anonymous__121147
        & Vvar__0__p__121144 = Vvar__0__p__121145 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__102381,Vvar__0___24Anonymous__102382] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__102381) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__102382)
     => Vvar__0___24Anonymous__102381 = Vvar__0___24Anonymous__102382 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__104047,Vvar__0__Qnum__104048,Vvar__1__Qden__104049,Vvar__1__Qden__104050] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104047,Vvar__1__Qden__104049) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104048,Vvar__1__Qden__104050)
     => ( Vvar__1__Qden__104049 = Vvar__1__Qden__104050
        & Vvar__0__Qnum__104047 = Vvar__0__Qnum__104048 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__118627,Vvar__0__nonzero__118628,Vvar__1__cond__nonzero__118629,Vvar__1__cond__nonzero__118630] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__118627) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__118628)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__118627 = Vvar__0__nonzero__118628 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__118746,Vvar__0__x__118747,Vvar__1__n__118748,Vvar__1__n__118749,Vvar__2___24Anonymous__118750,Vvar__2___24Anonymous__118751] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__118746,Vvar__1__n__118748) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__118747,Vvar__1__n__118749)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__118748 = Vvar__1__n__118749
        & Vvar__0__x__118746 = Vvar__0__x__118747 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__118736,Vvar__0__x__118737,Vvar__1___24Anonymous__118738,Vvar__1___24Anonymous__118739] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__118736) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__118737)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__118736 = Vvar__0__x__118737 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__118740,Vvar__0__x__118741,Vvar__1__n__118742,Vvar__1__n__118743,Vvar__2___24Anonymous__118744,Vvar__2___24Anonymous__118745] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__118740,Vvar__1__n__118742) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__118741,Vvar__1__n__118743)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__118742 = Vvar__1__n__118743
        & Vvar__0__x__118740 = Vvar__0__x__118741 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__11321,Vvar__0___24Anonymous__11322,Vvar__1___24Anonymous__11323,Vvar__1___24Anonymous__11324,Vvar__2___24Anonymous__11325,Vvar__2___24Anonymous__11326,Vvar__3___24Anonymous__11327,Vvar__3___24Anonymous__11328,Vvar__4___24Anonymous__11329,Vvar__4___24Anonymous__11330,Vvar__5___24Anonymous__11331,Vvar__5___24Anonymous__11332,Vvar__6___24Anonymous__11333,Vvar__6___24Anonymous__11334,Vvar__7___24Anonymous__11335,Vvar__7___24Anonymous__11336] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__11321,Vvar__1___24Anonymous__11323,Vvar__2___24Anonymous__11325,Vvar__3___24Anonymous__11327,Vvar__4___24Anonymous__11329,Vvar__5___24Anonymous__11331,Vvar__6___24Anonymous__11333,Vvar__7___24Anonymous__11335) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__11322,Vvar__1___24Anonymous__11324,Vvar__2___24Anonymous__11326,Vvar__3___24Anonymous__11328,Vvar__4___24Anonymous__11330,Vvar__5___24Anonymous__11332,Vvar__6___24Anonymous__11334,Vvar__7___24Anonymous__11336)
     => ( Vvar__7___24Anonymous__11335 = Vvar__7___24Anonymous__11336
        & Vvar__6___24Anonymous__11333 = Vvar__6___24Anonymous__11334
        & Vvar__5___24Anonymous__11331 = Vvar__5___24Anonymous__11332
        & Vvar__4___24Anonymous__11329 = Vvar__4___24Anonymous__11330
        & Vvar__3___24Anonymous__11327 = Vvar__3___24Anonymous__11328
        & Vvar__2___24Anonymous__11325 = Vvar__2___24Anonymous__11326
        & Vvar__1___24Anonymous__11323 = Vvar__1___24Anonymous__11324
        & Vvar__0___24Anonymous__11321 = Vvar__0___24Anonymous__11322 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__98658,Vvar__0___24Anonymous__98659,Vvar__1___24Anonymous__98660,Vvar__1___24Anonymous__98661] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__98658,Vvar__1___24Anonymous__98660) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__98659,Vvar__1___24Anonymous__98661)
     => ( Vvar__1___24Anonymous__98660 = Vvar__1___24Anonymous__98661
        & Vvar__0___24Anonymous__98658 = Vvar__0___24Anonymous__98659 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__118591,Vvar__0__X__118592,Vvar__1__lt__118593,Vvar__1__lt__118594,Vvar__2__eq__118595,Vvar__2__eq__118596,Vvar__3__x__118597,Vvar__3__x__118598,Vvar__4__y__118599,Vvar__4__y__118600,Vvar__5___24Anonymous__118601,Vvar__5___24Anonymous__118602] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__118591,Vvar__1__lt__118593,Vvar__2__eq__118595,Vvar__3__x__118597,Vvar__4__y__118599) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__118592,Vvar__1__lt__118594,Vvar__2__eq__118596,Vvar__3__x__118598,Vvar__4__y__118600)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__118599 = Vvar__4__y__118600
        & Vvar__3__x__118597 = Vvar__3__x__118598
        & Vvar__2__eq__118595 = Vvar__2__eq__118596
        & Vvar__1__lt__118593 = Vvar__1__lt__118594
        & Vvar__0__X__118591 = Vvar__0__X__118592 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__118603,Vvar__0__X__118604,Vvar__1__lt__118605,Vvar__1__lt__118606,Vvar__2__eq__118607,Vvar__2__eq__118608,Vvar__3__x__118609,Vvar__3__x__118610,Vvar__4__y__118611,Vvar__4__y__118612,Vvar__5___24Anonymous__118613,Vvar__5___24Anonymous__118614] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__118603,Vvar__1__lt__118605,Vvar__2__eq__118607,Vvar__3__x__118609,Vvar__4__y__118611) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__118604,Vvar__1__lt__118606,Vvar__2__eq__118608,Vvar__3__x__118610,Vvar__4__y__118612)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__118611 = Vvar__4__y__118612
        & Vvar__3__x__118609 = Vvar__3__x__118610
        & Vvar__2__eq__118607 = Vvar__2__eq__118608
        & Vvar__1__lt__118605 = Vvar__1__lt__118606
        & Vvar__0__X__118603 = Vvar__0__X__118604 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__118579,Vvar__0__X__118580,Vvar__1__lt__118581,Vvar__1__lt__118582,Vvar__2__eq__118583,Vvar__2__eq__118584,Vvar__3__x__118585,Vvar__3__x__118586,Vvar__4__y__118587,Vvar__4__y__118588,Vvar__5___24Anonymous__118589,Vvar__5___24Anonymous__118590] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__118579,Vvar__1__lt__118581,Vvar__2__eq__118583,Vvar__3__x__118585,Vvar__4__y__118587) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__118580,Vvar__1__lt__118582,Vvar__2__eq__118584,Vvar__3__x__118586,Vvar__4__y__118588)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__118587 = Vvar__4__y__118588
        & Vvar__3__x__118585 = Vvar__3__x__118586
        & Vvar__2__eq__118583 = Vvar__2__eq__118584
        & Vvar__1__lt__118581 = Vvar__1__lt__118582
        & Vvar__0__X__118579 = Vvar__0__X__118580 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__112963,Vvar__0__n__112964] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__112963) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__112964)
     => Vvar__0__n__112963 = Vvar__0__n__112964 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__112965,Vvar__0__n__112966,Vvar__1___24Anonymous__112967,Vvar__1___24Anonymous__112968] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__112965,Vvar__1___24Anonymous__112967) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__112966,Vvar__1___24Anonymous__112968)
     => ( Vvar__1___24Anonymous__112967 = Vvar__1___24Anonymous__112968
        & Vvar__0__n__112965 = Vvar__0__n__112966 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__100958,Vvar__0__A__100959,Vvar__1__h__100960,Vvar__1__h__100961,Vvar__2__n__100962,Vvar__2__n__100963,Vvar__3___24Anonymous__100964,Vvar__3___24Anonymous__100965] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__100958,Vvar__1__h__100960,Vvar__2__n__100962,Vvar__3___24Anonymous__100964) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__100959,Vvar__1__h__100961,Vvar__2__n__100963,Vvar__3___24Anonymous__100965)
     => ( Vvar__3___24Anonymous__100964 = Vvar__3___24Anonymous__100965
        & Vvar__2__n__100962 = Vvar__2__n__100963
        & Vvar__1__h__100960 = Vvar__1__h__100961
        & Vvar__0__A__100958 = Vvar__0__A__100959 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__100956,Vvar__0__A__100957] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__100956) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__100957)
     => Vvar__0__A__100956 = Vvar__0__A__100957 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__120880,Vvar__0__a__120881,Vvar__1__b__120882,Vvar__1__b__120883,Vvar__2__u__120884,Vvar__2__u__120885,Vvar__3__v__120886,Vvar__3__v__120887,Vvar__4__d__120888,Vvar__4__d__120889,Vvar__5___24Anonymous__120890,Vvar__5___24Anonymous__120891,Vvar__6___24Anonymous__120892,Vvar__6___24Anonymous__120893] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__120880,Vvar__1__b__120882,Vvar__2__u__120884,Vvar__3__v__120886,Vvar__4__d__120888) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__120881,Vvar__1__b__120883,Vvar__2__u__120885,Vvar__3__v__120887,Vvar__4__d__120889)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__120888 = Vvar__4__d__120889
        & Vvar__3__v__120886 = Vvar__3__v__120887
        & Vvar__2__u__120884 = Vvar__2__u__120885
        & Vvar__1__b__120882 = Vvar__1__b__120883
        & Vvar__0__a__120880 = Vvar__0__a__120881 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__120941,Vvar__0__x__120942,Vvar__1__p__120943,Vvar__1__p__120944,Vvar__2__q__120945,Vvar__2__q__120946,Vvar__3__r__120947,Vvar__3__r__120948,Vvar__4___24Anonymous__120949,Vvar__4___24Anonymous__120950,Vvar__5___24Anonymous__120951,Vvar__5___24Anonymous__120952,Vvar__6___24Anonymous__120953,Vvar__6___24Anonymous__120954] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__120941,Vvar__1__p__120943,Vvar__2__q__120945,Vvar__3__r__120947) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__120942,Vvar__1__p__120944,Vvar__2__q__120946,Vvar__3__r__120948)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__120947 = Vvar__3__r__120948
        & Vvar__2__q__120945 = Vvar__2__q__120946
        & Vvar__1__p__120943 = Vvar__1__p__120944
        & Vvar__0__x__120941 = Vvar__0__x__120942 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__106405,Vvar__0__C__106406,Vvar__1___24Anonymous__106407,Vvar__1___24Anonymous__106408] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__106405,Vvar__1___24Anonymous__106407) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__106406,Vvar__1___24Anonymous__106408)
     => ( Vvar__1___24Anonymous__106407 = Vvar__1___24Anonymous__106408
        & Vvar__0__C__106405 = Vvar__0__C__106406 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__106409,Vvar__0__C__106410,Vvar__1___24Anonymous__106411,Vvar__1___24Anonymous__106412,Vvar__2___24Anonymous__106413,Vvar__2___24Anonymous__106414] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__106409,Vvar__1___24Anonymous__106411,Vvar__2___24Anonymous__106413) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__106410,Vvar__1___24Anonymous__106412,Vvar__2___24Anonymous__106414)
     => ( Vvar__2___24Anonymous__106413 = Vvar__2___24Anonymous__106414
        & Vvar__1___24Anonymous__106411 = Vvar__1___24Anonymous__106412
        & Vvar__0__C__106409 = Vvar__0__C__106410 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__106401,Vvar__0__C__106402,Vvar__1___24Anonymous__106403,Vvar__1___24Anonymous__106404] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__106401,Vvar__1___24Anonymous__106403) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__106402,Vvar__1___24Anonymous__106404)
     => ( Vvar__1___24Anonymous__106403 = Vvar__1___24Anonymous__106404
        & Vvar__0__C__106401 = Vvar__0__C__106402 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__106421,Vvar__0__C__106422,Vvar__1___24Anonymous__106423,Vvar__1___24Anonymous__106424,Vvar__2___24Anonymous__106425,Vvar__2___24Anonymous__106426] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__106421,Vvar__1___24Anonymous__106423,Vvar__2___24Anonymous__106425) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__106422,Vvar__1___24Anonymous__106424,Vvar__2___24Anonymous__106426)
     => ( Vvar__2___24Anonymous__106425 = Vvar__2___24Anonymous__106426
        & Vvar__1___24Anonymous__106423 = Vvar__1___24Anonymous__106424
        & Vvar__0__C__106421 = Vvar__0__C__106422 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__106427,Vvar__0__C__106428,Vvar__1___24Anonymous__106429,Vvar__1___24Anonymous__106430] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__106427,Vvar__1___24Anonymous__106429) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__106428,Vvar__1___24Anonymous__106430)
     => ( Vvar__1___24Anonymous__106429 = Vvar__1___24Anonymous__106430
        & Vvar__0__C__106427 = Vvar__0__C__106428 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__106431,Vvar__0__C__106432,Vvar__1___24Anonymous__106433,Vvar__1___24Anonymous__106434,Vvar__2___24Anonymous__106435,Vvar__2___24Anonymous__106436] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__106431,Vvar__1___24Anonymous__106433,Vvar__2___24Anonymous__106435) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__106432,Vvar__1___24Anonymous__106434,Vvar__2___24Anonymous__106436)
     => ( Vvar__2___24Anonymous__106435 = Vvar__2___24Anonymous__106436
        & Vvar__1___24Anonymous__106433 = Vvar__1___24Anonymous__106434
        & Vvar__0__C__106431 = Vvar__0__C__106432 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__106415,Vvar__0__C__106416,Vvar__1___24Anonymous__106417,Vvar__1___24Anonymous__106418,Vvar__2___24Anonymous__106419,Vvar__2___24Anonymous__106420] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__106415,Vvar__1___24Anonymous__106417,Vvar__2___24Anonymous__106419) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__106416,Vvar__1___24Anonymous__106418,Vvar__2___24Anonymous__106420)
     => ( Vvar__2___24Anonymous__106419 = Vvar__2___24Anonymous__106420
        & Vvar__1___24Anonymous__106417 = Vvar__1___24Anonymous__106418
        & Vvar__0__C__106415 = Vvar__0__C__106416 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__4644,Vvar__0__C__4645,Vvar__1___24Anonymous__4646,Vvar__1___24Anonymous__4647,Vvar__2___24Anonymous__4648,Vvar__2___24Anonymous__4649,Vvar__3___24Anonymous__4650,Vvar__3___24Anonymous__4651] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4644,Vvar__1___24Anonymous__4646,Vvar__2___24Anonymous__4648,Vvar__3___24Anonymous__4650) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4645,Vvar__1___24Anonymous__4647,Vvar__2___24Anonymous__4649,Vvar__3___24Anonymous__4651)
     => ( Vvar__3___24Anonymous__4650 = Vvar__3___24Anonymous__4651
        & Vvar__2___24Anonymous__4648 = Vvar__2___24Anonymous__4649
        & Vvar__1___24Anonymous__4646 = Vvar__1___24Anonymous__4647
        & Vvar__0__C__4644 = Vvar__0__C__4645 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__4634,Vvar__0__C__4635,Vvar__1___24Anonymous__4636,Vvar__1___24Anonymous__4637] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4634,Vvar__1___24Anonymous__4636) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4635,Vvar__1___24Anonymous__4637)
     => ( Vvar__1___24Anonymous__4636 = Vvar__1___24Anonymous__4637
        & Vvar__0__C__4634 = Vvar__0__C__4635 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__4638,Vvar__0__C__4639,Vvar__1___24Anonymous__4640,Vvar__1___24Anonymous__4641,Vvar__2___24Anonymous__4642,Vvar__2___24Anonymous__4643] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4638,Vvar__1___24Anonymous__4640,Vvar__2___24Anonymous__4642) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4639,Vvar__1___24Anonymous__4641,Vvar__2___24Anonymous__4643)
     => ( Vvar__2___24Anonymous__4642 = Vvar__2___24Anonymous__4643
        & Vvar__1___24Anonymous__4640 = Vvar__1___24Anonymous__4641
        & Vvar__0__C__4638 = Vvar__0__C__4639 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__83564,Vvar__0___24Anonymous__83565,Vvar__1___24Anonymous__83566,Vvar__1___24Anonymous__83567] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__83564,Vvar__1___24Anonymous__83566) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__83565,Vvar__1___24Anonymous__83567)
     => ( Vvar__1___24Anonymous__83566 = Vvar__1___24Anonymous__83567
        & Vvar__0___24Anonymous__83564 = Vvar__0___24Anonymous__83565 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__83560,Vvar__0___24Anonymous__83561,Vvar__1___24Anonymous__83562,Vvar__1___24Anonymous__83563] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__83560,Vvar__1___24Anonymous__83562) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__83561,Vvar__1___24Anonymous__83563)
     => ( Vvar__1___24Anonymous__83562 = Vvar__1___24Anonymous__83563
        & Vvar__0___24Anonymous__83560 = Vvar__0___24Anonymous__83561 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__104090,Vvar__0__T__104091,Vvar__1__Flhs__104092,Vvar__1__Flhs__104093,Vvar__2__Fop__104094,Vvar__2__Fop__104095,Vvar__3__Frhs__104096,Vvar__3__Frhs__104097] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__104090,Vvar__1__Flhs__104092,Vvar__2__Fop__104094,Vvar__3__Frhs__104096) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__104091,Vvar__1__Flhs__104093,Vvar__2__Fop__104095,Vvar__3__Frhs__104097)
     => ( Vvar__3__Frhs__104096 = Vvar__3__Frhs__104097
        & Vvar__2__Fop__104094 = Vvar__2__Fop__104095
        & Vvar__1__Flhs__104092 = Vvar__1__Flhs__104093
        & Vvar__0__T__104090 = Vvar__0__T__104091 ) ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__99157,Vvar__0__TA__99158,Vvar__1__TX__99159,Vvar__1__TX__99160,Vvar__2__AA__99161,Vvar__2__AA__99162,Vvar__3__AF__99163,Vvar__3__AF__99164,Vvar__4___24Anonymous__99165,Vvar__4___24Anonymous__99166,Vvar__5___24Anonymous__99167,Vvar__5___24Anonymous__99168] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__99157,Vvar__1__TX__99159,Vvar__2__AA__99161,Vvar__3__AF__99163,Vvar__4___24Anonymous__99165,Vvar__5___24Anonymous__99167) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__99158,Vvar__1__TX__99160,Vvar__2__AA__99162,Vvar__3__AF__99164,Vvar__4___24Anonymous__99166,Vvar__5___24Anonymous__99168)
     => ( Vvar__5___24Anonymous__99167 = Vvar__5___24Anonymous__99168
        & Vvar__4___24Anonymous__99165 = Vvar__4___24Anonymous__99166
        & Vvar__3__AF__99163 = Vvar__3__AF__99164
        & Vvar__2__AA__99161 = Vvar__2__AA__99162
        & Vvar__1__TX__99159 = Vvar__1__TX__99160
        & Vvar__0__TA__99157 = Vvar__0__TA__99158 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__99169,Vvar__0__TA__99170,Vvar__1__TX__99171,Vvar__1__TX__99172,Vvar__2__AA__99173,Vvar__2__AA__99174,Vvar__3__AF__99175,Vvar__3__AF__99176,Vvar__4___24Anonymous__99177,Vvar__4___24Anonymous__99178,Vvar__5___24Anonymous__99179,Vvar__5___24Anonymous__99180] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__99169,Vvar__1__TX__99171,Vvar__2__AA__99173,Vvar__3__AF__99175,Vvar__4___24Anonymous__99177,Vvar__5___24Anonymous__99179) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__99170,Vvar__1__TX__99172,Vvar__2__AA__99174,Vvar__3__AF__99176,Vvar__4___24Anonymous__99178,Vvar__5___24Anonymous__99180)
     => ( Vvar__5___24Anonymous__99179 = Vvar__5___24Anonymous__99180
        & Vvar__4___24Anonymous__99177 = Vvar__4___24Anonymous__99178
        & Vvar__3__AF__99175 = Vvar__3__AF__99176
        & Vvar__2__AA__99173 = Vvar__2__AA__99174
        & Vvar__1__TX__99171 = Vvar__1__TX__99172
        & Vvar__0__TA__99169 = Vvar__0__TA__99170 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__99181,Vvar__0__TA__99182,Vvar__1__TX__99183,Vvar__1__TX__99184,Vvar__2__AA__99185,Vvar__2__AA__99186,Vvar__3__AF__99187,Vvar__3__AF__99188,Vvar__4___24Anonymous__99189,Vvar__4___24Anonymous__99190,Vvar__5___24Anonymous__99191,Vvar__5___24Anonymous__99192] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__99181,Vvar__1__TX__99183,Vvar__2__AA__99185,Vvar__3__AF__99187,Vvar__4___24Anonymous__99189,Vvar__5___24Anonymous__99191) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__99182,Vvar__1__TX__99184,Vvar__2__AA__99186,Vvar__3__AF__99188,Vvar__4___24Anonymous__99190,Vvar__5___24Anonymous__99192)
     => ( Vvar__5___24Anonymous__99191 = Vvar__5___24Anonymous__99192
        & Vvar__4___24Anonymous__99189 = Vvar__4___24Anonymous__99190
        & Vvar__3__AF__99187 = Vvar__3__AF__99188
        & Vvar__2__AA__99185 = Vvar__2__AA__99186
        & Vvar__1__TX__99183 = Vvar__1__TX__99184
        & Vvar__0__TA__99181 = Vvar__0__TA__99182 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__99139,Vvar__0__TA__99140,Vvar__1__TX__99141,Vvar__1__TX__99142,Vvar__2__AA__99143,Vvar__2__AA__99144,Vvar__3__AF__99145,Vvar__3__AF__99146] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__99139,Vvar__1__TX__99141,Vvar__2__AA__99143,Vvar__3__AF__99145) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__99140,Vvar__1__TX__99142,Vvar__2__AA__99144,Vvar__3__AF__99146)
     => ( Vvar__3__AF__99145 = Vvar__3__AF__99146
        & Vvar__2__AA__99143 = Vvar__2__AA__99144
        & Vvar__1__TX__99141 = Vvar__1__TX__99142
        & Vvar__0__TA__99139 = Vvar__0__TA__99140 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__99203,Vvar__0__TA__99204,Vvar__1__TX__99205,Vvar__1__TX__99206,Vvar__2__AA__99207,Vvar__2__AA__99208,Vvar__3__AF__99209,Vvar__3__AF__99210,Vvar__4___24Anonymous__99211,Vvar__4___24Anonymous__99212,Vvar__5___24Anonymous__99213,Vvar__5___24Anonymous__99214,Vvar__6___24Anonymous__99215,Vvar__6___24Anonymous__99216] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__99203,Vvar__1__TX__99205,Vvar__2__AA__99207,Vvar__3__AF__99209,Vvar__4___24Anonymous__99211,Vvar__5___24Anonymous__99213,Vvar__6___24Anonymous__99215) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__99204,Vvar__1__TX__99206,Vvar__2__AA__99208,Vvar__3__AF__99210,Vvar__4___24Anonymous__99212,Vvar__5___24Anonymous__99214,Vvar__6___24Anonymous__99216)
     => ( Vvar__6___24Anonymous__99215 = Vvar__6___24Anonymous__99216
        & Vvar__5___24Anonymous__99213 = Vvar__5___24Anonymous__99214
        & Vvar__4___24Anonymous__99211 = Vvar__4___24Anonymous__99212
        & Vvar__3__AF__99209 = Vvar__3__AF__99210
        & Vvar__2__AA__99207 = Vvar__2__AA__99208
        & Vvar__1__TX__99205 = Vvar__1__TX__99206
        & Vvar__0__TA__99203 = Vvar__0__TA__99204 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__99193,Vvar__0__TA__99194,Vvar__1__TX__99195,Vvar__1__TX__99196,Vvar__2__AA__99197,Vvar__2__AA__99198,Vvar__3__AF__99199,Vvar__3__AF__99200,Vvar__4___24Anonymous__99201,Vvar__4___24Anonymous__99202] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__99193,Vvar__1__TX__99195,Vvar__2__AA__99197,Vvar__3__AF__99199,Vvar__4___24Anonymous__99201) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__99194,Vvar__1__TX__99196,Vvar__2__AA__99198,Vvar__3__AF__99200,Vvar__4___24Anonymous__99202)
     => ( Vvar__4___24Anonymous__99201 = Vvar__4___24Anonymous__99202
        & Vvar__3__AF__99199 = Vvar__3__AF__99200
        & Vvar__2__AA__99197 = Vvar__2__AA__99198
        & Vvar__1__TX__99195 = Vvar__1__TX__99196
        & Vvar__0__TA__99193 = Vvar__0__TA__99194 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__99131,Vvar__0__TA__99132,Vvar__1__TX__99133,Vvar__1__TX__99134,Vvar__2__AA__99135,Vvar__2__AA__99136,Vvar__3__AF__99137,Vvar__3__AF__99138] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__99131,Vvar__1__TX__99133,Vvar__2__AA__99135,Vvar__3__AF__99137) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__99132,Vvar__1__TX__99134,Vvar__2__AA__99136,Vvar__3__AF__99138)
     => ( Vvar__3__AF__99137 = Vvar__3__AF__99138
        & Vvar__2__AA__99135 = Vvar__2__AA__99136
        & Vvar__1__TX__99133 = Vvar__1__TX__99134
        & Vvar__0__TA__99131 = Vvar__0__TA__99132 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__99147,Vvar__0__TA__99148,Vvar__1__TX__99149,Vvar__1__TX__99150,Vvar__2__AA__99151,Vvar__2__AA__99152,Vvar__3__AF__99153,Vvar__3__AF__99154,Vvar__4___24Anonymous__99155,Vvar__4___24Anonymous__99156] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__99147,Vvar__1__TX__99149,Vvar__2__AA__99151,Vvar__3__AF__99153,Vvar__4___24Anonymous__99155) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__99148,Vvar__1__TX__99150,Vvar__2__AA__99152,Vvar__3__AF__99154,Vvar__4___24Anonymous__99156)
     => ( Vvar__4___24Anonymous__99155 = Vvar__4___24Anonymous__99156
        & Vvar__3__AF__99153 = Vvar__3__AF__99154
        & Vvar__2__AA__99151 = Vvar__2__AA__99152
        & Vvar__1__TX__99149 = Vvar__1__TX__99150
        & Vvar__0__TA__99147 = Vvar__0__TA__99148 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__103076,Vvar__0__C__103077] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__103076) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__103077)
     => Vvar__0__C__103076 = Vvar__0__C__103077 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__103074,Vvar__0__C__103075] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__103074) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__103075)
     => Vvar__0__C__103074 = Vvar__0__C__103075 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__103082,Vvar__0__C__103083,Vvar__1___24Anonymous__103084,Vvar__1___24Anonymous__103085] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__103082,Vvar__1___24Anonymous__103084) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__103083,Vvar__1___24Anonymous__103085)
     => ( Vvar__1___24Anonymous__103084 = Vvar__1___24Anonymous__103085
        & Vvar__0__C__103082 = Vvar__0__C__103083 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__103086,Vvar__0__C__103087,Vvar__1___24Anonymous__103088,Vvar__1___24Anonymous__103089,Vvar__2___24Anonymous__103090,Vvar__2___24Anonymous__103091] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__103086,Vvar__1___24Anonymous__103088,Vvar__2___24Anonymous__103090) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__103087,Vvar__1___24Anonymous__103089,Vvar__2___24Anonymous__103091)
     => ( Vvar__2___24Anonymous__103090 = Vvar__2___24Anonymous__103091
        & Vvar__1___24Anonymous__103088 = Vvar__1___24Anonymous__103089
        & Vvar__0__C__103086 = Vvar__0__C__103087 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__103078,Vvar__0__C__103079,Vvar__1___24Anonymous__103080,Vvar__1___24Anonymous__103081] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__103078,Vvar__1___24Anonymous__103080) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__103079,Vvar__1___24Anonymous__103081)
     => ( Vvar__1___24Anonymous__103080 = Vvar__1___24Anonymous__103081
        & Vvar__0__C__103078 = Vvar__0__C__103079 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__103112,Vvar__0__C__103113,Vvar__1___24Anonymous__103114,Vvar__1___24Anonymous__103115,Vvar__2___24Anonymous__103116,Vvar__2___24Anonymous__103117] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__103112,Vvar__1___24Anonymous__103114,Vvar__2___24Anonymous__103116) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__103113,Vvar__1___24Anonymous__103115,Vvar__2___24Anonymous__103117)
     => ( Vvar__2___24Anonymous__103116 = Vvar__2___24Anonymous__103117
        & Vvar__1___24Anonymous__103114 = Vvar__1___24Anonymous__103115
        & Vvar__0__C__103112 = Vvar__0__C__103113 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__103108,Vvar__0__C__103109,Vvar__1___24Anonymous__103110,Vvar__1___24Anonymous__103111] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__103108,Vvar__1___24Anonymous__103110) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__103109,Vvar__1___24Anonymous__103111)
     => ( Vvar__1___24Anonymous__103110 = Vvar__1___24Anonymous__103111
        & Vvar__0__C__103108 = Vvar__0__C__103109 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__103098,Vvar__0__C__103099,Vvar__1___24Anonymous__103100,Vvar__1___24Anonymous__103101,Vvar__2___24Anonymous__103102,Vvar__2___24Anonymous__103103] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__103098,Vvar__1___24Anonymous__103100,Vvar__2___24Anonymous__103102) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__103099,Vvar__1___24Anonymous__103101,Vvar__2___24Anonymous__103103)
     => ( Vvar__2___24Anonymous__103102 = Vvar__2___24Anonymous__103103
        & Vvar__1___24Anonymous__103100 = Vvar__1___24Anonymous__103101
        & Vvar__0__C__103098 = Vvar__0__C__103099 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__103104,Vvar__0__C__103105,Vvar__1___24Anonymous__103106,Vvar__1___24Anonymous__103107] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__103104,Vvar__1___24Anonymous__103106) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__103105,Vvar__1___24Anonymous__103107)
     => ( Vvar__1___24Anonymous__103106 = Vvar__1___24Anonymous__103107
        & Vvar__0__C__103104 = Vvar__0__C__103105 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__103118,Vvar__0__C__103119,Vvar__1___24Anonymous__103120,Vvar__1___24Anonymous__103121,Vvar__2___24Anonymous__103122,Vvar__2___24Anonymous__103123] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__103118,Vvar__1___24Anonymous__103120,Vvar__2___24Anonymous__103122) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__103119,Vvar__1___24Anonymous__103121,Vvar__2___24Anonymous__103123)
     => ( Vvar__2___24Anonymous__103122 = Vvar__2___24Anonymous__103123
        & Vvar__1___24Anonymous__103120 = Vvar__1___24Anonymous__103121
        & Vvar__0__C__103118 = Vvar__0__C__103119 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__103092,Vvar__0__C__103093,Vvar__1___24Anonymous__103094,Vvar__1___24Anonymous__103095,Vvar__2___24Anonymous__103096,Vvar__2___24Anonymous__103097] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__103092,Vvar__1___24Anonymous__103094,Vvar__2___24Anonymous__103096) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__103093,Vvar__1___24Anonymous__103095,Vvar__2___24Anonymous__103097)
     => ( Vvar__2___24Anonymous__103096 = Vvar__2___24Anonymous__103097
        & Vvar__1___24Anonymous__103094 = Vvar__1___24Anonymous__103095
        & Vvar__0__C__103092 = Vvar__0__C__103093 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__103415,Vvar__0__C__103416,Vvar__1__num__103417,Vvar__1__num__103418,Vvar__2__denum__103419,Vvar__2__denum__103420,Vvar__3__condition__103421,Vvar__3__condition__103422] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__103415,Vvar__1__num__103417,Vvar__2__denum__103419,Vvar__3__condition__103421) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__103416,Vvar__1__num__103418,Vvar__2__denum__103420,Vvar__3__condition__103422)
     => ( Vvar__3__condition__103421 = Vvar__3__condition__103422
        & Vvar__2__denum__103419 = Vvar__2__denum__103420
        & Vvar__1__num__103417 = Vvar__1__num__103418
        & Vvar__0__C__103415 = Vvar__0__C__103416 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__87305,Vvar__0__C__87306,Vvar__1__rsplit__left__87307,Vvar__1__rsplit__left__87308,Vvar__2__rsplit__common__87309,Vvar__2__rsplit__common__87310,Vvar__3__rsplit__right__87311,Vvar__3__rsplit__right__87312] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__87305,Vvar__1__rsplit__left__87307,Vvar__2__rsplit__common__87309,Vvar__3__rsplit__right__87311) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__87306,Vvar__1__rsplit__left__87308,Vvar__2__rsplit__common__87310,Vvar__3__rsplit__right__87312)
     => ( Vvar__3__rsplit__right__87311 = Vvar__3__rsplit__right__87312
        & Vvar__2__rsplit__common__87309 = Vvar__2__rsplit__common__87310
        & Vvar__1__rsplit__left__87307 = Vvar__1__rsplit__left__87308
        & Vvar__0__C__87305 = Vvar__0__C__87306 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__10685,Vvar__0__C__10686] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10685) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10686)
     => Vvar__0__C__10685 = Vvar__0__C__10686 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__10683,Vvar__0__C__10684] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10683) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10684)
     => Vvar__0__C__10683 = Vvar__0__C__10684 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__10691,Vvar__0__C__10692,Vvar__1___24Anonymous__10693,Vvar__1___24Anonymous__10694] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10691,Vvar__1___24Anonymous__10693) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10692,Vvar__1___24Anonymous__10694)
     => ( Vvar__1___24Anonymous__10693 = Vvar__1___24Anonymous__10694
        & Vvar__0__C__10691 = Vvar__0__C__10692 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__10695,Vvar__0__C__10696,Vvar__1___24Anonymous__10697,Vvar__1___24Anonymous__10698,Vvar__2___24Anonymous__10699,Vvar__2___24Anonymous__10700] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10695,Vvar__1___24Anonymous__10697,Vvar__2___24Anonymous__10699) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10696,Vvar__1___24Anonymous__10698,Vvar__2___24Anonymous__10700)
     => ( Vvar__2___24Anonymous__10699 = Vvar__2___24Anonymous__10700
        & Vvar__1___24Anonymous__10697 = Vvar__1___24Anonymous__10698
        & Vvar__0__C__10695 = Vvar__0__C__10696 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__10687,Vvar__0__C__10688,Vvar__1___24Anonymous__10689,Vvar__1___24Anonymous__10690] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10687,Vvar__1___24Anonymous__10689) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10688,Vvar__1___24Anonymous__10690)
     => ( Vvar__1___24Anonymous__10689 = Vvar__1___24Anonymous__10690
        & Vvar__0__C__10687 = Vvar__0__C__10688 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__10707,Vvar__0__C__10708,Vvar__1___24Anonymous__10709,Vvar__1___24Anonymous__10710,Vvar__2___24Anonymous__10711,Vvar__2___24Anonymous__10712] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10707,Vvar__1___24Anonymous__10709,Vvar__2___24Anonymous__10711) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10708,Vvar__1___24Anonymous__10710,Vvar__2___24Anonymous__10712)
     => ( Vvar__2___24Anonymous__10711 = Vvar__2___24Anonymous__10712
        & Vvar__1___24Anonymous__10709 = Vvar__1___24Anonymous__10710
        & Vvar__0__C__10707 = Vvar__0__C__10708 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__10713,Vvar__0__C__10714,Vvar__1___24Anonymous__10715,Vvar__1___24Anonymous__10716] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10713,Vvar__1___24Anonymous__10715) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10714,Vvar__1___24Anonymous__10716)
     => ( Vvar__1___24Anonymous__10715 = Vvar__1___24Anonymous__10716
        & Vvar__0__C__10713 = Vvar__0__C__10714 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__10717,Vvar__0__C__10718,Vvar__1___24Anonymous__10719,Vvar__1___24Anonymous__10720,Vvar__2___24Anonymous__10721,Vvar__2___24Anonymous__10722] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10717,Vvar__1___24Anonymous__10719,Vvar__2___24Anonymous__10721) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10718,Vvar__1___24Anonymous__10720,Vvar__2___24Anonymous__10722)
     => ( Vvar__2___24Anonymous__10721 = Vvar__2___24Anonymous__10722
        & Vvar__1___24Anonymous__10719 = Vvar__1___24Anonymous__10720
        & Vvar__0__C__10717 = Vvar__0__C__10718 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__10701,Vvar__0__C__10702,Vvar__1___24Anonymous__10703,Vvar__1___24Anonymous__10704,Vvar__2___24Anonymous__10705,Vvar__2___24Anonymous__10706] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10701,Vvar__1___24Anonymous__10703,Vvar__2___24Anonymous__10705) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10702,Vvar__1___24Anonymous__10704,Vvar__2___24Anonymous__10706)
     => ( Vvar__2___24Anonymous__10705 = Vvar__2___24Anonymous__10706
        & Vvar__1___24Anonymous__10703 = Vvar__1___24Anonymous__10704
        & Vvar__0__C__10701 = Vvar__0__C__10702 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__220,Vvar__0__C__221,Vvar__1___24Anonymous__222,Vvar__1___24Anonymous__223,Vvar__2___24Anonymous__224,Vvar__2___24Anonymous__225,Vvar__3___24Anonymous__226,Vvar__3___24Anonymous__227] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__220,Vvar__1___24Anonymous__222,Vvar__2___24Anonymous__224,Vvar__3___24Anonymous__226) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__221,Vvar__1___24Anonymous__223,Vvar__2___24Anonymous__225,Vvar__3___24Anonymous__227)
     => ( Vvar__3___24Anonymous__226 = Vvar__3___24Anonymous__227
        & Vvar__2___24Anonymous__224 = Vvar__2___24Anonymous__225
        & Vvar__1___24Anonymous__222 = Vvar__1___24Anonymous__223
        & Vvar__0__C__220 = Vvar__0__C__221 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__210,Vvar__0__C__211,Vvar__1___24Anonymous__212,Vvar__1___24Anonymous__213] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__210,Vvar__1___24Anonymous__212) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__211,Vvar__1___24Anonymous__213)
     => ( Vvar__1___24Anonymous__212 = Vvar__1___24Anonymous__213
        & Vvar__0__C__210 = Vvar__0__C__211 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__214,Vvar__0__C__215,Vvar__1___24Anonymous__216,Vvar__1___24Anonymous__217,Vvar__2___24Anonymous__218,Vvar__2___24Anonymous__219] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__214,Vvar__1___24Anonymous__216,Vvar__2___24Anonymous__218) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__215,Vvar__1___24Anonymous__217,Vvar__2___24Anonymous__219)
     => ( Vvar__2___24Anonymous__218 = Vvar__2___24Anonymous__219
        & Vvar__1___24Anonymous__216 = Vvar__1___24Anonymous__217
        & Vvar__0__C__214 = Vvar__0__C__215 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__408,Vvar__0___24Anonymous__409,Vvar__1___24Anonymous__410,Vvar__1___24Anonymous__411] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__408,Vvar__1___24Anonymous__410) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__409,Vvar__1___24Anonymous__411)
     => ( Vvar__1___24Anonymous__410 = Vvar__1___24Anonymous__411
        & Vvar__0___24Anonymous__408 = Vvar__0___24Anonymous__409 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__404,Vvar__0___24Anonymous__405,Vvar__1___24Anonymous__406,Vvar__1___24Anonymous__407] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__404,Vvar__1___24Anonymous__406) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__405,Vvar__1___24Anonymous__407)
     => ( Vvar__1___24Anonymous__406 = Vvar__1___24Anonymous__407
        & Vvar__0___24Anonymous__404 = Vvar__0___24Anonymous__405 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__120631,Vvar__0__R__120632,Vvar__1__req__120633,Vvar__1__req__120634,Vvar__2__reqb__120635,Vvar__2__reqb__120636,Vvar__3___24Anonymous__120637,Vvar__3___24Anonymous__120638] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__120631,Vvar__1__req__120633,Vvar__2__reqb__120635) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__120632,Vvar__1__req__120634,Vvar__2__reqb__120636)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__120635 = Vvar__2__reqb__120636
        & Vvar__1__req__120633 = Vvar__1__req__120634
        & Vvar__0__R__120631 = Vvar__0__R__120632 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__120639,Vvar__0__R__120640,Vvar__1__rO__120641,Vvar__1__rO__120642,Vvar__2__rI__120643,Vvar__2__rI__120644,Vvar__3__radd__120645,Vvar__3__radd__120646,Vvar__4__rmul__120647,Vvar__4__rmul__120648,Vvar__5__rsub__120649,Vvar__5__rsub__120650,Vvar__6__ropp__120651,Vvar__6__ropp__120652,Vvar__7__req__120653,Vvar__7__req__120654,Vvar__8__C__120655,Vvar__8__C__120656,Vvar__9__cO__120657,Vvar__9__cO__120658,Vvar__10__cI__120659,Vvar__10__cI__120660,Vvar__11__cadd__120661,Vvar__11__cadd__120662,Vvar__12__cmul__120663,Vvar__12__cmul__120664,Vvar__13__csub__120665,Vvar__13__csub__120666,Vvar__14__copp__120667,Vvar__14__copp__120668,Vvar__15__ceqb__120669,Vvar__15__ceqb__120670,Vvar__16__phi__120671,Vvar__16__phi__120672,Vvar__17___24Anonymous__120673,Vvar__17___24Anonymous__120674] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__120639,Vvar__1__rO__120641,Vvar__2__rI__120643,Vvar__3__radd__120645,Vvar__4__rmul__120647,Vvar__5__rsub__120649,Vvar__6__ropp__120651,Vvar__7__req__120653,Vvar__8__C__120655,Vvar__9__cO__120657,Vvar__10__cI__120659,Vvar__11__cadd__120661,Vvar__12__cmul__120663,Vvar__13__csub__120665,Vvar__14__copp__120667,Vvar__15__ceqb__120669,Vvar__16__phi__120671) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__120640,Vvar__1__rO__120642,Vvar__2__rI__120644,Vvar__3__radd__120646,Vvar__4__rmul__120648,Vvar__5__rsub__120650,Vvar__6__ropp__120652,Vvar__7__req__120654,Vvar__8__C__120656,Vvar__9__cO__120658,Vvar__10__cI__120660,Vvar__11__cadd__120662,Vvar__12__cmul__120664,Vvar__13__csub__120666,Vvar__14__copp__120668,Vvar__15__ceqb__120670,Vvar__16__phi__120672)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__120671 = Vvar__16__phi__120672
        & Vvar__15__ceqb__120669 = Vvar__15__ceqb__120670
        & Vvar__14__copp__120667 = Vvar__14__copp__120668
        & Vvar__13__csub__120665 = Vvar__13__csub__120666
        & Vvar__12__cmul__120663 = Vvar__12__cmul__120664
        & Vvar__11__cadd__120661 = Vvar__11__cadd__120662
        & Vvar__10__cI__120659 = Vvar__10__cI__120660
        & Vvar__9__cO__120657 = Vvar__9__cO__120658
        & Vvar__8__C__120655 = Vvar__8__C__120656
        & Vvar__7__req__120653 = Vvar__7__req__120654
        & Vvar__6__ropp__120651 = Vvar__6__ropp__120652
        & Vvar__5__rsub__120649 = Vvar__5__rsub__120650
        & Vvar__4__rmul__120647 = Vvar__4__rmul__120648
        & Vvar__3__radd__120645 = Vvar__3__radd__120646
        & Vvar__2__rI__120643 = Vvar__2__rI__120644
        & Vvar__1__rO__120641 = Vvar__1__rO__120642
        & Vvar__0__R__120639 = Vvar__0__R__120640 ) ) ).

fof('$_inj_IntMap.Map.M0',axiom,
    ! [Vvar__0__A__133,Vvar__0__A__134] :
      ( cIntMap_2eMap_2eM0___24a1(Vvar__0__A__133) = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__134)
     => Vvar__0__A__133 = Vvar__0__A__134 ) ).

fof('$_inj_IntMap.Map.M1',axiom,
    ! [Vvar__0__A__135,Vvar__0__A__136,Vvar__1___24Anonymous__137,Vvar__1___24Anonymous__138,Vvar__2___24Anonymous__139,Vvar__2___24Anonymous__140] :
      ( cIntMap_2eMap_2eM1___24a3(Vvar__0__A__135,Vvar__1___24Anonymous__137,Vvar__2___24Anonymous__139) = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__136,Vvar__1___24Anonymous__138,Vvar__2___24Anonymous__140)
     => ( Vvar__2___24Anonymous__139 = Vvar__2___24Anonymous__140
        & Vvar__1___24Anonymous__137 = Vvar__1___24Anonymous__138
        & Vvar__0__A__135 = Vvar__0__A__136 ) ) ).

fof('$_inj_IntMap.Map.M2',axiom,
    ! [Vvar__0__A__141,Vvar__0__A__142,Vvar__1___24Anonymous__143,Vvar__1___24Anonymous__144,Vvar__2___24Anonymous__145,Vvar__2___24Anonymous__146] :
      ( cIntMap_2eMap_2eM2___24a3(Vvar__0__A__141,Vvar__1___24Anonymous__143,Vvar__2___24Anonymous__145) = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__142,Vvar__1___24Anonymous__144,Vvar__2___24Anonymous__146)
     => ( Vvar__2___24Anonymous__145 = Vvar__2___24Anonymous__146
        & Vvar__1___24Anonymous__143 = Vvar__1___24Anonymous__144
        & Vvar__0__A__141 = Vvar__0__A__142 ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__112945] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__112945)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__112945)
       => ( Vvar__0___24Anonymous__112945 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__112947] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__112947)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__112947)
              & Vvar__0___24Anonymous__112945 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__112947) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__112949] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__112949)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__112949)
       => ? [Vvar__0__n__112951] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__112951)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__112951)
            & Vvar__0___24Anonymous__112949 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__112951) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__102695,Vvar__1___24Anonymous__102696,VX102697] :
      ( cProp___24t(Vvar__0__P__102695)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__102696)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__102695,Vvar__1___24Anonymous__102696,VX102697)
         => ( ( p(Vvar__0__P__102695)
              & Vvar__1___24Anonymous__102696 = cCoq_2eInit_2eDatatypes_2etrue
              & VX102697 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__102695) )
            | ( ~ p(Vvar__0__P__102695)
              & Vvar__1___24Anonymous__102696 = cCoq_2eInit_2eDatatypes_2efalse
              & VX102697 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__102695) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX102425] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX102425)
     => ( VX102425 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__102426] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__102426)
            & ? [Vvar__1___24Anonymous__102427] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__102427)
                & ? [Vvar__2___24Anonymous__102428] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__102428)
                    & VX102425 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__102426,Vvar__1___24Anonymous__102427,Vvar__2___24Anonymous__102428) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX11356] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX11356)
     => ( VX11356 = cCoq_2eInit_2eByte_2ex00
        | VX11356 = cCoq_2eInit_2eByte_2ex01
        | VX11356 = cCoq_2eInit_2eByte_2ex02
        | VX11356 = cCoq_2eInit_2eByte_2ex03
        | VX11356 = cCoq_2eInit_2eByte_2ex04
        | VX11356 = cCoq_2eInit_2eByte_2ex05
        | VX11356 = cCoq_2eInit_2eByte_2ex06
        | VX11356 = cCoq_2eInit_2eByte_2ex07
        | VX11356 = cCoq_2eInit_2eByte_2ex08
        | VX11356 = cCoq_2eInit_2eByte_2ex09
        | VX11356 = cCoq_2eInit_2eByte_2ex0a
        | VX11356 = cCoq_2eInit_2eByte_2ex0b
        | VX11356 = cCoq_2eInit_2eByte_2ex0c
        | VX11356 = cCoq_2eInit_2eByte_2ex0d
        | VX11356 = cCoq_2eInit_2eByte_2ex0e
        | VX11356 = cCoq_2eInit_2eByte_2ex0f
        | VX11356 = cCoq_2eInit_2eByte_2ex10
        | VX11356 = cCoq_2eInit_2eByte_2ex11
        | VX11356 = cCoq_2eInit_2eByte_2ex12
        | VX11356 = cCoq_2eInit_2eByte_2ex13
        | VX11356 = cCoq_2eInit_2eByte_2ex14
        | VX11356 = cCoq_2eInit_2eByte_2ex15
        | VX11356 = cCoq_2eInit_2eByte_2ex16
        | VX11356 = cCoq_2eInit_2eByte_2ex17
        | VX11356 = cCoq_2eInit_2eByte_2ex18
        | VX11356 = cCoq_2eInit_2eByte_2ex19
        | VX11356 = cCoq_2eInit_2eByte_2ex1a
        | VX11356 = cCoq_2eInit_2eByte_2ex1b
        | VX11356 = cCoq_2eInit_2eByte_2ex1c
        | VX11356 = cCoq_2eInit_2eByte_2ex1d
        | VX11356 = cCoq_2eInit_2eByte_2ex1e
        | VX11356 = cCoq_2eInit_2eByte_2ex1f
        | VX11356 = cCoq_2eInit_2eByte_2ex20
        | VX11356 = cCoq_2eInit_2eByte_2ex21
        | VX11356 = cCoq_2eInit_2eByte_2ex22
        | VX11356 = cCoq_2eInit_2eByte_2ex23
        | VX11356 = cCoq_2eInit_2eByte_2ex24
        | VX11356 = cCoq_2eInit_2eByte_2ex25
        | VX11356 = cCoq_2eInit_2eByte_2ex26
        | VX11356 = cCoq_2eInit_2eByte_2ex27
        | VX11356 = cCoq_2eInit_2eByte_2ex28
        | VX11356 = cCoq_2eInit_2eByte_2ex29
        | VX11356 = cCoq_2eInit_2eByte_2ex2a
        | VX11356 = cCoq_2eInit_2eByte_2ex2b
        | VX11356 = cCoq_2eInit_2eByte_2ex2c
        | VX11356 = cCoq_2eInit_2eByte_2ex2d
        | VX11356 = cCoq_2eInit_2eByte_2ex2e
        | VX11356 = cCoq_2eInit_2eByte_2ex2f
        | VX11356 = cCoq_2eInit_2eByte_2ex30
        | VX11356 = cCoq_2eInit_2eByte_2ex31
        | VX11356 = cCoq_2eInit_2eByte_2ex32
        | VX11356 = cCoq_2eInit_2eByte_2ex33
        | VX11356 = cCoq_2eInit_2eByte_2ex34
        | VX11356 = cCoq_2eInit_2eByte_2ex35
        | VX11356 = cCoq_2eInit_2eByte_2ex36
        | VX11356 = cCoq_2eInit_2eByte_2ex37
        | VX11356 = cCoq_2eInit_2eByte_2ex38
        | VX11356 = cCoq_2eInit_2eByte_2ex39
        | VX11356 = cCoq_2eInit_2eByte_2ex3a
        | VX11356 = cCoq_2eInit_2eByte_2ex3b
        | VX11356 = cCoq_2eInit_2eByte_2ex3c
        | VX11356 = cCoq_2eInit_2eByte_2ex3d
        | VX11356 = cCoq_2eInit_2eByte_2ex3e
        | VX11356 = cCoq_2eInit_2eByte_2ex3f
        | VX11356 = cCoq_2eInit_2eByte_2ex40
        | VX11356 = cCoq_2eInit_2eByte_2ex41
        | VX11356 = cCoq_2eInit_2eByte_2ex42
        | VX11356 = cCoq_2eInit_2eByte_2ex43
        | VX11356 = cCoq_2eInit_2eByte_2ex44
        | VX11356 = cCoq_2eInit_2eByte_2ex45
        | VX11356 = cCoq_2eInit_2eByte_2ex46
        | VX11356 = cCoq_2eInit_2eByte_2ex47
        | VX11356 = cCoq_2eInit_2eByte_2ex48
        | VX11356 = cCoq_2eInit_2eByte_2ex49
        | VX11356 = cCoq_2eInit_2eByte_2ex4a
        | VX11356 = cCoq_2eInit_2eByte_2ex4b
        | VX11356 = cCoq_2eInit_2eByte_2ex4c
        | VX11356 = cCoq_2eInit_2eByte_2ex4d
        | VX11356 = cCoq_2eInit_2eByte_2ex4e
        | VX11356 = cCoq_2eInit_2eByte_2ex4f
        | VX11356 = cCoq_2eInit_2eByte_2ex50
        | VX11356 = cCoq_2eInit_2eByte_2ex51
        | VX11356 = cCoq_2eInit_2eByte_2ex52
        | VX11356 = cCoq_2eInit_2eByte_2ex53
        | VX11356 = cCoq_2eInit_2eByte_2ex54
        | VX11356 = cCoq_2eInit_2eByte_2ex55
        | VX11356 = cCoq_2eInit_2eByte_2ex56
        | VX11356 = cCoq_2eInit_2eByte_2ex57
        | VX11356 = cCoq_2eInit_2eByte_2ex58
        | VX11356 = cCoq_2eInit_2eByte_2ex59
        | VX11356 = cCoq_2eInit_2eByte_2ex5a
        | VX11356 = cCoq_2eInit_2eByte_2ex5b
        | VX11356 = cCoq_2eInit_2eByte_2ex5c
        | VX11356 = cCoq_2eInit_2eByte_2ex5d
        | VX11356 = cCoq_2eInit_2eByte_2ex5e
        | VX11356 = cCoq_2eInit_2eByte_2ex5f
        | VX11356 = cCoq_2eInit_2eByte_2ex60
        | VX11356 = cCoq_2eInit_2eByte_2ex61
        | VX11356 = cCoq_2eInit_2eByte_2ex62
        | VX11356 = cCoq_2eInit_2eByte_2ex63
        | VX11356 = cCoq_2eInit_2eByte_2ex64
        | VX11356 = cCoq_2eInit_2eByte_2ex65
        | VX11356 = cCoq_2eInit_2eByte_2ex66
        | VX11356 = cCoq_2eInit_2eByte_2ex67
        | VX11356 = cCoq_2eInit_2eByte_2ex68
        | VX11356 = cCoq_2eInit_2eByte_2ex69
        | VX11356 = cCoq_2eInit_2eByte_2ex6a
        | VX11356 = cCoq_2eInit_2eByte_2ex6b
        | VX11356 = cCoq_2eInit_2eByte_2ex6c
        | VX11356 = cCoq_2eInit_2eByte_2ex6d
        | VX11356 = cCoq_2eInit_2eByte_2ex6e
        | VX11356 = cCoq_2eInit_2eByte_2ex6f
        | VX11356 = cCoq_2eInit_2eByte_2ex70
        | VX11356 = cCoq_2eInit_2eByte_2ex71
        | VX11356 = cCoq_2eInit_2eByte_2ex72
        | VX11356 = cCoq_2eInit_2eByte_2ex73
        | VX11356 = cCoq_2eInit_2eByte_2ex74
        | VX11356 = cCoq_2eInit_2eByte_2ex75
        | VX11356 = cCoq_2eInit_2eByte_2ex76
        | VX11356 = cCoq_2eInit_2eByte_2ex77
        | VX11356 = cCoq_2eInit_2eByte_2ex78
        | VX11356 = cCoq_2eInit_2eByte_2ex79
        | VX11356 = cCoq_2eInit_2eByte_2ex7a
        | VX11356 = cCoq_2eInit_2eByte_2ex7b
        | VX11356 = cCoq_2eInit_2eByte_2ex7c
        | VX11356 = cCoq_2eInit_2eByte_2ex7d
        | VX11356 = cCoq_2eInit_2eByte_2ex7e
        | VX11356 = cCoq_2eInit_2eByte_2ex7f
        | VX11356 = cCoq_2eInit_2eByte_2ex80
        | VX11356 = cCoq_2eInit_2eByte_2ex81
        | VX11356 = cCoq_2eInit_2eByte_2ex82
        | VX11356 = cCoq_2eInit_2eByte_2ex83
        | VX11356 = cCoq_2eInit_2eByte_2ex84
        | VX11356 = cCoq_2eInit_2eByte_2ex85
        | VX11356 = cCoq_2eInit_2eByte_2ex86
        | VX11356 = cCoq_2eInit_2eByte_2ex87
        | VX11356 = cCoq_2eInit_2eByte_2ex88
        | VX11356 = cCoq_2eInit_2eByte_2ex89
        | VX11356 = cCoq_2eInit_2eByte_2ex8a
        | VX11356 = cCoq_2eInit_2eByte_2ex8b
        | VX11356 = cCoq_2eInit_2eByte_2ex8c
        | VX11356 = cCoq_2eInit_2eByte_2ex8d
        | VX11356 = cCoq_2eInit_2eByte_2ex8e
        | VX11356 = cCoq_2eInit_2eByte_2ex8f
        | VX11356 = cCoq_2eInit_2eByte_2ex90
        | VX11356 = cCoq_2eInit_2eByte_2ex91
        | VX11356 = cCoq_2eInit_2eByte_2ex92
        | VX11356 = cCoq_2eInit_2eByte_2ex93
        | VX11356 = cCoq_2eInit_2eByte_2ex94
        | VX11356 = cCoq_2eInit_2eByte_2ex95
        | VX11356 = cCoq_2eInit_2eByte_2ex96
        | VX11356 = cCoq_2eInit_2eByte_2ex97
        | VX11356 = cCoq_2eInit_2eByte_2ex98
        | VX11356 = cCoq_2eInit_2eByte_2ex99
        | VX11356 = cCoq_2eInit_2eByte_2ex9a
        | VX11356 = cCoq_2eInit_2eByte_2ex9b
        | VX11356 = cCoq_2eInit_2eByte_2ex9c
        | VX11356 = cCoq_2eInit_2eByte_2ex9d
        | VX11356 = cCoq_2eInit_2eByte_2ex9e
        | VX11356 = cCoq_2eInit_2eByte_2ex9f
        | VX11356 = cCoq_2eInit_2eByte_2exa0
        | VX11356 = cCoq_2eInit_2eByte_2exa1
        | VX11356 = cCoq_2eInit_2eByte_2exa2
        | VX11356 = cCoq_2eInit_2eByte_2exa3
        | VX11356 = cCoq_2eInit_2eByte_2exa4
        | VX11356 = cCoq_2eInit_2eByte_2exa5
        | VX11356 = cCoq_2eInit_2eByte_2exa6
        | VX11356 = cCoq_2eInit_2eByte_2exa7
        | VX11356 = cCoq_2eInit_2eByte_2exa8
        | VX11356 = cCoq_2eInit_2eByte_2exa9
        | VX11356 = cCoq_2eInit_2eByte_2exaa
        | VX11356 = cCoq_2eInit_2eByte_2exab
        | VX11356 = cCoq_2eInit_2eByte_2exac
        | VX11356 = cCoq_2eInit_2eByte_2exad
        | VX11356 = cCoq_2eInit_2eByte_2exae
        | VX11356 = cCoq_2eInit_2eByte_2exaf
        | VX11356 = cCoq_2eInit_2eByte_2exb0
        | VX11356 = cCoq_2eInit_2eByte_2exb1
        | VX11356 = cCoq_2eInit_2eByte_2exb2
        | VX11356 = cCoq_2eInit_2eByte_2exb3
        | VX11356 = cCoq_2eInit_2eByte_2exb4
        | VX11356 = cCoq_2eInit_2eByte_2exb5
        | VX11356 = cCoq_2eInit_2eByte_2exb6
        | VX11356 = cCoq_2eInit_2eByte_2exb7
        | VX11356 = cCoq_2eInit_2eByte_2exb8
        | VX11356 = cCoq_2eInit_2eByte_2exb9
        | VX11356 = cCoq_2eInit_2eByte_2exba
        | VX11356 = cCoq_2eInit_2eByte_2exbb
        | VX11356 = cCoq_2eInit_2eByte_2exbc
        | VX11356 = cCoq_2eInit_2eByte_2exbd
        | VX11356 = cCoq_2eInit_2eByte_2exbe
        | VX11356 = cCoq_2eInit_2eByte_2exbf
        | VX11356 = cCoq_2eInit_2eByte_2exc0
        | VX11356 = cCoq_2eInit_2eByte_2exc1
        | VX11356 = cCoq_2eInit_2eByte_2exc2
        | VX11356 = cCoq_2eInit_2eByte_2exc3
        | VX11356 = cCoq_2eInit_2eByte_2exc4
        | VX11356 = cCoq_2eInit_2eByte_2exc5
        | VX11356 = cCoq_2eInit_2eByte_2exc6
        | VX11356 = cCoq_2eInit_2eByte_2exc7
        | VX11356 = cCoq_2eInit_2eByte_2exc8
        | VX11356 = cCoq_2eInit_2eByte_2exc9
        | VX11356 = cCoq_2eInit_2eByte_2exca
        | VX11356 = cCoq_2eInit_2eByte_2excb
        | VX11356 = cCoq_2eInit_2eByte_2excc
        | VX11356 = cCoq_2eInit_2eByte_2excd
        | VX11356 = cCoq_2eInit_2eByte_2exce
        | VX11356 = cCoq_2eInit_2eByte_2excf
        | VX11356 = cCoq_2eInit_2eByte_2exd0
        | VX11356 = cCoq_2eInit_2eByte_2exd1
        | VX11356 = cCoq_2eInit_2eByte_2exd2
        | VX11356 = cCoq_2eInit_2eByte_2exd3
        | VX11356 = cCoq_2eInit_2eByte_2exd4
        | VX11356 = cCoq_2eInit_2eByte_2exd5
        | VX11356 = cCoq_2eInit_2eByte_2exd6
        | VX11356 = cCoq_2eInit_2eByte_2exd7
        | VX11356 = cCoq_2eInit_2eByte_2exd8
        | VX11356 = cCoq_2eInit_2eByte_2exd9
        | VX11356 = cCoq_2eInit_2eByte_2exda
        | VX11356 = cCoq_2eInit_2eByte_2exdb
        | VX11356 = cCoq_2eInit_2eByte_2exdc
        | VX11356 = cCoq_2eInit_2eByte_2exdd
        | VX11356 = cCoq_2eInit_2eByte_2exde
        | VX11356 = cCoq_2eInit_2eByte_2exdf
        | VX11356 = cCoq_2eInit_2eByte_2exe0
        | VX11356 = cCoq_2eInit_2eByte_2exe1
        | VX11356 = cCoq_2eInit_2eByte_2exe2
        | VX11356 = cCoq_2eInit_2eByte_2exe3
        | VX11356 = cCoq_2eInit_2eByte_2exe4
        | VX11356 = cCoq_2eInit_2eByte_2exe5
        | VX11356 = cCoq_2eInit_2eByte_2exe6
        | VX11356 = cCoq_2eInit_2eByte_2exe7
        | VX11356 = cCoq_2eInit_2eByte_2exe8
        | VX11356 = cCoq_2eInit_2eByte_2exe9
        | VX11356 = cCoq_2eInit_2eByte_2exea
        | VX11356 = cCoq_2eInit_2eByte_2exeb
        | VX11356 = cCoq_2eInit_2eByte_2exec
        | VX11356 = cCoq_2eInit_2eByte_2exed
        | VX11356 = cCoq_2eInit_2eByte_2exee
        | VX11356 = cCoq_2eInit_2eByte_2exef
        | VX11356 = cCoq_2eInit_2eByte_2exf0
        | VX11356 = cCoq_2eInit_2eByte_2exf1
        | VX11356 = cCoq_2eInit_2eByte_2exf2
        | VX11356 = cCoq_2eInit_2eByte_2exf3
        | VX11356 = cCoq_2eInit_2eByte_2exf4
        | VX11356 = cCoq_2eInit_2eByte_2exf5
        | VX11356 = cCoq_2eInit_2eByte_2exf6
        | VX11356 = cCoq_2eInit_2eByte_2exf7
        | VX11356 = cCoq_2eInit_2eByte_2exf8
        | VX11356 = cCoq_2eInit_2eByte_2exf9
        | VX11356 = cCoq_2eInit_2eByte_2exfa
        | VX11356 = cCoq_2eInit_2eByte_2exfb
        | VX11356 = cCoq_2eInit_2eByte_2exfc
        | VX11356 = cCoq_2eInit_2eByte_2exfd
        | VX11356 = cCoq_2eInit_2eByte_2exfe
        | VX11356 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__82795,Vvar__1__Q__82796,Vvar__2___24Anonymous__82797] :
      ( cProp___24t(Vvar__0__P__82795)
     => ( cProp___24t(Vvar__1__Q__82796)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__82797)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__82795,Vvar__1__Q__82796,Vvar__2___24Anonymous__82797)
           => ( ( p(Vvar__0__P__82795)
                & Vvar__2___24Anonymous__82797 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__82796)
                & Vvar__2___24Anonymous__82797 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__83015,Vvar__1__Plt__83016,Vvar__2__Pgt__83017,Vvar__3___24Anonymous__83018] :
      ( cProp___24t(Vvar__0__Peq__83015)
     => ( cProp___24t(Vvar__1__Plt__83016)
       => ( cProp___24t(Vvar__2__Pgt__83017)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__83018)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__83015,Vvar__1__Plt__83016,Vvar__2__Pgt__83017,Vvar__3___24Anonymous__83018)
             => ( ( p(Vvar__0__Peq__83015)
                  & Vvar__3___24Anonymous__83018 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__83016)
                  & Vvar__3___24Anonymous__83018 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__83017)
                  & Vvar__3___24Anonymous__83018 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__117279,Vvar__1__Plt__117280,Vvar__2__Pgt__117281,Vvar__3___24Anonymous__117282,VX117283] :
      ( cProp___24t(Vvar__0__Peq__117279)
     => ( cProp___24t(Vvar__1__Plt__117280)
       => ( cProp___24t(Vvar__2__Pgt__117281)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__117282)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__117279,Vvar__1__Plt__117280,Vvar__2__Pgt__117281,Vvar__3___24Anonymous__117282,VX117283)
             => ( ( p(Vvar__0__Peq__117279)
                  & Vvar__3___24Anonymous__117282 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX117283 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__117279,Vvar__1__Plt__117280,Vvar__2__Pgt__117281) )
                | ( p(Vvar__1__Plt__117280)
                  & Vvar__3___24Anonymous__117282 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX117283 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__117279,Vvar__1__Plt__117280,Vvar__2__Pgt__117281) )
                | ( p(Vvar__2__Pgt__117281)
                  & Vvar__3___24Anonymous__117282 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX117283 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__117279,Vvar__1__Plt__117280,Vvar__2__Pgt__117281) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX17] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX17)
     => ( VX17 = cCoq_2eInit_2eDatatypes_2etrue
        | VX17 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX4603] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX4603)
     => ( VX4603 = cCoq_2eInit_2eDatatypes_2eEq
        | VX4603 = cCoq_2eInit_2eDatatypes_2eLt
        | VX4603 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__514,VX515] :
      ( cType___24t(Vvar__0__A__514)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__514,VX515)
       => ( VX515 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__514)
          | ? [Vvar__1___24Anonymous__518] :
              ( t(Vvar__1___24Anonymous__518,Vvar__0__A__514)
              & ? [Vvar__2___24Anonymous__519] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__514,Vvar__2___24Anonymous__519)
                  & VX515 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__514,Vvar__1___24Anonymous__518,Vvar__2___24Anonymous__519) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
    ! [VX5163] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(VX5163)
     => ( VX5163 = cCoq_2eInit_2eDatatypes_2eO
        | ? [Vvar__0___24Anonymous__5164] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5164)
            & VX5163 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5164) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__18,VX19] :
      ( cType___24t(Vvar__0__A__18)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__18,VX19)
       => ( ? [Vvar__1___24Anonymous__21] :
              ( t(Vvar__1___24Anonymous__21,Vvar__0__A__18)
              & VX19 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__18,Vvar__1___24Anonymous__21) )
          | VX19 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__18) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__39,Vvar__1__B__40,VX41] :
      ( cType___24t(Vvar__0__A__39)
     => ( cType___24t(Vvar__1__B__40)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__39,Vvar__1__B__40,VX41)
         => ? [Vvar__2___24Anonymous__44] :
              ( t(Vvar__2___24Anonymous__44,Vvar__0__A__39)
              & ? [Vvar__3___24Anonymous__45] :
                  ( t(Vvar__3___24Anonymous__45,Vvar__1__B__40)
                  & VX41 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__39,Vvar__1__B__40,Vvar__2___24Anonymous__44,Vvar__3___24Anonymous__45) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__82862,Vvar__1__B__82863,VX82864] :
      ( cType___24t(Vvar__0__A__82862)
     => ( cType___24t(Vvar__1__B__82863)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__82862,Vvar__1__B__82863,VX82864)
         => ( ? [Vvar__2___24Anonymous__82867] :
                ( t(Vvar__2___24Anonymous__82867,Vvar__0__A__82862)
                & VX82864 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__82862,Vvar__1__B__82863,Vvar__2___24Anonymous__82867) )
            | ? [Vvar__2___24Anonymous__82870] :
                ( t(Vvar__2___24Anonymous__82870,Vvar__1__B__82863)
                & VX82864 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__82862,Vvar__1__B__82863,Vvar__2___24Anonymous__82870) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX513] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX513)
     => VX513 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__90387,Vvar__1___24Anonymous__90388] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__90387)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__90388)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__90387,Vvar__1___24Anonymous__90388)
         => ( Vvar__1___24Anonymous__90388 = Vvar__0__n__90387
            | ? [Vvar__1__m__90392] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__90392)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__90387,Vvar__1__m__90392)
                & Vvar__1___24Anonymous__90388 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__90392) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__98501,Vvar__1__P__98502,VX98505] :
      ( cType___24t(Vvar__0__A__98501)
     => ( c_24__type__98515___24t(Vvar__0__A__98501,Vvar__1__P__98502,Vvar__1__P__98502)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__98501,Vvar__1__P__98502,VX98505)
         => ? [Vvar__2__x__98510] :
              ( t(Vvar__2__x__98510,Vvar__0__A__98501)
              & p(happ(Vvar__1__P__98502,Vvar__2__x__98510))
              & VX98505 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__98501,Vvar__1__P__98502,Vvar__2__x__98510) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__113420,Vvar__1__P__113421,Vvar__2__Q__113424,VX113427] :
      ( cType___24t(Vvar__0__A__113420)
     => ( c_24__type__113444___24t(Vvar__0__A__113420,Vvar__1__P__113421,Vvar__2__Q__113424,Vvar__1__P__113421)
       => ( c_24__type__113452___24t(Vvar__0__A__113420,Vvar__1__P__113421,Vvar__2__Q__113424,Vvar__2__Q__113424)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__113420,Vvar__1__P__113421,Vvar__2__Q__113424,VX113427)
           => ? [Vvar__3__x__113435] :
                ( t(Vvar__3__x__113435,Vvar__0__A__113420)
                & p(happ(Vvar__1__P__113421,Vvar__3__x__113435))
                & p(happ(Vvar__2__Q__113424,Vvar__3__x__113435))
                & VX113427 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__113420,Vvar__1__P__113421,Vvar__2__Q__113424,Vvar__3__x__113435) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__111539,Vvar__1__P__111540,VX111543] :
      ( cType___24t(Vvar__0__A__111539)
     => ( c_24__type__111553___24t(Vvar__0__A__111539,Vvar__1__P__111540,Vvar__1__P__111540)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__111539,Vvar__1__P__111540,VX111543)
         => ? [Vvar__2__x__111548] :
              ( t(Vvar__2__x__111548,Vvar__0__A__111539)
              & ? [Vvar__3___24Anonymous__111549] :
                  ( t(Vvar__3___24Anonymous__111549,happ(Vvar__1__P__111540,Vvar__2__x__111548))
                  & VX111543 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__111539,Vvar__1__P__111540,Vvar__2__x__111548,Vvar__3___24Anonymous__111549) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__113498,Vvar__1__P__113499,Vvar__2__Q__113502,VX113505] :
      ( cType___24t(Vvar__0__A__113498)
     => ( c_24__type__113522___24t(Vvar__0__A__113498,Vvar__1__P__113499,Vvar__2__Q__113502,Vvar__1__P__113499)
       => ( c_24__type__113530___24t(Vvar__0__A__113498,Vvar__1__P__113499,Vvar__2__Q__113502,Vvar__2__Q__113502)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__113498,Vvar__1__P__113499,Vvar__2__Q__113502,VX113505)
           => ? [Vvar__3__x__113513] :
                ( t(Vvar__3__x__113513,Vvar__0__A__113498)
                & ? [Vvar__4___24Anonymous__113514] :
                    ( t(Vvar__4___24Anonymous__113514,happ(Vvar__1__P__113499,Vvar__3__x__113513))
                    & ? [Vvar__5___24Anonymous__113515] :
                        ( t(Vvar__5___24Anonymous__113515,happ(Vvar__2__Q__113502,Vvar__3__x__113513))
                        & VX113505 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__113498,Vvar__1__P__113499,Vvar__2__Q__113502,Vvar__3__x__113513,Vvar__4___24Anonymous__113514,Vvar__5___24Anonymous__113515) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__11139,Vvar__1__B__11140,VX11141] :
      ( cProp___24t(Vvar__0__A__11139)
     => ( cProp___24t(Vvar__1__B__11140)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__11139,Vvar__1__B__11140,VX11141)
         => ( ( p(Vvar__0__A__11139)
              & VX11141 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11139,Vvar__1__B__11140) )
            | ( p(Vvar__1__B__11140)
              & VX11141 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11139,Vvar__1__B__11140) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__98548,Vvar__1__B__98549,VX98550] :
      ( cType___24t(Vvar__0__A__98548)
     => ( cProp___24t(Vvar__1__B__98549)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__98548,Vvar__1__B__98549,VX98550)
         => ( ? [Vvar__2___24Anonymous__98553] :
                ( t(Vvar__2___24Anonymous__98553,Vvar__0__A__98548)
                & VX98550 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__98548,Vvar__1__B__98549,Vvar__2___24Anonymous__98553) )
            | ( p(Vvar__1__B__98549)
              & VX98550 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__98548,Vvar__1__B__98549) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__101265,Vvar__1__R__101266,Vvar__2__x__101271] :
      ( cType___24t(Vvar__0__A__101265)
     => ( c_24__type__101300___24t(Vvar__0__A__101265,Vvar__1__R__101266,Vvar__2__x__101271,Vvar__1__R__101266)
       => ( t(Vvar__2__x__101271,Vvar__0__A__101265)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__101265,Vvar__1__R__101266,Vvar__2__x__101271)
           => ( ! [Vvar__var__var__var__var__3__y__101281__101283__101285__101287__101289] :
                  ( t(Vvar__var__var__var__var__3__y__101281__101283__101285__101287__101289,Vvar__0__A__101265)
                 => ( p(happ(happ(Vvar__1__R__101266,Vvar__var__var__var__var__3__y__101281__101283__101285__101287__101289),Vvar__2__x__101271))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__101265,Vvar__1__R__101266,Vvar__var__var__var__var__3__y__101281__101283__101285__101287__101289) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__118300,Vvar__1__a__118301,Vvar__2___24Anonymous__118302,Vvar__3___24Anonymous__118303] :
      ( cType___24t(Vvar__0__A__118300)
     => ( t(Vvar__1__a__118301,Vvar__0__A__118300)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118300,Vvar__2___24Anonymous__118302)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118300,Vvar__3___24Anonymous__118303)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__118300,Vvar__1__a__118301,Vvar__2___24Anonymous__118302,Vvar__3___24Anonymous__118303)
             => ( ? [Vvar__2__l__118307] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118300,Vvar__2__l__118307)
                    & Vvar__3___24Anonymous__118303 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118300,Vvar__1__a__118301,Vvar__2__l__118307)
                    & Vvar__2___24Anonymous__118302 = Vvar__2__l__118307 )
                | ? [Vvar__2__x__118310] :
                    ( t(Vvar__2__x__118310,Vvar__0__A__118300)
                    & ? [Vvar__3__l__118311] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118300,Vvar__3__l__118311)
                        & ? [Vvar__4__l_27__118312] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118300,Vvar__4__l_27__118312)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__118300,Vvar__1__a__118301,Vvar__3__l__118311,Vvar__4__l_27__118312)
                            & Vvar__3___24Anonymous__118303 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118300,Vvar__2__x__118310,Vvar__4__l_27__118312)
                            & Vvar__2___24Anonymous__118302 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118300,Vvar__2__x__118310,Vvar__3__l__118311) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__118314,Vvar__1__P__118315,Vvar__2___24Anonymous__118318] :
      ( cType___24t(Vvar__0__A__118314)
     => ( c_24__type__118336___24t(Vvar__0__A__118314,Vvar__1__P__118315,Vvar__2___24Anonymous__118318,Vvar__1__P__118315)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118314,Vvar__2___24Anonymous__118318)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__118314,Vvar__1__P__118315,Vvar__2___24Anonymous__118318)
           => ( Vvar__2___24Anonymous__118318 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__118314)
              | ? [Vvar__2__x__118328] :
                  ( t(Vvar__2__x__118328,Vvar__0__A__118314)
                  & ? [Vvar__3__l__118329] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118314,Vvar__3__l__118329)
                      & p(happ(Vvar__1__P__118315,Vvar__2__x__118328))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__118314,Vvar__1__P__118315,Vvar__3__l__118329)
                      & Vvar__2___24Anonymous__118318 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118314,Vvar__2__x__118328,Vvar__3__l__118329) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__118338,Vvar__1__B__118339,Vvar__2__R__118340,Vvar__3___24Anonymous__118345,Vvar__4___24Anonymous__118346] :
      ( cType___24t(Vvar__0__A__118338)
     => ( cType___24t(Vvar__1__B__118339)
       => ( c_24__type__118383___24t(Vvar__0__A__118338,Vvar__1__B__118339,Vvar__2__R__118340,Vvar__3___24Anonymous__118345,Vvar__4___24Anonymous__118346,Vvar__2__R__118340)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118338,Vvar__3___24Anonymous__118345)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__118339,Vvar__4___24Anonymous__118346)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__118338,Vvar__1__B__118339,Vvar__2__R__118340,Vvar__3___24Anonymous__118345,Vvar__4___24Anonymous__118346)
               => ( ( Vvar__4___24Anonymous__118346 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__118339)
                    & Vvar__3___24Anonymous__118345 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__118338) )
                  | ? [Vvar__3__x__118362] :
                      ( t(Vvar__3__x__118362,Vvar__0__A__118338)
                      & ? [Vvar__4__y__118363] :
                          ( t(Vvar__4__y__118363,Vvar__1__B__118339)
                          & ? [Vvar__5__l__118364] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118338,Vvar__5__l__118364)
                              & ? [Vvar__6__l_27__118365] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__118339,Vvar__6__l_27__118365)
                                  & p(happ(happ(Vvar__2__R__118340,Vvar__3__x__118362),Vvar__4__y__118363))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__118338,Vvar__1__B__118339,Vvar__2__R__118340,Vvar__5__l__118364,Vvar__6__l_27__118365)
                                  & Vvar__4___24Anonymous__118346 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__118339,Vvar__4__y__118363,Vvar__6__l_27__118365)
                                  & Vvar__3___24Anonymous__118345 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118338,Vvar__3__x__118362,Vvar__5__l__118364) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__118385,Vvar__1__R__118386,Vvar__2___24Anonymous__118391] :
      ( cType___24t(Vvar__0__A__118385)
     => ( c_24__type__118418___24t(Vvar__0__A__118385,Vvar__1__R__118386,Vvar__2___24Anonymous__118391,Vvar__1__R__118386)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118385,Vvar__2___24Anonymous__118391)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__118385,Vvar__1__R__118386,Vvar__2___24Anonymous__118391)
           => ( Vvar__2___24Anonymous__118391 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__118385)
              | ? [Vvar__2__a__118405] :
                  ( t(Vvar__2__a__118405,Vvar__0__A__118385)
                  & ? [Vvar__3__l__118406] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__118385,Vvar__3__l__118406)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__118385,happ(Vvar__1__R__118386,Vvar__2__a__118405),Vvar__3__l__118406)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__118385,Vvar__1__R__118386,Vvar__3__l__118406)
                      & Vvar__2___24Anonymous__118391 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__118385,Vvar__2__a__118405,Vvar__3__l__118406) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__88305,Vvar__1___24Anonymous__88306] :
      ( cType___24t(Vvar__0__A__88305)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__88305,Vvar__1___24Anonymous__88306)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__88305,Vvar__1___24Anonymous__88306)
         => ( Vvar__1___24Anonymous__88306 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__88305)
            | ? [Vvar__1__x__88310] :
                ( t(Vvar__1__x__88310,Vvar__0__A__88305)
                & ? [Vvar__2__l__88311] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__88305,Vvar__2__l__88311)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__88305,Vvar__1__x__88310,Vvar__2__l__88311)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__88305,Vvar__2__l__88311)
                    & Vvar__1___24Anonymous__88306 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__88305,Vvar__1__x__88310,Vvar__2__l__88311) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__98277,Vvar__1__eqA__98278,Vvar__2__x__98283,Vvar__3___24Anonymous__98284] :
      ( cType___24t(Vvar__0__A__98277)
     => ( c_24__type__98317___24t(Vvar__0__A__98277,Vvar__1__eqA__98278,Vvar__2__x__98283,Vvar__3___24Anonymous__98284,Vvar__1__eqA__98278)
       => ( t(Vvar__2__x__98283,Vvar__0__A__98277)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__98277,Vvar__3___24Anonymous__98284)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__98277,Vvar__1__eqA__98278,Vvar__2__x__98283,Vvar__3___24Anonymous__98284)
             => ( ? [Vvar__3__y__98293] :
                    ( t(Vvar__3__y__98293,Vvar__0__A__98277)
                    & ? [Vvar__4__l__98294] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__98277,Vvar__4__l__98294)
                        & p(happ(happ(Vvar__1__eqA__98278,Vvar__2__x__98283),Vvar__3__y__98293))
                        & Vvar__3___24Anonymous__98284 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__98277,Vvar__3__y__98293,Vvar__4__l__98294) ) )
                | ? [Vvar__3__y__98303] :
                    ( t(Vvar__3__y__98303,Vvar__0__A__98277)
                    & ? [Vvar__4__l__98304] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__98277,Vvar__4__l__98304)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__98277,Vvar__1__eqA__98278,Vvar__2__x__98283,Vvar__4__l__98304)
                        & Vvar__3___24Anonymous__98284 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__98277,Vvar__3__y__98303,Vvar__4__l__98304) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__98325,Vvar__1__eqA__98326,Vvar__2___24Anonymous__98331] :
      ( cType___24t(Vvar__0__A__98325)
     => ( c_24__type__98358___24t(Vvar__0__A__98325,Vvar__1__eqA__98326,Vvar__2___24Anonymous__98331,Vvar__1__eqA__98326)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__98325,Vvar__2___24Anonymous__98331)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__98325,Vvar__1__eqA__98326,Vvar__2___24Anonymous__98331)
           => ( Vvar__2___24Anonymous__98331 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__98325)
              | ? [Vvar__2__x__98345] :
                  ( t(Vvar__2__x__98345,Vvar__0__A__98325)
                  & ? [Vvar__3__l__98346] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__98325,Vvar__3__l__98346)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__98325,Vvar__1__eqA__98326,Vvar__2__x__98345,Vvar__3__l__98346)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__98325,Vvar__1__eqA__98326,Vvar__3__l__98346)
                      & Vvar__2___24Anonymous__98331 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__98325,Vvar__2__x__98345,Vvar__3__l__98346) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__117140,Vvar__1__P__117141,Vvar__2__p__117144,Vvar__3__x__117145,Vvar__4__q__117146,Vvar__5___24Anonymous__117147] :
      ( cType___24t(Vvar__0__U__117140)
     => ( c_24__type__117162___24t(Vvar__0__U__117140,Vvar__1__P__117141,Vvar__2__p__117144,Vvar__3__x__117145,Vvar__4__q__117146,Vvar__5___24Anonymous__117147,Vvar__1__P__117141)
       => ( t(Vvar__2__p__117144,Vvar__0__U__117140)
         => ( t(Vvar__3__x__117145,happ(Vvar__1__P__117141,Vvar__2__p__117144))
           => ( t(Vvar__4__q__117146,Vvar__0__U__117140)
             => ( t(Vvar__5___24Anonymous__117147,happ(Vvar__1__P__117141,Vvar__4__q__117146))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__117140,Vvar__1__P__117141,Vvar__2__p__117144,Vvar__3__x__117145,Vvar__4__q__117146,Vvar__5___24Anonymous__117147)
                 => ( Vvar__5___24Anonymous__117147 = Vvar__3__x__117145
                    & Vvar__4__q__117146 = Vvar__2__p__117144 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__112909,Vvar__1__P__112910,Vvar__2__p__112913,Vvar__3__x__112914,Vvar__4__q__112915,Vvar__5__y__112916] :
      ( cType___24t(Vvar__0__U__112909)
     => ( c_24__type__112935___24t(Vvar__0__U__112909,Vvar__1__P__112910,Vvar__2__p__112913,Vvar__3__x__112914,Vvar__4__q__112915,Vvar__5__y__112916,Vvar__1__P__112910)
       => ( t(Vvar__2__p__112913,Vvar__0__U__112909)
         => ( t(Vvar__3__x__112914,happ(Vvar__1__P__112910,Vvar__2__p__112913))
           => ( t(Vvar__4__q__112915,Vvar__0__U__112909)
             => ( t(Vvar__5__y__112916,happ(Vvar__1__P__112910,Vvar__4__q__112915))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__112909,Vvar__1__P__112910,Vvar__2__p__112913,Vvar__3__x__112914,Vvar__4__q__112915,Vvar__5__y__112916)
                 => ( Vvar__4__q__112915 = Vvar__2__p__112913
                    & Vvar__3__x__112914 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__112909,Vvar__4__q__112915,Vvar__1__P__112910,Vvar__5__y__112916,Vvar__2__p__112913)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX5156] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX5156)
     => ( VX5156 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__5157] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5157)
            & VX5156 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5157) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX4585] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX4585)
     => ( VX4585 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__4586] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4586)
            & VX4585 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4586) )
        | ? [Vvar__0___24Anonymous__4587] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4587)
            & VX4585 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4587) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX6] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX6)
     => ( ? [Vvar__0___24Anonymous__7] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7)
            & VX6 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7) )
        | ? [Vvar__0___24Anonymous__8] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8)
            & VX6 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__8) )
        | VX6 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__121083,VX121084] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__121083)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__121083,VX121084)
       => ( ( Vvar__0___24Anonymous__121083 = cCoq_2eNumbers_2eBinNums_2exH
            & VX121084 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__121085] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__121085)
              & ? [Vvar__1___24Anonymous__121086] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__121085,Vvar__1___24Anonymous__121086)
                  & Vvar__0___24Anonymous__121083 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121___24a2(Vvar__0___24Anonymous__121083,Vvar__0__p__121085)
                  & VX121084 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__121085,Vvar__1___24Anonymous__121086) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__116412,Vvar__1__q__116413,Vvar__2___24Anonymous__116414] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__116412)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__116413)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__116414)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__116412,Vvar__1__q__116413,Vvar__2___24Anonymous__116414)
           => ( ( Vvar__0__p__116412 = Vvar__1__q__116413
                & Vvar__2___24Anonymous__116414 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__116421] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__116421)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__116413,Vvar__2__r__116421) = Vvar__0__p__116412
                  & Vvar__2___24Anonymous__116414 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__116421) )
              | ? [Vvar__2__r__116425] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__116425)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__116412,Vvar__2__r__116425) = Vvar__1__q__116413
                  & Vvar__2___24Anonymous__116414 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX102377] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX102377)
     => ( VX102377 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__102378] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102378)
            & VX102377 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__102378) )
        | VX102377 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX104044] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX104044)
     => ? [Vvar__0__Qnum__104045] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__104045)
          & ? [Vvar__1__Qden__104046] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__104046)
              & VX104044 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104045,Vvar__1__Qden__104046) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX118624] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX118624)
     => ? [Vvar__0__nonzero__118625] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__118625)
          & Vvar__0__nonzero__118625 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX118624 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__118625) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__118663,Vvar__1___24Anonymous__118664,VX118665] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__118663)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__118664)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__118663,Vvar__1___24Anonymous__118664,VX118665)
         => ( ( Vvar__0__x__118663 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__118664 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX118665 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__118663) )
            | ? [Vvar__1__n__118669] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__118669)
                & Vvar__0__x__118663 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__118669)
                & Vvar__1___24Anonymous__118664 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24118689___24a3(Vvar__0__x__118663,Vvar__1___24Anonymous__118664,Vvar__1__n__118669)
                & VX118665 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__118663,Vvar__1__n__118669) )
            | ? [Vvar__1__n__118674] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__118674)
                & Vvar__0__x__118663 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__118674))
                & Vvar__1___24Anonymous__118664 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706___24a3(Vvar__0__x__118663,Vvar__1___24Anonymous__118664,Vvar__1__n__118674)
                & VX118665 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__118663,Vvar__1__n__118674) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
    ! [Vvar__0__A__118637,Vvar__1__R__118638] :
      ( cType___24t(Vvar__0__A__118637)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__118637,Vvar__1__R__118638)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__118637,Vvar__1__R__118638)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__118637,Vvar__1__R__118638)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__118637,Vvar__1__R__118638)
            & cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__118637,Vvar__1__R__118638)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__120706,Vvar__1__R__120707,Vvar__2__a__120712,Vvar__3___24Anonymous__120713] :
      ( cType___24t(Vvar__0__A__120706)
     => ( c_24__type__120743___24t(Vvar__0__A__120706,Vvar__1__R__120707,Vvar__2__a__120712,Vvar__3___24Anonymous__120713,Vvar__1__R__120707)
       => ( t(Vvar__2__a__120712,Vvar__0__A__120706)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120706,Vvar__3___24Anonymous__120713)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__120706,Vvar__1__R__120707,Vvar__2__a__120712,Vvar__3___24Anonymous__120713)
             => ( Vvar__3___24Anonymous__120713 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__120706)
                | ? [Vvar__3__b__120729] :
                    ( t(Vvar__3__b__120729,Vvar__0__A__120706)
                    & ? [Vvar__4__l__120730] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120706,Vvar__4__l__120730)
                        & p(happ(happ(Vvar__1__R__120707,Vvar__2__a__120712),Vvar__3__b__120729))
                        & Vvar__3___24Anonymous__120713 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120706,Vvar__3__b__120729,Vvar__4__l__120730) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__120745,Vvar__1__R__120746,Vvar__2___24Anonymous__120751] :
      ( cType___24t(Vvar__0__A__120745)
     => ( c_24__type__120778___24t(Vvar__0__A__120745,Vvar__1__R__120746,Vvar__2___24Anonymous__120751,Vvar__1__R__120746)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120745,Vvar__2___24Anonymous__120751)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__120745,Vvar__1__R__120746,Vvar__2___24Anonymous__120751)
           => ( Vvar__2___24Anonymous__120751 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__120745)
              | ? [Vvar__2__a__120765] :
                  ( t(Vvar__2__a__120765,Vvar__0__A__120745)
                  & ? [Vvar__3__l__120766] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120745,Vvar__3__l__120766)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__120745,Vvar__1__R__120746,Vvar__3__l__120766)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__120745,Vvar__1__R__120746,Vvar__2__a__120765,Vvar__3__l__120766)
                      & Vvar__2___24Anonymous__120751 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120745,Vvar__2__a__120765,Vvar__3__l__120766) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__120780,Vvar__1__R__120781,Vvar__2___24Anonymous__120786] :
      ( cType___24t(Vvar__0__A__120780)
     => ( c_24__type__120813___24t(Vvar__0__A__120780,Vvar__1__R__120781,Vvar__2___24Anonymous__120786,Vvar__1__R__120781)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120780,Vvar__2___24Anonymous__120786)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__120780,Vvar__1__R__120781,Vvar__2___24Anonymous__120786)
           => ( Vvar__2___24Anonymous__120786 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__120780)
              | ? [Vvar__2__a__120800] :
                  ( t(Vvar__2__a__120800,Vvar__0__A__120780)
                  & ? [Vvar__3__l__120801] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__120780,Vvar__3__l__120801)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__120780,Vvar__1__R__120781,Vvar__3__l__120801)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__120780,happ(Vvar__1__R__120781,Vvar__2__a__120800),Vvar__3__l__120801)
                      & Vvar__2___24Anonymous__120786 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__120780,Vvar__2__a__120800,Vvar__3__l__120801) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX11312] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX11312)
     => ? [Vvar__0___24Anonymous__11313] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__11313)
          & ? [Vvar__1___24Anonymous__11314] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__11314)
              & ? [Vvar__2___24Anonymous__11315] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__11315)
                  & ? [Vvar__3___24Anonymous__11316] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__11316)
                      & ? [Vvar__4___24Anonymous__11317] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__11317)
                          & ? [Vvar__5___24Anonymous__11318] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__11318)
                              & ? [Vvar__6___24Anonymous__11319] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__11319)
                                  & ? [Vvar__7___24Anonymous__11320] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__11320)
                                      & VX11312 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__11313,Vvar__1___24Anonymous__11314,Vvar__2___24Anonymous__11315,Vvar__3___24Anonymous__11316,Vvar__4___24Anonymous__11317,Vvar__5___24Anonymous__11318,Vvar__6___24Anonymous__11319,Vvar__7___24Anonymous__11320) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX98653] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX98653)
     => ( VX98653 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__98654] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__98654)
            & ? [Vvar__1___24Anonymous__98655] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__98655)
                & VX98653 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__98654,Vvar__1___24Anonymous__98655) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435,VX118436] :
      ( cType___24t(Vvar__0__X__118423)
     => ( c_24__type__118496___24t(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435,Vvar__1__lt__118424)
       => ( c_24__type__118515___24t(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435,Vvar__2__eq__118429)
         => ( t(Vvar__3__x__118434,Vvar__0__X__118423)
           => ( t(Vvar__4__y__118435,Vvar__0__X__118423)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435,VX118436)
               => ( ( p(happ(happ(Vvar__1__lt__118424,Vvar__3__x__118434),Vvar__4__y__118435))
                    & VX118436 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435) )
                  | ( p(happ(happ(Vvar__2__eq__118429,Vvar__3__x__118434),Vvar__4__y__118435))
                    & VX118436 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435) )
                  | ( p(happ(happ(Vvar__1__lt__118424,Vvar__4__y__118435),Vvar__3__x__118434))
                    & VX118436 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__118423,Vvar__1__lt__118424,Vvar__2__eq__118429,Vvar__3__x__118434,Vvar__4__y__118435) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__121165,Vvar__1___24Anonymous__121166] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__121165)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__121166)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__121165,Vvar__1___24Anonymous__121166)
         => ( ? [Vvar__0__a__121168] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__121168)
                & ? [Vvar__1__s__121169] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__121169)
                    & Vvar__1___24Anonymous__121166 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__121168,Vvar__1__s__121169)
                    & Vvar__0___24Anonymous__121165 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__121170] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__121170)
                & ? [Vvar__1__s1__121171] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__121171)
                    & ? [Vvar__2__s2__121172] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__121172)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__121171,Vvar__2__s2__121172)
                        & Vvar__1___24Anonymous__121166 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__121170,Vvar__2__s2__121172)
                        & Vvar__0___24Anonymous__121165 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__121170,Vvar__1__s1__121171) ) ) )
            | ? [Vvar__0__a__121174] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__121174)
                & ? [Vvar__1__b__121175] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__121175)
                    & ? [Vvar__2__s1__121176] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__121176)
                        & ? [Vvar__3__s2__121177] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__121177)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__121174),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__121175))
                            & Vvar__1___24Anonymous__121166 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__121175,Vvar__3__s2__121177)
                            & Vvar__0___24Anonymous__121165 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__121174,Vvar__2__s1__121176) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX117185] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX117185)
     => ( VX117185 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX117185 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX117185 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__112953,VX112954] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__112953)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__112953,VX112954)
       => ( ? [Vvar__0__n__112955] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__112955)
              & Vvar__0___24Anonymous__112953 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__112955)
              & VX112954 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__112955) )
          | ? [Vvar__0__n__112956] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__112956)
              & ? [Vvar__1___24Anonymous__112957] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__112956,Vvar__1___24Anonymous__112957)
                  & Vvar__0___24Anonymous__112953 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__112956)
                  & VX112954 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__112956,Vvar__1___24Anonymous__112957) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__100940,Vvar__1___24Anonymous__100941,VX100942] :
      ( cType___24t(Vvar__0__A__100940)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__100941)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__100940,Vvar__1___24Anonymous__100941,VX100942)
         => ( ( Vvar__1___24Anonymous__100941 = cCoq_2eInit_2eDatatypes_2eO
              & VX100942 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__100940) )
            | ? [Vvar__1__h__100945] :
                ( t(Vvar__1__h__100945,Vvar__0__A__100940)
                & ? [Vvar__2__n__100946] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__100946)
                    & ? [Vvar__3___24Anonymous__100947] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__100940,Vvar__2__n__100946,Vvar__3___24Anonymous__100947)
                        & Vvar__1___24Anonymous__100941 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__100946)
                        & VX100942 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__100940,Vvar__1__h__100945,Vvar__2__n__100946,Vvar__3___24Anonymous__100947) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__120894,Vvar__1__b__120895,Vvar__2__d__120896] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__120894)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__120895)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__120896)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__120894,Vvar__1__b__120895,Vvar__2__d__120896)
           => ? [Vvar__3__u__120901] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__120901)
                & ? [Vvar__4__v__120902] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__120902)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__120901,Vvar__0__a__120894),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__120902,Vvar__1__b__120895)) = Vvar__2__d__120896
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__120869,Vvar__1__b__120870,VX120871] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__120869)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__120870)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__120869,Vvar__1__b__120870,VX120871)
         => ? [Vvar__2__u__120874] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__120874)
              & ? [Vvar__3__v__120875] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__120875)
                  & ? [Vvar__4__d__120876] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__120876)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__120874,Vvar__0__a__120869),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__120875,Vvar__1__b__120870)) = Vvar__4__d__120876
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__120869,Vvar__1__b__120870,Vvar__4__d__120876)
                      & VX120871 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__120869,Vvar__1__b__120870,Vvar__2__u__120874,Vvar__3__v__120875,Vvar__4__d__120876) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__5125,Vvar__1__b__5126,Vvar__2__g__5127] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__5125)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__5126)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__5127)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__5125,Vvar__1__b__5126,Vvar__2__g__5127)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__5127,Vvar__0__a__5125)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__5127,Vvar__1__b__5126)
              & ! [Vvar__var__var__var__var__5__x__5135__5138__5141__5144__5147] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__5135__5138__5141__5144__5147)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__5135__5138__5141__5144__5147,Vvar__0__a__5125)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__5135__5138__5141__5144__5147,Vvar__1__b__5126)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__5135__5138__5141__5144__5147,Vvar__2__g__5127) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__120904] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__120904)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__120904)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__120904))
          & ! [Vvar__var__var__2__n__120909__120911__120913] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__120909__120911__120913)
             => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__120909__120911__120913))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__120909__120911__120913,Vvar__0__p__120904)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__120909__120911__120913,Vvar__0__p__120904) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__120917,Vvar__1__p__120918,VX120919] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__120917)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__120918)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__120917,Vvar__1__p__120918,VX120919)
         => ? [Vvar__2__q__120922] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__120922)
              & ? [Vvar__3__r__120923] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__120923)
                  & Vvar__0__x__120917 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__120922,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__120918)),Vvar__3__r__120923)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__120923))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__120923,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__120918)))
                  & VX120919 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__120917,Vvar__1__p__120918,Vvar__2__q__120922,Vvar__3__r__120923) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX83547] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX83547)
     => ( VX83547 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__83548] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83548)
            & ? [Vvar__1___24Anonymous__83549] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__83549)
                & VX83547 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__83548,Vvar__1___24Anonymous__83549) ) )
        | ? [Vvar__0___24Anonymous__83550] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83550)
            & ? [Vvar__1___24Anonymous__83551] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__83551)
                & VX83547 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__83550,Vvar__1___24Anonymous__83551) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__106273,VX106274] :
      ( cType___24t(Vvar__0__C__106273)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,VX106274)
       => ( ? [Vvar__1___24Anonymous__106276] :
              ( t(Vvar__1___24Anonymous__106276,Vvar__0__C__106273)
              & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__106273,Vvar__1___24Anonymous__106276) )
          | ? [Vvar__1___24Anonymous__106278] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__106278)
              & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__106273,Vvar__1___24Anonymous__106278) )
          | ? [Vvar__1___24Anonymous__106280] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__1___24Anonymous__106280)
              & ? [Vvar__2___24Anonymous__106281] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__2___24Anonymous__106281)
                  & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__106273,Vvar__1___24Anonymous__106280,Vvar__2___24Anonymous__106281) ) )
          | ? [Vvar__1___24Anonymous__106283] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__1___24Anonymous__106283)
              & ? [Vvar__2___24Anonymous__106284] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__2___24Anonymous__106284)
                  & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__106273,Vvar__1___24Anonymous__106283,Vvar__2___24Anonymous__106284) ) )
          | ? [Vvar__1___24Anonymous__106286] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__1___24Anonymous__106286)
              & ? [Vvar__2___24Anonymous__106287] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__2___24Anonymous__106287)
                  & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__106273,Vvar__1___24Anonymous__106286,Vvar__2___24Anonymous__106287) ) )
          | ? [Vvar__1___24Anonymous__106289] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__1___24Anonymous__106289)
              & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__106273,Vvar__1___24Anonymous__106289) )
          | ? [Vvar__1___24Anonymous__106291] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__106273,Vvar__1___24Anonymous__106291)
              & ? [Vvar__2___24Anonymous__106292] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__106292)
                  & VX106274 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__106273,Vvar__1___24Anonymous__106291,Vvar__2___24Anonymous__106292) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__4605,VX4606] :
      ( cType___24t(Vvar__0__C__4605)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4605,VX4606)
       => ( ? [Vvar__1___24Anonymous__4608] :
              ( t(Vvar__1___24Anonymous__4608,Vvar__0__C__4605)
              & VX4606 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4605,Vvar__1___24Anonymous__4608) )
          | ? [Vvar__1___24Anonymous__4610] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4610)
              & ? [Vvar__2___24Anonymous__4611] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4605,Vvar__2___24Anonymous__4611)
                  & VX4606 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4605,Vvar__1___24Anonymous__4610,Vvar__2___24Anonymous__4611) ) )
          | ? [Vvar__1___24Anonymous__4613] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4605,Vvar__1___24Anonymous__4613)
              & ? [Vvar__2___24Anonymous__4614] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__4614)
                  & ? [Vvar__3___24Anonymous__4615] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4605,Vvar__3___24Anonymous__4615)
                      & VX4606 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4605,Vvar__1___24Anonymous__4613,Vvar__2___24Anonymous__4614,Vvar__3___24Anonymous__4615) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014] :
      ( cType___24t(Vvar__0__R__88983)
     => ( t(Vvar__1__rO__88984,Vvar__0__R__88983)
       => ( t(Vvar__2__rI__88985,Vvar__0__R__88983)
         => ( c_24__type__89415___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__3__rplus__88986)
           => ( c_24__type__89516___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__4__rtimes__88991)
             => ( c_24__type__89617___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__5__rminus__88996)
               => ( c_24__type__89707___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__6__ropp__89001)
                 => ( c_24__type__89808___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__7__req__89004)
                   => ( c_24__type__89909___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__8__rle__89009)
                     => ( c_24__type__90010___24t(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014,Vvar__9__rlt__89014)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004,Vvar__8__rle__89009,Vvar__9__rlt__89014)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__88983,Vvar__7__req__89004)
                            & ! [Vvar__var__var__var__var__11__x1__89058__89064__89169__89175__89181] :
                                ( t(Vvar__var__var__var__var__11__x1__89058__89064__89169__89175__89181,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__12__x2__89059__89065__89170__89176__89182] :
                                    ( t(Vvar__var__var__var__var__12__x2__89059__89065__89170__89176__89182,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__11__x1__89058__89064__89169__89175__89181),Vvar__var__var__var__var__12__x2__89059__89065__89170__89176__89182))
                                     => ! [Vvar__var__var__var__var__14__y1__89060__89066__89171__89177__89183] :
                                          ( t(Vvar__var__var__var__var__14__y1__89060__89066__89171__89177__89183,Vvar__0__R__88983)
                                         => ! [Vvar__var__var__var__var__15__y2__89061__89067__89172__89178__89184] :
                                              ( t(Vvar__var__var__var__var__15__y2__89061__89067__89172__89178__89184,Vvar__0__R__88983)
                                             => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__14__y1__89060__89066__89171__89177__89183),Vvar__var__var__var__var__15__y2__89061__89067__89172__89178__89184))
                                               => p(happ(happ(Vvar__7__req__89004,happ(happ(Vvar__3__rplus__88986,Vvar__var__var__var__var__11__x1__89058__89064__89169__89175__89181),Vvar__var__var__var__var__14__y1__89060__89066__89171__89177__89183)),happ(happ(Vvar__3__rplus__88986,Vvar__var__var__var__var__12__x2__89059__89065__89170__89176__89182),Vvar__var__var__var__var__15__y2__89061__89067__89172__89178__89184))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__89071__89077__89187__89193__89199] :
                                ( t(Vvar__var__var__var__var__12__x1__89071__89077__89187__89193__89199,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__13__x2__89072__89078__89188__89194__89200] :
                                    ( t(Vvar__var__var__var__var__13__x2__89072__89078__89188__89194__89200,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__12__x1__89071__89077__89187__89193__89199),Vvar__var__var__var__var__13__x2__89072__89078__89188__89194__89200))
                                     => ! [Vvar__var__var__var__var__15__y1__89073__89079__89189__89195__89201] :
                                          ( t(Vvar__var__var__var__var__15__y1__89073__89079__89189__89195__89201,Vvar__0__R__88983)
                                         => ! [Vvar__var__var__var__var__16__y2__89074__89080__89190__89196__89202] :
                                              ( t(Vvar__var__var__var__var__16__y2__89074__89080__89190__89196__89202,Vvar__0__R__88983)
                                             => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__15__y1__89073__89079__89189__89195__89201),Vvar__var__var__var__var__16__y2__89074__89080__89190__89196__89202))
                                               => p(happ(happ(Vvar__7__req__89004,happ(happ(Vvar__4__rtimes__88991,Vvar__var__var__var__var__12__x1__89071__89077__89187__89193__89199),Vvar__var__var__var__var__15__y1__89073__89079__89189__89195__89201)),happ(happ(Vvar__4__rtimes__88991,Vvar__var__var__var__var__13__x2__89072__89078__89188__89194__89200),Vvar__var__var__var__var__16__y2__89074__89080__89190__89196__89202))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__89084__89087__89205__89208__89211] :
                                ( t(Vvar__var__var__var__var__13__x1__89084__89087__89205__89208__89211,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__14__x2__89085__89088__89206__89209__89212] :
                                    ( t(Vvar__var__var__var__var__14__x2__89085__89088__89206__89209__89212,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__13__x1__89084__89087__89205__89208__89211),Vvar__var__var__var__var__14__x2__89085__89088__89206__89209__89212))
                                     => p(happ(happ(Vvar__7__req__89004,happ(Vvar__6__ropp__89001,Vvar__var__var__var__var__13__x1__89084__89087__89205__89208__89211)),happ(Vvar__6__ropp__89001,Vvar__var__var__var__var__14__x2__89085__89088__89206__89209__89212))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__89091__89097__89214__89220__89226] :
                                ( t(Vvar__var__var__var__var__14__x1__89091__89097__89214__89220__89226,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__15__x2__89092__89098__89215__89221__89227] :
                                    ( t(Vvar__var__var__var__var__15__x2__89092__89098__89215__89221__89227,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__14__x1__89091__89097__89214__89220__89226),Vvar__var__var__var__var__15__x2__89092__89098__89215__89221__89227))
                                     => ! [Vvar__var__var__var__var__17__y1__89093__89099__89216__89222__89228] :
                                          ( t(Vvar__var__var__var__var__17__y1__89093__89099__89216__89222__89228,Vvar__0__R__88983)
                                         => ! [Vvar__var__var__var__var__18__y2__89094__89100__89217__89223__89229] :
                                              ( t(Vvar__var__var__var__var__18__y2__89094__89100__89217__89223__89229,Vvar__0__R__88983)
                                             => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__17__y1__89093__89099__89216__89222__89228),Vvar__var__var__var__var__18__y2__89094__89100__89217__89223__89229))
                                               => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__14__x1__89091__89097__89214__89220__89226),Vvar__var__var__var__var__17__y1__89093__89099__89216__89222__89228))
                                                <=> p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__15__x2__89092__89098__89215__89221__89227),Vvar__var__var__var__var__18__y2__89094__89100__89217__89223__89229)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__89104__89110__89232__89238__89244] :
                                ( t(Vvar__var__var__var__var__15__x1__89104__89110__89232__89238__89244,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__16__x2__89105__89111__89233__89239__89245] :
                                    ( t(Vvar__var__var__var__var__16__x2__89105__89111__89233__89239__89245,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__15__x1__89104__89110__89232__89238__89244),Vvar__var__var__var__var__16__x2__89105__89111__89233__89239__89245))
                                     => ! [Vvar__var__var__var__var__18__y1__89106__89112__89234__89240__89246] :
                                          ( t(Vvar__var__var__var__var__18__y1__89106__89112__89234__89240__89246,Vvar__0__R__88983)
                                         => ! [Vvar__var__var__var__var__19__y2__89107__89113__89235__89241__89247] :
                                              ( t(Vvar__var__var__var__var__19__y2__89107__89113__89235__89241__89247,Vvar__0__R__88983)
                                             => ( p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__18__y1__89106__89112__89234__89240__89246),Vvar__var__var__var__var__19__y2__89107__89113__89235__89241__89247))
                                               => ( p(happ(happ(Vvar__9__rlt__89014,Vvar__var__var__var__var__15__x1__89104__89110__89232__89238__89244),Vvar__var__var__var__var__18__y1__89106__89112__89234__89240__89246))
                                                <=> p(happ(happ(Vvar__9__rlt__89014,Vvar__var__var__var__var__16__x2__89105__89111__89233__89239__89245),Vvar__var__var__var__var__19__y2__89107__89113__89235__89241__89247)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__88983,Vvar__1__rO__88984,Vvar__2__rI__88985,Vvar__3__rplus__88986,Vvar__4__rtimes__88991,Vvar__5__rminus__88996,Vvar__6__ropp__89001,Vvar__7__req__89004)
                            & ! [Vvar__var__var__var__17__n__89118__89119__89250__89251] :
                                ( t(Vvar__var__var__var__17__n__89118__89119__89250__89251,Vvar__0__R__88983)
                               => p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__17__n__89118__89119__89250__89251),Vvar__var__var__var__17__n__89118__89119__89250__89251)) )
                            & ! [Vvar__var__var__var__var__18__n__89121__89125__89252__89256__89260] :
                                ( t(Vvar__var__var__var__var__18__n__89121__89125__89252__89256__89260,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__19__m__89122__89126__89253__89257__89261] :
                                    ( t(Vvar__var__var__var__var__19__m__89122__89126__89253__89257__89261,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__18__n__89121__89125__89252__89256__89260),Vvar__var__var__var__var__19__m__89122__89126__89253__89257__89261))
                                     => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__19__m__89122__89126__89253__89257__89261),Vvar__var__var__var__var__18__n__89121__89125__89252__89256__89260))
                                       => p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__18__n__89121__89125__89252__89256__89260),Vvar__var__var__var__var__19__m__89122__89126__89253__89257__89261)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__89130__89135__89264__89269] :
                                ( t(Vvar__var__var__var__19__n__89130__89135__89264__89269,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__20__m__89131__89136__89265__89270] :
                                    ( t(Vvar__var__var__var__20__m__89131__89136__89265__89270,Vvar__0__R__88983)
                                   => ! [Vvar__var__var__var__21__p__89132__89137__89266__89271] :
                                        ( t(Vvar__var__var__var__21__p__89132__89137__89266__89271,Vvar__0__R__88983)
                                       => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__19__n__89130__89135__89264__89269),Vvar__var__var__var__20__m__89131__89136__89265__89270))
                                         => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__20__m__89131__89136__89265__89270),Vvar__var__var__var__21__p__89132__89137__89266__89271))
                                           => p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__19__n__89130__89135__89264__89269),Vvar__var__var__var__21__p__89132__89137__89266__89271)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__89141__89143__89274__89276__89278__89280] :
                                ( t(Vvar__var__var__var__var__var__20__n__89141__89143__89274__89276__89278__89280,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__var__21__m__89142__89144__89275__89277__89279__89281] :
                                    ( t(Vvar__var__var__var__var__var__21__m__89142__89144__89275__89277__89279__89281,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__9__rlt__89014,Vvar__var__var__var__var__var__20__n__89141__89143__89274__89276__89278__89280),Vvar__var__var__var__var__var__21__m__89142__89144__89275__89277__89279__89281))
                                    <=> ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__var__20__n__89141__89143__89274__89276__89278__89280),Vvar__var__var__var__var__var__21__m__89142__89144__89275__89277__89279__89281))
                                        & ~ p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__var__20__n__89141__89143__89274__89276__89278__89280),Vvar__var__var__var__var__var__21__m__89142__89144__89275__89277__89279__89281)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__89146__89148__89282__89284__89286] :
                                ( t(Vvar__var__var__var__var__21__n__89146__89148__89282__89284__89286,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__22__m__89147__89149__89283__89285__89287] :
                                    ( t(Vvar__var__var__var__var__22__m__89147__89149__89283__89285__89287,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__9__rlt__89014,Vvar__var__var__var__var__21__n__89146__89148__89282__89284__89286),Vvar__var__var__var__var__22__m__89147__89149__89283__89285__89287))
                                      | p(happ(happ(Vvar__7__req__89004,Vvar__var__var__var__var__21__n__89146__89148__89282__89284__89286),Vvar__var__var__var__var__22__m__89147__89149__89283__89285__89287))
                                      | p(happ(happ(Vvar__9__rlt__89014,Vvar__var__var__var__var__22__m__89147__89149__89283__89285__89287),Vvar__var__var__var__var__21__n__89146__89148__89282__89284__89286)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__89151__89155__89288__89292__89296] :
                                ( t(Vvar__var__var__var__var__22__n__89151__89155__89288__89292__89296,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__23__m__89152__89156__89289__89293__89297] :
                                    ( t(Vvar__var__var__var__var__23__m__89152__89156__89289__89293__89297,Vvar__0__R__88983)
                                   => ! [Vvar__var__var__var__var__24__p__89153__89157__89290__89294__89298] :
                                        ( t(Vvar__var__var__var__var__24__p__89153__89157__89290__89294__89298,Vvar__0__R__88983)
                                       => ( p(happ(happ(Vvar__8__rle__89009,Vvar__var__var__var__var__22__n__89151__89155__89288__89292__89296),Vvar__var__var__var__var__23__m__89152__89156__89289__89293__89297))
                                         => p(happ(happ(Vvar__8__rle__89009,happ(happ(Vvar__3__rplus__88986,Vvar__var__var__var__var__24__p__89153__89157__89290__89294__89298),Vvar__var__var__var__var__22__n__89151__89155__89288__89292__89296)),happ(happ(Vvar__3__rplus__88986,Vvar__var__var__var__var__24__p__89153__89157__89290__89294__89298),Vvar__var__var__var__var__23__m__89152__89156__89289__89293__89297))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__89160__89164__89300__89304__89308__89312] :
                                ( t(Vvar__var__var__var__var__var__23__n__89160__89164__89300__89304__89308__89312,Vvar__0__R__88983)
                               => ! [Vvar__var__var__var__var__var__24__m__89161__89165__89301__89305__89309__89313] :
                                    ( t(Vvar__var__var__var__var__var__24__m__89161__89165__89301__89305__89309__89313,Vvar__0__R__88983)
                                   => ( p(happ(happ(Vvar__9__rlt__89014,Vvar__1__rO__88984),Vvar__var__var__var__var__var__23__n__89160__89164__89300__89304__89308__89312))
                                     => ( p(happ(happ(Vvar__9__rlt__89014,Vvar__1__rO__88984),Vvar__var__var__var__var__var__24__m__89161__89165__89301__89305__89309__89313))
                                       => p(happ(happ(Vvar__9__rlt__89014,Vvar__1__rO__88984),happ(happ(Vvar__4__rtimes__88991,Vvar__var__var__var__var__var__23__n__89160__89164__89300__89304__89308__89312),Vvar__var__var__var__var__var__24__m__89161__89165__89301__89305__89309__89313))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__89004,Vvar__1__rO__88984),Vvar__2__rI__88985))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__104084,VX104085] :
      ( cType___24t(Vvar__0__T__104084)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__104084,VX104085)
       => ? [Vvar__1__Flhs__104087] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__104084,Vvar__1__Flhs__104087)
            & ? [Vvar__2__Fop__104088] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__104088)
                & ? [Vvar__3__Frhs__104089] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__104084,Vvar__3__Frhs__104089)
                    & VX104085 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__104084,Vvar__1__Flhs__104087,Vvar__2__Fop__104088,Vvar__3__Frhs__104089) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX532] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX532)
     => ( VX532 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX532 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX532 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX532 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX118752] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX118752)
     => ( VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX118752 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741] :
      ( cType___24t(Vvar__0__R__90672)
     => ( t(Vvar__1__rO__90673,Vvar__0__R__90672)
       => ( t(Vvar__2__rI__90674,Vvar__0__R__90672)
         => ( c_24__type__91205___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__3__rplus__90675)
           => ( c_24__type__91551___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__4__rtimes__90680)
             => ( c_24__type__91897___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__5__rminus__90685)
               => ( c_24__type__92220___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__6__ropp__90690)
                 => ( c_24__type__92566___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__7__req__90693)
                   => ( c_24__type__92912___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__8__rle__90698)
                     => ( cType___24t(Vvar__9__C__90703)
                       => ( t(Vvar__10__cO__90704,Vvar__9__C__90703)
                         => ( t(Vvar__11__cI__90705,Vvar__9__C__90703)
                           => ( c_24__type__93258___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__12__cplus__90706)
                             => ( c_24__type__93604___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__13__ctimes__90711)
                               => ( c_24__type__93950___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__14__cminus__90716)
                                 => ( c_24__type__94273___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__15__copp__90721)
                                   => ( c_24__type__94619___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__16__ceqb__90724)
                                     => ( c_24__type__94965___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__17__cleb__90729)
                                       => ( c_24__type__95288___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__18__phi__90734)
                                         => ( cType___24t(Vvar__19__E__90737)
                                           => ( c_24__type__95611___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__20__pow__phi__90738)
                                             => ( c_24__type__95957___24t(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741,Vvar__21__rpow__90741)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__8__rle__90698,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__17__cleb__90729,Vvar__18__phi__90734,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__90672,Vvar__1__rO__90673,Vvar__2__rI__90674,Vvar__3__rplus__90675,Vvar__4__rtimes__90680,Vvar__5__rminus__90685,Vvar__6__ropp__90690,Vvar__7__req__90693,Vvar__9__C__90703,Vvar__10__cO__90704,Vvar__11__cI__90705,Vvar__12__cplus__90706,Vvar__13__ctimes__90711,Vvar__14__cminus__90716,Vvar__15__copp__90721,Vvar__16__ceqb__90724,Vvar__18__phi__90734)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__90672,Vvar__2__rI__90674,Vvar__4__rtimes__90680,Vvar__7__req__90693,Vvar__19__E__90737,Vvar__20__pow__phi__90738,Vvar__21__rpow__90741)
                                                    & ! [Vvar__var__var__var__var__var__24__x__90824__90827__90837__90840__90843__90846] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__90824__90827__90837__90840__90843__90846,Vvar__9__C__90703)
                                                       => ! [Vvar__var__var__var__var__var__25__y__90825__90828__90838__90841__90844__90847] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__90825__90828__90838__90841__90844__90847,Vvar__9__C__90703)
                                                           => ( happ(happ(Vvar__16__ceqb__90724,Vvar__var__var__var__var__var__24__x__90824__90827__90837__90840__90843__90846),Vvar__var__var__var__var__var__25__y__90825__90828__90838__90841__90844__90847) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__90693,happ(Vvar__18__phi__90734,Vvar__var__var__var__var__var__24__x__90824__90827__90837__90840__90843__90846)),happ(Vvar__18__phi__90734,Vvar__var__var__var__var__var__25__y__90825__90828__90838__90841__90844__90847))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__90831__90834__90849__90852__90855__90858] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__90831__90834__90849__90852__90855__90858,Vvar__9__C__90703)
                                                       => ! [Vvar__var__var__var__var__var__26__y__90832__90835__90850__90853__90856__90859] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__90832__90835__90850__90853__90856__90859,Vvar__9__C__90703)
                                                           => ( happ(happ(Vvar__17__cleb__90729,Vvar__var__var__var__var__var__25__x__90831__90834__90849__90852__90855__90858),Vvar__var__var__var__var__var__26__y__90832__90835__90850__90853__90856__90859) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__90698,happ(Vvar__18__phi__90734,Vvar__var__var__var__var__var__25__x__90831__90834__90849__90852__90855__90858)),happ(Vvar__18__phi__90734,Vvar__var__var__var__var__var__26__y__90832__90835__90850__90853__90856__90859))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,VX98778] :
      ( cType___24t(Vvar__0__TA__98774)
     => ( cType___24t(Vvar__1__TX__98775)
       => ( cType___24t(Vvar__2__AA__98776)
         => ( cType___24t(Vvar__3__AF__98777)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,VX98778)
             => ( VX98778 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777)
                | VX98778 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777)
                | ? [Vvar__4___24Anonymous__98791] :
                    ( t(Vvar__4___24Anonymous__98791,Vvar__1__TX__98775)
                    & VX98778 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98791) )
                | ? [Vvar__4___24Anonymous__98796] :
                    ( t(Vvar__4___24Anonymous__98796,Vvar__0__TA__98774)
                    & ? [Vvar__5___24Anonymous__98797] :
                        ( t(Vvar__5___24Anonymous__98797,Vvar__2__AA__98776)
                        & VX98778 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98796,Vvar__5___24Anonymous__98797) ) )
                | ? [Vvar__4___24Anonymous__98802] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98802)
                    & ? [Vvar__5___24Anonymous__98803] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__5___24Anonymous__98803)
                        & VX98778 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98802,Vvar__5___24Anonymous__98803) ) )
                | ? [Vvar__4___24Anonymous__98808] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98808)
                    & ? [Vvar__5___24Anonymous__98809] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__5___24Anonymous__98809)
                        & VX98778 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98808,Vvar__5___24Anonymous__98809) ) )
                | ? [Vvar__4___24Anonymous__98814] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98814)
                    & VX98778 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98814) )
                | ? [Vvar__4___24Anonymous__98819] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98819)
                    & ? [Vvar__5___24Anonymous__98820] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__98777,Vvar__5___24Anonymous__98820)
                        & ? [Vvar__6___24Anonymous__98821] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__6___24Anonymous__98821)
                            & VX98778 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__98774,Vvar__1__TX__98775,Vvar__2__AA__98776,Vvar__3__AF__98777,Vvar__4___24Anonymous__98819,Vvar__5___24Anonymous__98820,Vvar__6___24Anonymous__98821) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__117189] :
      ( cProp___24t(Vvar__0___24Anonymous__117189)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__117189)
       => ( ? [Vvar__0__S__117191] :
              ( cType___24t(Vvar__0__S__117191)
              & ? [Vvar__1__x__117192] :
                  ( t(Vvar__1__x__117192,Vvar__0__S__117191)
                  & ? [Vvar__2__y__117193] :
                      ( t(Vvar__2__y__117193,Vvar__0__S__117191)
                      & Vvar__0___24Anonymous__117189 = c_24__prop__117213___24a4(Vvar__0___24Anonymous__117189,Vvar__0__S__117191,Vvar__1__x__117192,Vvar__2__y__117193) ) ) )
          | ? [Vvar__0__x__117194] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__117194)
              & ? [Vvar__1__y__117195] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__117195)
                  & Vvar__0___24Anonymous__117189 = c_24__prop__117214___24a3(Vvar__0___24Anonymous__117189,Vvar__0__x__117194,Vvar__1__y__117195) ) )
          | ? [Vvar__0__x__117196] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__117196)
              & ? [Vvar__1__s__117197] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__117197)
                  & Vvar__0___24Anonymous__117189 = c_24__prop__117215___24a3(Vvar__0___24Anonymous__117189,Vvar__0__x__117196,Vvar__1__s__117197) ) )
          | Vvar__0___24Anonymous__117189 = c_24True
          | Vvar__0___24Anonymous__117189 = c_24False
          | ? [Vvar__0__P__117198] :
              ( cProp___24t(Vvar__0__P__117198)
              & ? [Vvar__1__Q__117199] :
                  ( cProp___24t(Vvar__1__Q__117199)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__117198)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__117199)
                  & Vvar__0___24Anonymous__117189 = c_24__prop__117216___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117198,Vvar__1__Q__117199) ) )
          | ? [Vvar__0__P__117202] :
              ( cProp___24t(Vvar__0__P__117202)
              & ? [Vvar__1__Q__117203] :
                  ( cProp___24t(Vvar__1__Q__117203)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__117202)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__117203)
                  & Vvar__0___24Anonymous__117189 = c_24__prop__117217___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117202,Vvar__1__Q__117203) ) )
          | ? [Vvar__0__P__117206] :
              ( cProp___24t(Vvar__0__P__117206)
              & ? [Vvar__1__Q__117207] :
                  ( cProp___24t(Vvar__1__Q__117207)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__117206)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__117207)
                  & Vvar__0___24Anonymous__117189 = c_24__prop__117218___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117206,Vvar__1__Q__117207) ) )
          | ? [Vvar__0__P__117211] :
              ( cProp___24t(Vvar__0__P__117211)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__117211)
              & Vvar__0___24Anonymous__117189 = c_24__prop__117219___24a2(Vvar__0___24Anonymous__117189,Vvar__0__P__117211) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__120815,Vvar__1__env__120816,Vvar__2__env_27__120819,Vvar__3__x__120822] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__120815)
     => ( c_24__type__120843___24t(Vvar__0__fr__120815,Vvar__1__env__120816,Vvar__2__env_27__120819,Vvar__3__x__120822,Vvar__1__env__120816)
       => ( c_24__type__120852___24t(Vvar__0__fr__120815,Vvar__1__env__120816,Vvar__2__env_27__120819,Vvar__3__x__120822,Vvar__2__env_27__120819)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__120822)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__120815,Vvar__1__env__120816,Vvar__2__env_27__120819,Vvar__3__x__120822)
             => ( happ(Vvar__1__env__120816,Vvar__3__x__120822) = happ(Vvar__2__env_27__120819,Vvar__3__x__120822)
                & happ(Vvar__1__env__120816,Vvar__3__x__120822) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__120819,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__120815,Vvar__3__x__120822))),happ(Vvar__2__env_27__120819,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__120815,Vvar__3__x__120822))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__120819,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__120815,Vvar__3__x__120822))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__120819,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__120815,Vvar__3__x__120822))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__102797,VX102798] :
      ( cType___24t(Vvar__0__C__102797)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,VX102798)
       => ( VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__102797)
          | VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__102797)
          | ? [Vvar__1___24Anonymous__102802] :
              ( t(Vvar__1___24Anonymous__102802,Vvar__0__C__102797)
              & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__102797,Vvar__1___24Anonymous__102802) )
          | ? [Vvar__1___24Anonymous__102804] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__102804)
              & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__102797,Vvar__1___24Anonymous__102804) )
          | ? [Vvar__1___24Anonymous__102806] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102806)
              & ? [Vvar__2___24Anonymous__102807] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__2___24Anonymous__102807)
                  & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__102797,Vvar__1___24Anonymous__102806,Vvar__2___24Anonymous__102807) ) )
          | ? [Vvar__1___24Anonymous__102809] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102809)
              & ? [Vvar__2___24Anonymous__102810] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__2___24Anonymous__102810)
                  & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__102797,Vvar__1___24Anonymous__102809,Vvar__2___24Anonymous__102810) ) )
          | ? [Vvar__1___24Anonymous__102812] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102812)
              & ? [Vvar__2___24Anonymous__102813] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__2___24Anonymous__102813)
                  & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__102797,Vvar__1___24Anonymous__102812,Vvar__2___24Anonymous__102813) ) )
          | ? [Vvar__1___24Anonymous__102815] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102815)
              & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__102797,Vvar__1___24Anonymous__102815) )
          | ? [Vvar__1___24Anonymous__102817] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102817)
              & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__102797,Vvar__1___24Anonymous__102817) )
          | ? [Vvar__1___24Anonymous__102819] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102819)
              & ? [Vvar__2___24Anonymous__102820] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__2___24Anonymous__102820)
                  & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__102797,Vvar__1___24Anonymous__102819,Vvar__2___24Anonymous__102820) ) )
          | ? [Vvar__1___24Anonymous__102822] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__102797,Vvar__1___24Anonymous__102822)
              & ? [Vvar__2___24Anonymous__102823] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__102823)
                  & VX102798 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__102797,Vvar__1___24Anonymous__102822,Vvar__2___24Anonymous__102823) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116] :
      ( cType___24t(Vvar__0__R__85087)
     => ( t(Vvar__1__rO__85088,Vvar__0__R__85087)
       => ( t(Vvar__2__rI__85089,Vvar__0__R__85087)
         => ( c_24__type__85281___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__3__radd__85090)
           => ( c_24__type__85374___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__4__rmul__85095)
             => ( c_24__type__85467___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__5__rsub__85100)
               => ( c_24__type__85549___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__6__ropp__85105)
                 => ( c_24__type__85642___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__7__rdiv__85108)
                   => ( c_24__type__85724___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__8__rinv__85113)
                     => ( c_24__type__85817___24t(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116,Vvar__9__req__85116)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__7__rdiv__85108,Vvar__8__rinv__85113,Vvar__9__req__85116)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__85087,Vvar__1__rO__85088,Vvar__2__rI__85089,Vvar__3__radd__85090,Vvar__4__rmul__85095,Vvar__5__rsub__85100,Vvar__6__ropp__85105,Vvar__9__req__85116)
                            & ~ p(happ(happ(Vvar__9__req__85116,Vvar__2__rI__85089),Vvar__1__rO__85088))
                            & ! [Vvar__var__var__var__var__var__var__12__p__85159__85161__85168__85170__85172__85174__85176] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__85159__85161__85168__85170__85172__85174__85176,Vvar__0__R__85087)
                               => ! [Vvar__var__var__var__var__var__var__13__q__85160__85162__85169__85171__85173__85175__85177] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__85160__85162__85169__85171__85173__85175__85177,Vvar__0__R__85087)
                                   => p(happ(happ(Vvar__9__req__85116,happ(happ(Vvar__7__rdiv__85108,Vvar__var__var__var__var__var__var__12__p__85159__85161__85168__85170__85172__85174__85176),Vvar__var__var__var__var__var__var__13__q__85160__85162__85169__85171__85173__85175__85177)),happ(happ(Vvar__4__rmul__85095,Vvar__var__var__var__var__var__var__12__p__85159__85161__85168__85170__85172__85174__85176),happ(Vvar__8__rinv__85113,Vvar__var__var__var__var__var__var__13__q__85160__85162__85169__85171__85173__85175__85177)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__85164__85166__85178__85180__85182__85184__85186__85188] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__85164__85166__85178__85180__85182__85184__85186__85188,Vvar__0__R__85087)
                               => ( ~ p(happ(happ(Vvar__9__req__85116,Vvar__var__var__var__var__var__var__var__13__p__85164__85166__85178__85180__85182__85184__85186__85188),Vvar__1__rO__85088))
                                 => p(happ(happ(Vvar__9__req__85116,happ(happ(Vvar__4__rmul__85095,happ(Vvar__8__rinv__85113,Vvar__var__var__var__var__var__var__var__13__p__85164__85166__85178__85180__85182__85184__85186__85188)),Vvar__var__var__var__var__var__var__var__13__p__85164__85166__85178__85180__85182__85184__85186__85188)),Vvar__2__rI__85089)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472] :
      ( cType___24t(Vvar__0__R__117443)
     => ( t(Vvar__1__rO__117444,Vvar__0__R__117443)
       => ( t(Vvar__2__rI__117445,Vvar__0__R__117443)
         => ( c_24__type__117637___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__3__radd__117446)
           => ( c_24__type__117730___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__4__rmul__117451)
             => ( c_24__type__117823___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__5__rsub__117456)
               => ( c_24__type__117905___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__6__ropp__117461)
                 => ( c_24__type__117998___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__7__rdiv__117464)
                   => ( c_24__type__118080___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__8__rinv__117469)
                     => ( c_24__type__118173___24t(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472,Vvar__9__req__117472)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__7__rdiv__117464,Vvar__8__rinv__117469,Vvar__9__req__117472)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__117443,Vvar__1__rO__117444,Vvar__2__rI__117445,Vvar__3__radd__117446,Vvar__4__rmul__117451,Vvar__5__rsub__117456,Vvar__6__ropp__117461,Vvar__9__req__117472)
                            & ~ p(happ(happ(Vvar__9__req__117472,Vvar__2__rI__117445),Vvar__1__rO__117444))
                            & ! [Vvar__var__var__var__var__var__var__12__p__117515__117517__117524__117526__117528__117530__117532] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__117515__117517__117524__117526__117528__117530__117532,Vvar__0__R__117443)
                               => ! [Vvar__var__var__var__var__var__var__13__q__117516__117518__117525__117527__117529__117531__117533] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__117516__117518__117525__117527__117529__117531__117533,Vvar__0__R__117443)
                                   => p(happ(happ(Vvar__9__req__117472,happ(happ(Vvar__7__rdiv__117464,Vvar__var__var__var__var__var__var__12__p__117515__117517__117524__117526__117528__117530__117532),Vvar__var__var__var__var__var__var__13__q__117516__117518__117525__117527__117529__117531__117533)),happ(happ(Vvar__4__rmul__117451,Vvar__var__var__var__var__var__var__12__p__117515__117517__117524__117526__117528__117530__117532),happ(Vvar__8__rinv__117469,Vvar__var__var__var__var__var__var__13__q__117516__117518__117525__117527__117529__117531__117533)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__117520__117522__117534__117536__117538__117540__117542__117544] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__117520__117522__117534__117536__117538__117540__117542__117544,Vvar__0__R__117443)
                               => ( ~ p(happ(happ(Vvar__9__req__117472,Vvar__var__var__var__var__var__var__var__13__p__117520__117522__117534__117536__117538__117540__117542__117544),Vvar__1__rO__117444))
                                 => p(happ(happ(Vvar__9__req__117472,happ(happ(Vvar__4__rmul__117451,happ(Vvar__8__rinv__117469,Vvar__var__var__var__var__var__var__var__13__p__117520__117522__117534__117536__117538__117540__117542__117544)),Vvar__var__var__var__var__var__var__var__13__p__117520__117522__117534__117536__117538__117540__117542__117544)),Vvar__2__rI__117445)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__103409,VX103410] :
      ( cType___24t(Vvar__0__C__103409)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__103409,VX103410)
       => ? [Vvar__1__num__103412] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__103409,Vvar__1__num__103412)
            & ? [Vvar__2__denum__103413] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__103409,Vvar__2__denum__103413)
                & ? [Vvar__3__condition__103414] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__103409),Vvar__3__condition__103414)
                    & VX103410 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__103409,Vvar__1__num__103412,Vvar__2__denum__103413,Vvar__3__condition__103414) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__87299,VX87300] :
      ( cType___24t(Vvar__0__C__87299)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__87299,VX87300)
       => ? [Vvar__1__rsplit__left__87302] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__87299,Vvar__1__rsplit__left__87302)
            & ? [Vvar__2__rsplit__common__87303] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__87299,Vvar__2__rsplit__common__87303)
                & ? [Vvar__3__rsplit__right__87304] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__87299,Vvar__3__rsplit__right__87304)
                    & VX87300 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__87299,Vvar__1__rsplit__left__87302,Vvar__2__rsplit__common__87303,Vvar__3__rsplit__right__87304) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX391] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX391)
     => ( VX391 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__392] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__392)
            & ? [Vvar__1___24Anonymous__393] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__393)
                & VX391 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__392,Vvar__1___24Anonymous__393) ) )
        | ? [Vvar__0___24Anonymous__394] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__394)
            & ? [Vvar__1___24Anonymous__395] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__395)
                & VX391 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__394,Vvar__1___24Anonymous__395) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__10501,VX10502] :
      ( cType___24t(Vvar__0__C__10501)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,VX10502)
       => ( VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10501)
          | VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10501)
          | ? [Vvar__1___24Anonymous__10506] :
              ( t(Vvar__1___24Anonymous__10506,Vvar__0__C__10501)
              & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10501,Vvar__1___24Anonymous__10506) )
          | ? [Vvar__1___24Anonymous__10508] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10508)
              & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10501,Vvar__1___24Anonymous__10508) )
          | ? [Vvar__1___24Anonymous__10510] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__1___24Anonymous__10510)
              & ? [Vvar__2___24Anonymous__10511] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__2___24Anonymous__10511)
                  & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10501,Vvar__1___24Anonymous__10510,Vvar__2___24Anonymous__10511) ) )
          | ? [Vvar__1___24Anonymous__10513] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__1___24Anonymous__10513)
              & ? [Vvar__2___24Anonymous__10514] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__2___24Anonymous__10514)
                  & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10501,Vvar__1___24Anonymous__10513,Vvar__2___24Anonymous__10514) ) )
          | ? [Vvar__1___24Anonymous__10516] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__1___24Anonymous__10516)
              & ? [Vvar__2___24Anonymous__10517] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__2___24Anonymous__10517)
                  & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10501,Vvar__1___24Anonymous__10516,Vvar__2___24Anonymous__10517) ) )
          | ? [Vvar__1___24Anonymous__10519] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__1___24Anonymous__10519)
              & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10501,Vvar__1___24Anonymous__10519) )
          | ? [Vvar__1___24Anonymous__10521] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10501,Vvar__1___24Anonymous__10521)
              & ? [Vvar__2___24Anonymous__10522] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10522)
                  & VX10502 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10501,Vvar__1___24Anonymous__10521,Vvar__2___24Anonymous__10522) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__181,VX182] :
      ( cType___24t(Vvar__0__C__181)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__181,VX182)
       => ( ? [Vvar__1___24Anonymous__184] :
              ( t(Vvar__1___24Anonymous__184,Vvar__0__C__181)
              & VX182 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__181,Vvar__1___24Anonymous__184) )
          | ? [Vvar__1___24Anonymous__186] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__186)
              & ? [Vvar__2___24Anonymous__187] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__181,Vvar__2___24Anonymous__187)
                  & VX182 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__181,Vvar__1___24Anonymous__186,Vvar__2___24Anonymous__187) ) )
          | ? [Vvar__1___24Anonymous__189] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__181,Vvar__1___24Anonymous__189)
              & ? [Vvar__2___24Anonymous__190] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__190)
                  & ? [Vvar__3___24Anonymous__191] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__181,Vvar__3___24Anonymous__191)
                      & VX182 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__181,Vvar__1___24Anonymous__189,Vvar__2___24Anonymous__190,Vvar__3___24Anonymous__191) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196] :
      ( cType___24t(Vvar__0__R__1175)
     => ( t(Vvar__1__rO__1176,Vvar__0__R__1175)
       => ( t(Vvar__2__rI__1177,Vvar__0__R__1175)
         => ( c_24__type__1424___24t(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196,Vvar__3__radd__1178)
           => ( c_24__type__1487___24t(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196,Vvar__4__rmul__1183)
             => ( c_24__type__1550___24t(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196,Vvar__5__rsub__1188)
               => ( c_24__type__1604___24t(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196,Vvar__6__ropp__1193)
                 => ( c_24__type__1667___24t(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196,Vvar__7__req__1196)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__1175,Vvar__1__rO__1176,Vvar__2__rI__1177,Vvar__3__radd__1178,Vvar__4__rmul__1183,Vvar__5__rsub__1188,Vvar__6__ropp__1193,Vvar__7__req__1196)
                     => ( ! [Vvar__var__var__var__var__var__8__x__1229__1230__1283__1284__1285__1286] :
                            ( t(Vvar__var__var__var__var__var__8__x__1229__1230__1283__1284__1285__1286,Vvar__0__R__1175)
                           => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__3__radd__1178,Vvar__1__rO__1176),Vvar__var__var__var__var__var__8__x__1229__1230__1283__1284__1285__1286)),Vvar__var__var__var__var__var__8__x__1229__1230__1283__1284__1285__1286)) )
                        & ! [Vvar__var__var__var__var__9__x__1232__1234__1287__1289__1291] :
                            ( t(Vvar__var__var__var__var__9__x__1232__1234__1287__1289__1291,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__10__y__1233__1235__1288__1290__1292] :
                                ( t(Vvar__var__var__var__var__10__y__1233__1235__1288__1290__1292,Vvar__0__R__1175)
                               => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__9__x__1232__1234__1287__1289__1291),Vvar__var__var__var__var__10__y__1233__1235__1288__1290__1292)),happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__10__y__1233__1235__1288__1290__1292),Vvar__var__var__var__var__9__x__1232__1234__1287__1289__1291))) ) )
                        & ! [Vvar__var__var__var__var__10__x__1237__1240__1293__1296__1299] :
                            ( t(Vvar__var__var__var__var__10__x__1237__1240__1293__1296__1299,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__11__y__1238__1241__1294__1297__1300] :
                                ( t(Vvar__var__var__var__var__11__y__1238__1241__1294__1297__1300,Vvar__0__R__1175)
                               => ! [Vvar__var__var__var__var__12__z__1239__1242__1295__1298__1301] :
                                    ( t(Vvar__var__var__var__var__12__z__1239__1242__1295__1298__1301,Vvar__0__R__1175)
                                   => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__10__x__1237__1240__1293__1296__1299),happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__11__y__1238__1241__1294__1297__1300),Vvar__var__var__var__var__12__z__1239__1242__1295__1298__1301))),happ(happ(Vvar__3__radd__1178,happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__10__x__1237__1240__1293__1296__1299),Vvar__var__var__var__var__11__y__1238__1241__1294__1297__1300)),Vvar__var__var__var__var__12__z__1239__1242__1295__1298__1301))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__1244__1245__1302__1303__1304__1305] :
                            ( t(Vvar__var__var__var__var__var__11__x__1244__1245__1302__1303__1304__1305,Vvar__0__R__1175)
                           => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__4__rmul__1183,Vvar__2__rI__1177),Vvar__var__var__var__var__var__11__x__1244__1245__1302__1303__1304__1305)),Vvar__var__var__var__var__var__11__x__1244__1245__1302__1303__1304__1305)) )
                        & ! [Vvar__var__var__var__var__var__12__x__1247__1248__1306__1307__1308__1309] :
                            ( t(Vvar__var__var__var__var__var__12__x__1247__1248__1306__1307__1308__1309,Vvar__0__R__1175)
                           => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__4__rmul__1183,Vvar__1__rO__1176),Vvar__var__var__var__var__var__12__x__1247__1248__1306__1307__1308__1309)),Vvar__1__rO__1176)) )
                        & ! [Vvar__var__var__var__var__13__x__1250__1252__1310__1312__1314] :
                            ( t(Vvar__var__var__var__var__13__x__1250__1252__1310__1312__1314,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__14__y__1251__1253__1311__1313__1315] :
                                ( t(Vvar__var__var__var__var__14__y__1251__1253__1311__1313__1315,Vvar__0__R__1175)
                               => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__13__x__1250__1252__1310__1312__1314),Vvar__var__var__var__var__14__y__1251__1253__1311__1313__1315)),happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__14__y__1251__1253__1311__1313__1315),Vvar__var__var__var__var__13__x__1250__1252__1310__1312__1314))) ) )
                        & ! [Vvar__var__var__var__var__14__x__1255__1258__1316__1319__1322] :
                            ( t(Vvar__var__var__var__var__14__x__1255__1258__1316__1319__1322,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__15__y__1256__1259__1317__1320__1323] :
                                ( t(Vvar__var__var__var__var__15__y__1256__1259__1317__1320__1323,Vvar__0__R__1175)
                               => ! [Vvar__var__var__var__var__16__z__1257__1260__1318__1321__1324] :
                                    ( t(Vvar__var__var__var__var__16__z__1257__1260__1318__1321__1324,Vvar__0__R__1175)
                                   => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__14__x__1255__1258__1316__1319__1322),happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__15__y__1256__1259__1317__1320__1323),Vvar__var__var__var__var__16__z__1257__1260__1318__1321__1324))),happ(happ(Vvar__4__rmul__1183,happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__14__x__1255__1258__1316__1319__1322),Vvar__var__var__var__var__15__y__1256__1259__1317__1320__1323)),Vvar__var__var__var__var__16__z__1257__1260__1318__1321__1324))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__1262__1265__1325__1328__1331__1334] :
                            ( t(Vvar__var__var__var__var__var__15__x__1262__1265__1325__1328__1331__1334,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__var__16__y__1263__1266__1326__1329__1332__1335] :
                                ( t(Vvar__var__var__var__var__var__16__y__1263__1266__1326__1329__1332__1335,Vvar__0__R__1175)
                               => ! [Vvar__var__var__var__var__var__17__z__1264__1267__1327__1330__1333__1336] :
                                    ( t(Vvar__var__var__var__var__var__17__z__1264__1267__1327__1330__1333__1336,Vvar__0__R__1175)
                                   => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__4__rmul__1183,happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__var__15__x__1262__1265__1325__1328__1331__1334),Vvar__var__var__var__var__var__16__y__1263__1266__1326__1329__1332__1335)),Vvar__var__var__var__var__var__17__z__1264__1267__1327__1330__1333__1336)),happ(happ(Vvar__3__radd__1178,happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__var__15__x__1262__1265__1325__1328__1331__1334),Vvar__var__var__var__var__var__17__z__1264__1267__1327__1330__1333__1336)),happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__var__16__y__1263__1266__1326__1329__1332__1335),Vvar__var__var__var__var__var__17__z__1264__1267__1327__1330__1333__1336)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__1269__1271__1337__1339__1341__1343] :
                            ( t(Vvar__var__var__var__var__var__16__x__1269__1271__1337__1339__1341__1343,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__var__17__y__1270__1272__1338__1340__1342__1344] :
                                ( t(Vvar__var__var__var__var__var__17__y__1270__1272__1338__1340__1342__1344,Vvar__0__R__1175)
                               => p(happ(happ(Vvar__7__req__1196,happ(Vvar__6__ropp__1193,happ(happ(Vvar__4__rmul__1183,Vvar__var__var__var__var__var__16__x__1269__1271__1337__1339__1341__1343),Vvar__var__var__var__var__var__17__y__1270__1272__1338__1340__1342__1344))),happ(happ(Vvar__4__rmul__1183,happ(Vvar__6__ropp__1193,Vvar__var__var__var__var__var__16__x__1269__1271__1337__1339__1341__1343)),Vvar__var__var__var__var__var__17__y__1270__1272__1338__1340__1342__1344))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__1274__1276__1345__1347__1349__1351] :
                            ( t(Vvar__var__var__var__var__var__17__x__1274__1276__1345__1347__1349__1351,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__var__18__y__1275__1277__1346__1348__1350__1352] :
                                ( t(Vvar__var__var__var__var__var__18__y__1275__1277__1346__1348__1350__1352,Vvar__0__R__1175)
                               => p(happ(happ(Vvar__7__req__1196,happ(Vvar__6__ropp__1193,happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__var__17__x__1274__1276__1345__1347__1349__1351),Vvar__var__var__var__var__var__18__y__1275__1277__1346__1348__1350__1352))),happ(happ(Vvar__3__radd__1178,happ(Vvar__6__ropp__1193,Vvar__var__var__var__var__var__17__x__1274__1276__1345__1347__1349__1351)),happ(Vvar__6__ropp__1193,Vvar__var__var__var__var__var__18__y__1275__1277__1346__1348__1350__1352)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__1279__1281__1353__1355__1357__1359__1361] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__1279__1281__1353__1355__1357__1359__1361,Vvar__0__R__1175)
                           => ! [Vvar__var__var__var__var__var__var__19__y__1280__1282__1354__1356__1358__1360__1362] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__1280__1282__1354__1356__1358__1360__1362,Vvar__0__R__1175)
                               => p(happ(happ(Vvar__7__req__1196,happ(happ(Vvar__5__rsub__1188,Vvar__var__var__var__var__var__var__18__x__1279__1281__1353__1355__1357__1359__1361),Vvar__var__var__var__var__var__var__19__y__1280__1282__1354__1356__1358__1360__1362)),happ(happ(Vvar__3__radd__1178,Vvar__var__var__var__var__var__var__18__x__1279__1281__1353__1355__1357__1359__1361),happ(Vvar__6__ropp__1193,Vvar__var__var__var__var__var__var__19__y__1280__1282__1354__1356__1358__1360__1362)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746] :
      ( cType___24t(Vvar__0__R__10726)
     => ( c_24__type__10866___24t(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__1__req__10727)
       => ( cType___24t(Vvar__2__C__10732)
         => ( c_24__type__10916___24t(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__3__cadd__10733)
           => ( c_24__type__10966___24t(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__4__cmul__10738)
             => ( c_24__type__11008___24t(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__5__phi__10743)
               => ( c_24__type__11058___24t(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__6__cdiv__10746)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__10778__10783__10788__10793__10798__10803__10808__10813] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__10778__10783__10788__10793__10798__10803__10808__10813,Vvar__2__C__10732)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__10779__10784__10789__10794__10799__10804__10809__10814] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__10779__10784__10789__10794__10799__10804__10809__10814,Vvar__2__C__10732)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411121___24a9(Vvar__0__R__10726,Vvar__1__req__10727,Vvar__2__C__10732,Vvar__3__cadd__10733,Vvar__4__cmul__10738,Vvar__5__phi__10743,Vvar__6__cdiv__10746,Vvar__var__var__var__var__var__var__var__7__a__10778__10783__10788__10793__10798__10803__10808__10813,Vvar__var__var__var__var__var__var__var__8__b__10779__10784__10789__10794__10799__10804__10809__10814) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033] :
      ( cType___24t(Vvar__0__R__98017)
     => ( t(Vvar__1__rI__98018,Vvar__0__R__98017)
       => ( c_24__type__98119___24t(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033,Vvar__2__rmul__98019)
         => ( c_24__type__98163___24t(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033,Vvar__3__req__98024)
           => ( cType___24t(Vvar__4__Cpow__98029)
             => ( c_24__type__98199___24t(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033,Vvar__5__Cp__phi__98030)
               => ( c_24__type__98243___24t(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033,Vvar__6__rpow__98033)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__3__req__98024,Vvar__4__Cpow__98029,Vvar__5__Cp__phi__98030,Vvar__6__rpow__98033)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__98061__98063__98065__98067__98069__98071__98073__98075] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__98061__98063__98065__98067__98069__98071__98073__98075,Vvar__0__R__98017)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__98062__98064__98066__98068__98070__98072__98074__98076] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__98062__98064__98066__98068__98070__98072__98074__98076)
                             => p(happ(happ(Vvar__3__req__98024,happ(happ(Vvar__6__rpow__98033,Vvar__var__var__var__var__var__var__var__7__r__98061__98063__98065__98067__98069__98071__98073__98075),happ(Vvar__5__Cp__phi__98030,Vvar__var__var__var__var__var__var__var__8__n__98062__98064__98066__98068__98070__98072__98074__98076))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__98017,Vvar__1__rI__98018,Vvar__2__rmul__98019,Vvar__var__var__var__var__var__var__var__7__r__98061__98063__98065__98067__98069__98071__98073__98075,Vvar__var__var__var__var__var__var__var__8__n__98062__98064__98066__98068__98070__98072__98074__98076))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718] :
      ( cType___24t(Vvar__0__R__1704)
     => ( c_24__type__1809___24t(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718,Vvar__1__radd__1705)
       => ( c_24__type__1839___24t(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718,Vvar__2__rmul__1710)
         => ( c_24__type__1863___24t(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718,Vvar__3__ropp__1715)
           => ( c_24__type__1893___24t(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718,Vvar__4__req__1718)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1923___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1704,c_24__type__1947___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718),Vvar__4__req__1718,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1704,Vvar__0__R__1704,Vvar__4__req__1718,Vvar__4__req__1718)),Vvar__1__radd__1705)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1980___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1704,c_24__type__2004___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718),Vvar__4__req__1718,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1704,Vvar__0__R__1704,Vvar__4__req__1718,Vvar__4__req__1718)),Vvar__2__rmul__1710)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2031___24a5(Vvar__0__R__1704,Vvar__1__radd__1705,Vvar__2__rmul__1710,Vvar__3__ropp__1715,Vvar__4__req__1718),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__1704,Vvar__0__R__1704,Vvar__4__req__1718,Vvar__4__req__1718),Vvar__3__ropp__1715)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX120466] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX120466)
     => ( VX120466 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__120467] :
            ( cType___24t(Vvar__0__R__120467)
            & ? [Vvar__1__req__120468] :
                ( c_24__type__161___24t(Vvar__0__R__120467,Vvar__1__req__120468)
                & ? [Vvar__2__reqb__120473] :
                    ( c_24__type__375___24t(Vvar__0__R__120467,Vvar__2__reqb__120473)
                    & ! [Vvar__var__3__x__120479__120482] :
                        ( t(Vvar__var__3__x__120479__120482,Vvar__0__R__120467)
                       => ! [Vvar__var__4__y__120480__120483] :
                            ( t(Vvar__var__4__y__120480__120483,Vvar__0__R__120467)
                           => ( happ(happ(Vvar__2__reqb__120473,Vvar__var__3__x__120479__120482),Vvar__var__4__y__120480__120483) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__120468,Vvar__var__3__x__120479__120482),Vvar__var__4__y__120480__120483)) ) ) )
                    & VX120466 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__120467,Vvar__1__req__120468,Vvar__2__reqb__120473) ) ) )
        | ? [Vvar__0__R__120485] :
            ( cType___24t(Vvar__0__R__120485)
            & ? [Vvar__1__rO__120486] :
                ( t(Vvar__1__rO__120486,Vvar__0__R__120485)
                & ? [Vvar__2__rI__120487] :
                    ( t(Vvar__2__rI__120487,Vvar__0__R__120485)
                    & ? [Vvar__3__radd__120488] :
                        ( c_24__type__150___24t(Vvar__0__R__120485,Vvar__3__radd__120488)
                        & ? [Vvar__4__rmul__120493] :
                            ( c_24__type__150___24t(Vvar__0__R__120485,Vvar__4__rmul__120493)
                            & ? [Vvar__5__rsub__120498] :
                                ( c_24__type__150___24t(Vvar__0__R__120485,Vvar__5__rsub__120498)
                                & ? [Vvar__6__ropp__120503] :
                                    ( c_24__type__156___24t(Vvar__0__R__120485,Vvar__6__ropp__120503)
                                    & ? [Vvar__7__req__120506] :
                                        ( c_24__type__161___24t(Vvar__0__R__120485,Vvar__7__req__120506)
                                        & ? [Vvar__8__C__120511] :
                                            ( cType___24t(Vvar__8__C__120511)
                                            & ? [Vvar__9__cO__120512] :
                                                ( t(Vvar__9__cO__120512,Vvar__8__C__120511)
                                                & ? [Vvar__10__cI__120513] :
                                                    ( t(Vvar__10__cI__120513,Vvar__8__C__120511)
                                                    & ? [Vvar__11__cadd__120514] :
                                                        ( c_24__type__440___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__11__cadd__120514)
                                                        & ? [Vvar__12__cmul__120519] :
                                                            ( c_24__type__440___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__12__cmul__120519)
                                                            & ? [Vvar__13__csub__120524] :
                                                                ( c_24__type__440___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__13__csub__120524)
                                                                & ? [Vvar__14__copp__120529] :
                                                                    ( c_24__type__454___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__14__copp__120529)
                                                                    & ? [Vvar__15__ceqb__120532] :
                                                                        ( c_24__type__461___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__15__ceqb__120532)
                                                                        & ? [Vvar__16__phi__120537] :
                                                                            ( c_24__type__465___24t(Vvar__0__R__120485,Vvar__8__C__120511,Vvar__16__phi__120537)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__120485,Vvar__1__rO__120486,Vvar__2__rI__120487,Vvar__3__radd__120488,Vvar__4__rmul__120493,Vvar__5__rsub__120498,Vvar__6__ropp__120503,Vvar__7__req__120506,Vvar__8__C__120511,Vvar__9__cO__120512,Vvar__10__cI__120513,Vvar__11__cadd__120514,Vvar__12__cmul__120519,Vvar__13__csub__120524,Vvar__14__copp__120529,Vvar__15__ceqb__120532,Vvar__16__phi__120537)
                                                                            & VX120466 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__120485,Vvar__1__rO__120486,Vvar__2__rI__120487,Vvar__3__radd__120488,Vvar__4__rmul__120493,Vvar__5__rsub__120498,Vvar__6__ropp__120503,Vvar__7__req__120506,Vvar__8__C__120511,Vvar__9__cO__120512,Vvar__10__cI__120513,Vvar__11__cadd__120514,Vvar__12__cmul__120519,Vvar__13__csub__120524,Vvar__14__copp__120529,Vvar__15__ceqb__120532,Vvar__16__phi__120537) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086] :
      ( cType___24t(Vvar__0__R__2034)
     => ( t(Vvar__1__rO__2035,Vvar__0__R__2034)
       => ( t(Vvar__2__rI__2036,Vvar__0__R__2034)
         => ( c_24__type__2430___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__3__radd__2037)
           => ( c_24__type__2643___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__4__rmul__2042)
             => ( c_24__type__2856___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__5__rsub__2047)
               => ( c_24__type__3051___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__6__ropp__2052)
                 => ( c_24__type__3264___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__7__req__2055)
                   => ( cType___24t(Vvar__8__C__2060)
                     => ( t(Vvar__9__cO__2061,Vvar__8__C__2060)
                       => ( t(Vvar__10__cI__2062,Vvar__8__C__2060)
                         => ( c_24__type__3477___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__11__cadd__2063)
                           => ( c_24__type__3690___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__12__cmul__2068)
                             => ( c_24__type__3903___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__13__csub__2073)
                               => ( c_24__type__4098___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__14__copp__2078)
                                 => ( c_24__type__4311___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__15__ceqb__2081)
                                   => ( c_24__type__4506___24t(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086,Vvar__16__phi__2086)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__2034,Vvar__1__rO__2035,Vvar__2__rI__2036,Vvar__3__radd__2037,Vvar__4__rmul__2042,Vvar__5__rsub__2047,Vvar__6__ropp__2052,Vvar__7__req__2055,Vvar__8__C__2060,Vvar__9__cO__2061,Vvar__10__cI__2062,Vvar__11__cadd__2063,Vvar__12__cmul__2068,Vvar__13__csub__2073,Vvar__14__copp__2078,Vvar__15__ceqb__2081,Vvar__16__phi__2086)
                                       => ( p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,Vvar__9__cO__2061)),Vvar__1__rO__2035))
                                          & p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,Vvar__10__cI__2062)),Vvar__2__rI__2036))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__2148__2150__2172__2174__2176__2178__2180] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__2148__2150__2172__2174__2176__2178__2180,Vvar__8__C__2060)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__2149__2151__2173__2175__2177__2179__2181] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__2149__2151__2173__2175__2177__2179__2181,Vvar__8__C__2060)
                                                 => p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,happ(happ(Vvar__11__cadd__2063,Vvar__var__var__var__var__var__var__19__x__2148__2150__2172__2174__2176__2178__2180),Vvar__var__var__var__var__var__var__20__y__2149__2151__2173__2175__2177__2179__2181))),happ(happ(Vvar__3__radd__2037,happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__19__x__2148__2150__2172__2174__2176__2178__2180)),happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__20__y__2149__2151__2173__2175__2177__2179__2181)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__2153__2155__2182__2184__2186__2188__2190] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__2153__2155__2182__2184__2186__2188__2190,Vvar__8__C__2060)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__2154__2156__2183__2185__2187__2189__2191] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__2154__2156__2183__2185__2187__2189__2191,Vvar__8__C__2060)
                                                 => p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,happ(happ(Vvar__13__csub__2073,Vvar__var__var__var__var__var__var__20__x__2153__2155__2182__2184__2186__2188__2190),Vvar__var__var__var__var__var__var__21__y__2154__2156__2183__2185__2187__2189__2191))),happ(happ(Vvar__5__rsub__2047,happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__20__x__2153__2155__2182__2184__2186__2188__2190)),happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__21__y__2154__2156__2183__2185__2187__2189__2191)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__2158__2160__2192__2194__2196__2198__2200] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__2158__2160__2192__2194__2196__2198__2200,Vvar__8__C__2060)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__2159__2161__2193__2195__2197__2199__2201] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__2159__2161__2193__2195__2197__2199__2201,Vvar__8__C__2060)
                                                 => p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,happ(happ(Vvar__12__cmul__2068,Vvar__var__var__var__var__var__var__21__x__2158__2160__2192__2194__2196__2198__2200),Vvar__var__var__var__var__var__var__22__y__2159__2161__2193__2195__2197__2199__2201))),happ(happ(Vvar__4__rmul__2042,happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__21__x__2158__2160__2192__2194__2196__2198__2200)),happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__22__y__2159__2161__2193__2195__2197__2199__2201)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__2163__2164__2202__2203__2204__2205__2206] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__2163__2164__2202__2203__2204__2205__2206,Vvar__8__C__2060)
                                             => p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,happ(Vvar__14__copp__2078,Vvar__var__var__var__var__var__var__22__x__2163__2164__2202__2203__2204__2205__2206))),happ(Vvar__6__ropp__2052,happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__var__22__x__2163__2164__2202__2203__2204__2205__2206)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__2166__2169__2207__2210__2213__2216] :
                                              ( t(Vvar__var__var__var__var__var__23__x__2166__2169__2207__2210__2213__2216,Vvar__8__C__2060)
                                             => ! [Vvar__var__var__var__var__var__24__y__2167__2170__2208__2211__2214__2217] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__2167__2170__2208__2211__2214__2217,Vvar__8__C__2060)
                                                 => ( happ(happ(Vvar__15__ceqb__2081,Vvar__var__var__var__var__var__23__x__2166__2169__2207__2210__2213__2216),Vvar__var__var__var__var__var__24__y__2167__2170__2208__2211__2214__2217) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__2055,happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__23__x__2166__2169__2207__2210__2213__2216)),happ(Vvar__16__phi__2086,Vvar__var__var__var__var__var__24__y__2167__2170__2208__2211__2214__2217))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774] :
      ( cType___24t(Vvar__0__R__118753)
     => ( t(Vvar__1__rO__118754,Vvar__0__R__118753)
       => ( t(Vvar__2__rI__118755,Vvar__0__R__118753)
         => ( c_24__type__118977___24t(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774,Vvar__3__radd__118756)
           => ( c_24__type__119040___24t(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774,Vvar__4__rmul__118761)
             => ( c_24__type__119103___24t(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774,Vvar__5__rsub__118766)
               => ( c_24__type__119157___24t(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774,Vvar__6__ropp__118771)
                 => ( c_24__type__119220___24t(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774,Vvar__7__req__118774)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__118753,Vvar__1__rO__118754,Vvar__2__rI__118755,Vvar__3__radd__118756,Vvar__4__rmul__118761,Vvar__5__rsub__118766,Vvar__6__ropp__118771,Vvar__7__req__118774)
                     => ( ! [Vvar__var__var__var__var__var__8__x__118807__118808__118851__118852__118853__118854] :
                            ( t(Vvar__var__var__var__var__var__8__x__118807__118808__118851__118852__118853__118854,Vvar__0__R__118753)
                           => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__3__radd__118756,Vvar__1__rO__118754),Vvar__var__var__var__var__var__8__x__118807__118808__118851__118852__118853__118854)),Vvar__var__var__var__var__var__8__x__118807__118808__118851__118852__118853__118854)) )
                        & ! [Vvar__var__var__var__var__9__x__118810__118812__118855__118857__118859] :
                            ( t(Vvar__var__var__var__var__9__x__118810__118812__118855__118857__118859,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__10__y__118811__118813__118856__118858__118860] :
                                ( t(Vvar__var__var__var__var__10__y__118811__118813__118856__118858__118860,Vvar__0__R__118753)
                               => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__9__x__118810__118812__118855__118857__118859),Vvar__var__var__var__var__10__y__118811__118813__118856__118858__118860)),happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__10__y__118811__118813__118856__118858__118860),Vvar__var__var__var__var__9__x__118810__118812__118855__118857__118859))) ) )
                        & ! [Vvar__var__var__var__var__10__x__118815__118818__118861__118864__118867] :
                            ( t(Vvar__var__var__var__var__10__x__118815__118818__118861__118864__118867,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__11__y__118816__118819__118862__118865__118868] :
                                ( t(Vvar__var__var__var__var__11__y__118816__118819__118862__118865__118868,Vvar__0__R__118753)
                               => ! [Vvar__var__var__var__var__12__z__118817__118820__118863__118866__118869] :
                                    ( t(Vvar__var__var__var__var__12__z__118817__118820__118863__118866__118869,Vvar__0__R__118753)
                                   => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__10__x__118815__118818__118861__118864__118867),happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__11__y__118816__118819__118862__118865__118868),Vvar__var__var__var__var__12__z__118817__118820__118863__118866__118869))),happ(happ(Vvar__3__radd__118756,happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__10__x__118815__118818__118861__118864__118867),Vvar__var__var__var__var__11__y__118816__118819__118862__118865__118868)),Vvar__var__var__var__var__12__z__118817__118820__118863__118866__118869))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__118822__118823__118870__118871__118872__118873] :
                            ( t(Vvar__var__var__var__var__var__11__x__118822__118823__118870__118871__118872__118873,Vvar__0__R__118753)
                           => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__4__rmul__118761,Vvar__2__rI__118755),Vvar__var__var__var__var__var__11__x__118822__118823__118870__118871__118872__118873)),Vvar__var__var__var__var__var__11__x__118822__118823__118870__118871__118872__118873)) )
                        & ! [Vvar__var__var__var__var__12__x__118825__118827__118874__118876__118878] :
                            ( t(Vvar__var__var__var__var__12__x__118825__118827__118874__118876__118878,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__13__y__118826__118828__118875__118877__118879] :
                                ( t(Vvar__var__var__var__var__13__y__118826__118828__118875__118877__118879,Vvar__0__R__118753)
                               => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__12__x__118825__118827__118874__118876__118878),Vvar__var__var__var__var__13__y__118826__118828__118875__118877__118879)),happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__13__y__118826__118828__118875__118877__118879),Vvar__var__var__var__var__12__x__118825__118827__118874__118876__118878))) ) )
                        & ! [Vvar__var__var__var__var__13__x__118830__118833__118880__118883__118886] :
                            ( t(Vvar__var__var__var__var__13__x__118830__118833__118880__118883__118886,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__14__y__118831__118834__118881__118884__118887] :
                                ( t(Vvar__var__var__var__var__14__y__118831__118834__118881__118884__118887,Vvar__0__R__118753)
                               => ! [Vvar__var__var__var__var__15__z__118832__118835__118882__118885__118888] :
                                    ( t(Vvar__var__var__var__var__15__z__118832__118835__118882__118885__118888,Vvar__0__R__118753)
                                   => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__13__x__118830__118833__118880__118883__118886),happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__14__y__118831__118834__118881__118884__118887),Vvar__var__var__var__var__15__z__118832__118835__118882__118885__118888))),happ(happ(Vvar__4__rmul__118761,happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__13__x__118830__118833__118880__118883__118886),Vvar__var__var__var__var__14__y__118831__118834__118881__118884__118887)),Vvar__var__var__var__var__15__z__118832__118835__118882__118885__118888))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__118837__118840__118889__118892__118895__118898] :
                            ( t(Vvar__var__var__var__var__var__14__x__118837__118840__118889__118892__118895__118898,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__var__15__y__118838__118841__118890__118893__118896__118899] :
                                ( t(Vvar__var__var__var__var__var__15__y__118838__118841__118890__118893__118896__118899,Vvar__0__R__118753)
                               => ! [Vvar__var__var__var__var__var__16__z__118839__118842__118891__118894__118897__118900] :
                                    ( t(Vvar__var__var__var__var__var__16__z__118839__118842__118891__118894__118897__118900,Vvar__0__R__118753)
                                   => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__4__rmul__118761,happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__var__14__x__118837__118840__118889__118892__118895__118898),Vvar__var__var__var__var__var__15__y__118838__118841__118890__118893__118896__118899)),Vvar__var__var__var__var__var__16__z__118839__118842__118891__118894__118897__118900)),happ(happ(Vvar__3__radd__118756,happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__var__14__x__118837__118840__118889__118892__118895__118898),Vvar__var__var__var__var__var__16__z__118839__118842__118891__118894__118897__118900)),happ(happ(Vvar__4__rmul__118761,Vvar__var__var__var__var__var__15__y__118838__118841__118890__118893__118896__118899),Vvar__var__var__var__var__var__16__z__118839__118842__118891__118894__118897__118900)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__118844__118846__118901__118903__118905__118907__118909] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__118844__118846__118901__118903__118905__118907__118909,Vvar__0__R__118753)
                           => ! [Vvar__var__var__var__var__var__var__16__y__118845__118847__118902__118904__118906__118908__118910] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__118845__118847__118902__118904__118906__118908__118910,Vvar__0__R__118753)
                               => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__5__rsub__118766,Vvar__var__var__var__var__var__var__15__x__118844__118846__118901__118903__118905__118907__118909),Vvar__var__var__var__var__var__var__16__y__118845__118847__118902__118904__118906__118908__118910)),happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__var__var__15__x__118844__118846__118901__118903__118905__118907__118909),happ(Vvar__6__ropp__118771,Vvar__var__var__var__var__var__var__16__y__118845__118847__118902__118904__118906__118908__118910)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__118849__118850__118911__118912__118913__118914__118915] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__118849__118850__118911__118912__118913__118914__118915,Vvar__0__R__118753)
                           => p(happ(happ(Vvar__7__req__118774,happ(happ(Vvar__3__radd__118756,Vvar__var__var__var__var__var__var__16__x__118849__118850__118911__118912__118913__118914__118915),happ(Vvar__6__ropp__118771,Vvar__var__var__var__var__var__var__16__x__118849__118850__118911__118912__118913__118914__118915))),Vvar__1__rO__118754)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498] :
      ( cType___24t(Vvar__0__R__119462)
     => ( t(Vvar__1__rO__119463,Vvar__0__R__119462)
       => ( t(Vvar__2__rI__119464,Vvar__0__R__119462)
         => ( c_24__type__119715___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__3__radd__119465)
           => ( c_24__type__119840___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__4__rmul__119470)
             => ( c_24__type__119965___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__5__req__119475)
               => ( cType___24t(Vvar__6__C__119480)
                 => ( t(Vvar__7__cO__119481,Vvar__6__C__119480)
                   => ( t(Vvar__8__cI__119482,Vvar__6__C__119480)
                     => ( c_24__type__120090___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__9__cadd__119483)
                       => ( c_24__type__120215___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__10__cmul__119488)
                         => ( c_24__type__120340___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__11__ceqb__119493)
                           => ( c_24__type__120451___24t(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498,Vvar__12__phi__119498)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__119462,Vvar__1__rO__119463,Vvar__2__rI__119464,Vvar__3__radd__119465,Vvar__4__rmul__119470,Vvar__5__req__119475,Vvar__6__C__119480,Vvar__7__cO__119481,Vvar__8__cI__119482,Vvar__9__cadd__119483,Vvar__10__cmul__119488,Vvar__11__ceqb__119493,Vvar__12__phi__119498)
                               => ( p(happ(happ(Vvar__5__req__119475,happ(Vvar__12__phi__119498,Vvar__7__cO__119481)),Vvar__1__rO__119463))
                                  & p(happ(happ(Vvar__5__req__119475,happ(Vvar__12__phi__119498,Vvar__8__cI__119482)),Vvar__2__rI__119464))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__119544__119546__119560__119562__119564__119566__119568] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__119544__119546__119560__119562__119564__119566__119568,Vvar__6__C__119480)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__119545__119547__119561__119563__119565__119567__119569] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__119545__119547__119561__119563__119565__119567__119569,Vvar__6__C__119480)
                                         => p(happ(happ(Vvar__5__req__119475,happ(Vvar__12__phi__119498,happ(happ(Vvar__9__cadd__119483,Vvar__var__var__var__var__var__var__15__x__119544__119546__119560__119562__119564__119566__119568),Vvar__var__var__var__var__var__var__16__y__119545__119547__119561__119563__119565__119567__119569))),happ(happ(Vvar__3__radd__119465,happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__var__15__x__119544__119546__119560__119562__119564__119566__119568)),happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__var__16__y__119545__119547__119561__119563__119565__119567__119569)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__119549__119551__119570__119572__119574__119576__119578] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__119549__119551__119570__119572__119574__119576__119578,Vvar__6__C__119480)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__119550__119552__119571__119573__119575__119577__119579] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__119550__119552__119571__119573__119575__119577__119579,Vvar__6__C__119480)
                                         => p(happ(happ(Vvar__5__req__119475,happ(Vvar__12__phi__119498,happ(happ(Vvar__10__cmul__119488,Vvar__var__var__var__var__var__var__16__x__119549__119551__119570__119572__119574__119576__119578),Vvar__var__var__var__var__var__var__17__y__119550__119552__119571__119573__119575__119577__119579))),happ(happ(Vvar__4__rmul__119470,happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__var__16__x__119549__119551__119570__119572__119574__119576__119578)),happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__var__17__y__119550__119552__119571__119573__119575__119577__119579)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__119554__119557__119580__119583__119586__119589] :
                                      ( t(Vvar__var__var__var__var__var__17__x__119554__119557__119580__119583__119586__119589,Vvar__6__C__119480)
                                     => ! [Vvar__var__var__var__var__var__18__y__119555__119558__119581__119584__119587__119590] :
                                          ( t(Vvar__var__var__var__var__var__18__y__119555__119558__119581__119584__119587__119590,Vvar__6__C__119480)
                                         => ( happ(happ(Vvar__11__ceqb__119493,Vvar__var__var__var__var__var__17__x__119554__119557__119580__119583__119586__119589),Vvar__var__var__var__var__var__18__y__119555__119558__119581__119584__119587__119590) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__119475,happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__17__x__119554__119557__119580__119583__119586__119589)),happ(Vvar__12__phi__119498,Vvar__var__var__var__var__var__18__y__119555__119558__119581__119584__119587__119590))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
    ! [Vvar__0__C__97908,Vvar__1__copp__97909,Vvar__2__ceqb__97912,Vvar__3__get__sign__97917] :
      ( cType___24t(Vvar__0__C__97908)
     => ( c_24__type__97964___24t(Vvar__0__C__97908,Vvar__1__copp__97909,Vvar__2__ceqb__97912,Vvar__3__get__sign__97917,Vvar__1__copp__97909)
       => ( c_24__type__97983___24t(Vvar__0__C__97908,Vvar__1__copp__97909,Vvar__2__ceqb__97912,Vvar__3__get__sign__97917,Vvar__2__ceqb__97912)
         => ( c_24__type__97997___24t(Vvar__0__C__97908,Vvar__1__copp__97909,Vvar__2__ceqb__97912,Vvar__3__get__sign__97917,Vvar__3__get__sign__97917)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__97908,Vvar__1__copp__97909,Vvar__2__ceqb__97912,Vvar__3__get__sign__97917)
             => ( ! [Vvar__var__var__var__var__var__4__c__97934__97937__97940__97943__97946__97949] :
                    ( t(Vvar__var__var__var__var__var__4__c__97934__97937__97940__97943__97946__97949,Vvar__0__C__97908)
                   => ! [Vvar__var__var__var__var__var__5__c_27__97935__97938__97941__97944__97947__97950] :
                        ( t(Vvar__var__var__var__var__var__5__c_27__97935__97938__97941__97944__97947__97950,Vvar__0__C__97908)
                       => ( happ(Vvar__3__get__sign__97917,Vvar__var__var__var__var__var__4__c__97934__97937__97940__97943__97946__97949) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__97908,Vvar__var__var__var__var__var__5__c_27__97935__97938__97941__97944__97947__97950)
                         => happ(happ(Vvar__2__ceqb__97912,Vvar__var__var__var__var__var__4__c__97934__97937__97940__97943__97946__97949),happ(Vvar__1__copp__97909,Vvar__var__var__var__var__var__5__c_27__97935__97938__97941__97944__97947__97950)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251] :
      ( cType___24t(Vvar__0__R__119240)
     => ( c_24__type__119326___24t(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251,Vvar__1__radd__119241)
       => ( c_24__type__119349___24t(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251,Vvar__2__rmul__119246)
         => ( c_24__type__119372___24t(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251,Vvar__3__req__119251)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__119395___24a4(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__119240,c_24__type__119413___24a4(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251),Vvar__3__req__119251,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__119240,Vvar__0__R__119240,Vvar__3__req__119251,Vvar__3__req__119251)),Vvar__1__radd__119241)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__119439___24a4(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__119240,c_24__type__119457___24a4(Vvar__0__R__119240,Vvar__1__radd__119241,Vvar__2__rmul__119246,Vvar__3__req__119251),Vvar__3__req__119251,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__119240,Vvar__0__R__119240,Vvar__3__req__119251,Vvar__3__req__119251)),Vvar__2__rmul__119246)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_IntMap.Map.Map',axiom,
    ! [Vvar__0__A__110,VX111] :
      ( cType___24t(Vvar__0__A__110)
     => ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__110,VX111)
       => ( VX111 = cIntMap_2eMap_2eM0___24a1(Vvar__0__A__110)
          | ? [Vvar__1___24Anonymous__114] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__114)
              & ? [Vvar__2___24Anonymous__115] :
                  ( t(Vvar__2___24Anonymous__115,Vvar__0__A__110)
                  & VX111 = cIntMap_2eMap_2eM1___24a3(Vvar__0__A__110,Vvar__1___24Anonymous__114,Vvar__2___24Anonymous__115) ) )
          | ? [Vvar__1___24Anonymous__117] :
              ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__110,Vvar__1___24Anonymous__117)
              & ? [Vvar__2___24Anonymous__118] :
                  ( cIntMap_2eMap_2eMap___24t(Vvar__0__A__110,Vvar__2___24Anonymous__118)
                  & VX111 = cIntMap_2eMap_2eM2___24a3(Vvar__0__A__110,Vvar__1___24Anonymous__117,Vvar__2___24Anonymous__118) ) ) ) ) ) ).

fof('$_lam_102335',axiom,
    ! [Vv__CANONICAL__0] :
      ( c_24__lam__102335___24a1(Vv__CANONICAL__0)
    <=> cCoq_2eNumbers_2eBinNums_2eN0 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__0) ) ).

fof('$_lam_102338',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__102338___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_102345',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( c_24__lam__102345___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
    <=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vv__CANONICAL__1) ) ).

fof('$_lam_111469',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__111469___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_111471',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__111471___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(Vv__CANONICAL__1)) ).

fof('$_lam_113374',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__113374___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_117405',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__117405___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).

fof('$_lam_118656',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( c_24__lam__118656___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
    <=> happ(Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ) ).

fof('$_lam_120981',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__120981___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_121048',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__121048___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__121049] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121049)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121049)
            & c_24__lam__121048___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__121049) ) ) ) ).

fof('$_lam_121055',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__121055___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__121056] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121056)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121056)
            & c_24__lam__121055___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__121056) ) ) ) ).

fof('$_lam_121059',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__121059___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__121060] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121060)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121060)
            & c_24__lam__121059___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_lam_467',axiom,
    ! [Vv__CANONICAL__0] : c_24__lam__467___24a1(Vv__CANONICAL__0) = Vv__CANONICAL__0 ).

fof('$_lam_7001',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__7001___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ).

fof('$_lam_7009',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__7009___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__7009___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_lam_7036',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__7036___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0) )
          | ? [Vvar__0___24Anonymous__7037] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7037)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7037)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7037)
                    & ( ? [Vvar__0___24Anonymous__7041] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7041)
                          & Vvar__0___24Anonymous__7037 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7041)
                          & c_24__lam__7036___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7041)) )
                      | ? [Vvar__0___24Anonymous__7042] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7042)
                          & Vvar__0___24Anonymous__7037 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7042)
                          & c_24__lam__7036___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7042)) )
                      | ( Vvar__0___24Anonymous__7037 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__7036___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_7103',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eN0
              & c_24__lam__7103___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4) )
            | ? [Vvar__0___24Anonymous__7104] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7104)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7104)
                & c_24__lam__7103___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__0___24Anonymous__7104) ) ) ) ) ) ).

fof('$_lam_7140',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__7140___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
          | ? [Vvar__0___24Anonymous__7141] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7141)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7141)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7141)
                    & ( ? [Vvar__0___24Anonymous__7145] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7145)
                          & Vvar__0___24Anonymous__7141 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7145)
                          & c_24__lam__7140___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7145),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__7146] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7146)
                          & Vvar__0___24Anonymous__7141 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7146)
                          & c_24__lam__7140___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7146),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__7141 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__7140___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_7164',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__7164___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__7164___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) ) ) ) ) ) ).

fof('$_lam_7228',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__7228___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_7236',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__7236___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__7236___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ) ).

fof('$_lam_7244',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__7244___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3))) )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__7244___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(Vv__CANONICAL__3)),Vv__CANONICAL__2) ) ) ) ) ).

fof('$_lam_7257',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__7257___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
            | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
              & c_24__lam__7257___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_lam_7292',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__7292___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).

fof('$_lam_7304',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__7307] :
                ( t(Vvar__1___24Anonymous__7307,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__7307)
                & c_24__lam__7304___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__7304___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ) ) ) ).

fof('$_lam_7354',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
       => ( ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)
            & c_24__lam__7354___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__7358] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7358)
              & ? [Vvar__2___24Anonymous__7359] :
                  ( t(Vvar__2___24Anonymous__7359,Vv__CANONICAL__0)
                  & ( cType___24t(Vv__CANONICAL__0)
                   => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
                     => ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__7358)
                       => ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__7358,Vvar__2___24Anonymous__7359)
                          & ( ? [Vvar__1___24Anonymous__7367] :
                                ( t(Vvar__1___24Anonymous__7367,Vv__CANONICAL__0)
                                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__7358) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__7367)
                                & c_24__lam__7354___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__7358) )
                            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__7358) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                              & c_24__lam__7354___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__7358,Vvar__2___24Anonymous__7359) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__7370] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7370)
              & ? [Vvar__2___24Anonymous__7371] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__7371)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__7370,Vvar__2___24Anonymous__7371)
                  & c_24__lam__7354___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__7370),cIntMap_2eMap_2eMapDelta___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__7371)) ) ) ) ) ) ).

fof('$_lam_87793',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__87793___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ).

fof('$_lam_87808',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__87811] :
                  ( t(Vvar__1___24Anonymous__87811,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__87811)
                  & c_24__lam__87808___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__87808___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_lam_87866',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
         => ( ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__1)
              & c_24__lam__87866___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
            | ? [Vvar__1___24Anonymous__87870] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__87870)
                & ? [Vvar__2___24Anonymous__87871] :
                    ( t(Vvar__2___24Anonymous__87871,Vv__CANONICAL__1)
                    & ( cType___24t(Vv__CANONICAL__0)
                     => ( cType___24t(Vv__CANONICAL__1)
                       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                         => ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__87870)
                           => ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__87870,Vvar__2___24Anonymous__87871)
                              & ( ? [Vvar__1___24Anonymous__87879] :
                                    ( t(Vvar__1___24Anonymous__87879,Vv__CANONICAL__0)
                                    & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__87870) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__87879)
                                    & c_24__lam__87866___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__87870,Vvar__1___24Anonymous__87879) )
                                | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__87870) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                                  & c_24__lam__87866___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) )
            | ? [Vvar__1___24Anonymous__87882] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__87882)
                & ? [Vvar__2___24Anonymous__87883] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__87883)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__87882,Vvar__2___24Anonymous__87883)
                    & c_24__lam__87866___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__1___24Anonymous__87882),cIntMap_2eFset_2eMapDomRestrTo___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__87883)) ) ) ) ) ) ) ).

fof('$_lam_87907',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__87910] :
                  ( t(Vvar__1___24Anonymous__87910,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__87910)
                  & c_24__lam__87907___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__87907___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_lam_87957',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__87960] :
                  ( t(Vvar__1___24Anonymous__87960,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__87960)
                  & c_24__lam__87957___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__87957___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ) ).

fof('$_lam_87999',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
         => ( ( Vv__CANONICAL__5 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__1)
              & c_24__lam__87999___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__2 )
            | ? [Vvar__1___24Anonymous__88003] :
                ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88003)
                & ? [Vvar__2___24Anonymous__88004] :
                    ( t(Vvar__2___24Anonymous__88004,Vv__CANONICAL__1)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__88003,Vvar__2___24Anonymous__88004)
                    & c_24__lam__87999___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eMapRemove___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__88003) ) )
            | ? [Vvar__1___24Anonymous__88007] :
                ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__1___24Anonymous__88007)
                & ? [Vvar__2___24Anonymous__88008] :
                    ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__88008)
                    & Vv__CANONICAL__5 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__88007,Vvar__2___24Anonymous__88008)
                    & c_24__lam__87999___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2emakeM2___24a3(Vv__CANONICAL__0,cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__1___24Anonymous__88007),cIntMap_2eFset_2eMapDomRestrBy___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vvar__2___24Anonymous__88008)) ) ) ) ) ) ) ).

fof('$_lam_88030',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
         => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
           => ( ? [Vvar__1___24Anonymous__88033] :
                  ( t(Vvar__1___24Anonymous__88033,Vv__CANONICAL__1)
                  & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__1,Vvar__1___24Anonymous__88033)
                  & c_24__lam__88030___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
              | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__1)
                & c_24__lam__88030___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).

fof('$_lam_88463',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( c_24__lam__88463___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ) ).

fof('$_lam_88603',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__5)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
              & c_24__lam__88603___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__5)
                 => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
                        & c_24__lam__88603___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__4) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
                        & c_24__lam__88603___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_88712',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eN0
              & c_24__lam__88712___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__1 )
            | ? [Vvar__0___24Anonymous__88713] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88713)
                & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__88713)
                & c_24__lam__88712___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cIntMap_2eMap_2eMapPut1___24a6(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__0___24Anonymous__88713) ) ) ) ) ) ).

fof('$_lam_88749',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
       => ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
            & c_24__lam__88749___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4),Vv__CANONICAL__2) )
          | ? [Vvar__0___24Anonymous__88750] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88750)
              & ( cType___24t(Vv__CANONICAL__0)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88750)
                 => ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__88750)
                    & ( ? [Vvar__0___24Anonymous__88754] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88754)
                          & Vvar__0___24Anonymous__88750 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__88754)
                          & c_24__lam__88749___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__88754),Vv__CANONICAL__4)) )
                      | ? [Vvar__0___24Anonymous__88755] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88755)
                          & Vvar__0___24Anonymous__88750 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__88755)
                          & c_24__lam__88749___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__88755),Vv__CANONICAL__4),Vv__CANONICAL__2) )
                      | ( Vvar__0___24Anonymous__88750 = cCoq_2eNumbers_2eBinNums_2exH
                        & c_24__lam__88749___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0,Vv__CANONICAL__4)) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_88800',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
         => ( ? [Vvar__1___24Anonymous__88803] :
                ( t(Vvar__1___24Anonymous__88803,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88803)
                & c_24__lam__88800___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88803) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__4)
                 => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                    & ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
                        & c_24__lam__88800___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3) )
                      | ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
                        & c_24__lam__88800___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_lam_88848',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__88848___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapPut__behind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__2) ).

fof('$_lam_88880',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
       => ( ( Vv__CANONICAL__4 = cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)
            & c_24__lam__88880___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
          | ? [Vvar__1___24Anonymous__88884] :
              ( cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__88884)
              & ? [Vvar__2___24Anonymous__88885] :
                  ( t(Vvar__2___24Anonymous__88885,Vv__CANONICAL__0)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__88884,Vvar__2___24Anonymous__88885)
                  & c_24__lam__88880___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eMapPut___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__88884,Vvar__2___24Anonymous__88885) ) )
          | ? [Vvar__1___24Anonymous__88888] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__88888)
              & ? [Vvar__2___24Anonymous__88889] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__88889)
                  & Vv__CANONICAL__4 = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__88888,Vvar__2___24Anonymous__88889)
                  & c_24__lam__88880___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vvar__1___24Anonymous__88888),cIntMap_2eMap_2eMapMerge___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vvar__2___24Anonymous__88889)) ) ) ) ) ) ).

fof('$_lam_88905',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__88908] :
                ( t(Vvar__1___24Anonymous__88908,Vv__CANONICAL__0)
                & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88908)
                & c_24__lam__88905___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88908) )
            | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
              & c_24__lam__88905___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ) ).

fof('$_lam_88939',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
       => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
         => ( ? [Vvar__1___24Anonymous__88942] :
                ( t(Vvar__1___24Anonymous__88942,Vv__CANONICAL__0)
                & ( cType___24t(Vv__CANONICAL__0)
                 => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                   => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88942)
                        & ( ? [Vvar__1___24Anonymous__88947] :
                              ( t(Vvar__1___24Anonymous__88947,Vv__CANONICAL__0)
                              & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88947)
                              & c_24__lam__88939___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) )
                          | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                            & c_24__lam__88939___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88942) ) ) ) ) ) ) )
            | ( cType___24t(Vv__CANONICAL__0)
             => ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
               => ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                 => ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                    & ( ? [Vvar__1___24Anonymous__88952] :
                          ( t(Vvar__1___24Anonymous__88952,Vv__CANONICAL__0)
                          & cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88952)
                          & c_24__lam__88939___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__88952) )
                      | ( cIntMap_2eMap_2eMapGet___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0)
                        & c_24__lam__88939___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ).

fof('$_prop_102336',axiom,
    ( p(c_24__prop__102336)
  <=> cCoq_2eNumbers_2eBinNums_2eN0 = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('$_prop_102339',axiom,
    ! [Vvar__0___24Anonymous__102332] :
      ( p(c_24__prop__102339___24a1(Vvar__0___24Anonymous__102332))
    <=> cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__102332) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('$_prop_102346',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__102346___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('$_prop_11175',axiom,
    ( p(c_24__prop__11175)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_11176',axiom,
    ( p(c_24__prop__11176)
  <=> cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_11177',axiom,
    ( p(c_24__prop__11177)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_11178',axiom,
    ( p(c_24__prop__11178)
  <=> cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_11181',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__11181___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_11182',axiom,
    ! [Vv__CANONICAL__0] :
      ( p(c_24__prop__11182___24a1(Vv__CANONICAL__0))
    <=> Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('$_prop_11310',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__11310___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_117213',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__S__117191,Vvar__1__x__117192,Vvar__2__y__117193] :
      ( p(c_24__prop__117213___24a4(Vvar__0___24Anonymous__117189,Vvar__0__S__117191,Vvar__1__x__117192,Vvar__2__y__117193))
    <=> Vvar__1__x__117192 = Vvar__2__y__117193 ) ).

fof('$_prop_117214',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__x__117194,Vvar__1__y__117195] :
      ( p(c_24__prop__117214___24a3(Vvar__0___24Anonymous__117189,Vvar__0__x__117194,Vvar__1__y__117195))
    <=> Vvar__0__x__117194 = Vvar__1__y__117195 ) ).

fof('$_prop_117215',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__x__117196,Vvar__1__s__117197] :
      ( p(c_24__prop__117215___24a3(Vvar__0___24Anonymous__117189,Vvar__0__x__117196,Vvar__1__s__117197))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__117196,Vvar__1__s__117197) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_117216',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__P__117198,Vvar__1__Q__117199] :
      ( p(c_24__prop__117216___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117198,Vvar__1__Q__117199))
    <=> ( p(Vvar__0__P__117198)
        & p(Vvar__1__Q__117199) ) ) ).

fof('$_prop_117217',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__P__117202,Vvar__1__Q__117203] :
      ( p(c_24__prop__117217___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117202,Vvar__1__Q__117203))
    <=> ( p(Vvar__0__P__117202)
        | p(Vvar__1__Q__117203) ) ) ).

fof('$_prop_117218',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__P__117206,Vvar__1__Q__117207] :
      ( p(c_24__prop__117218___24a3(Vvar__0___24Anonymous__117189,Vvar__0__P__117206,Vvar__1__Q__117207))
    <=> ( p(Vvar__0__P__117206)
       => p(Vvar__1__Q__117207) ) ) ).

fof('$_prop_117219',axiom,
    ! [Vvar__0___24Anonymous__117189,Vvar__0__P__117211] :
      ( p(c_24__prop__117219___24a2(Vvar__0___24Anonymous__117189,Vvar__0__P__117211))
    <=> ~ p(Vvar__0__P__117211) ) ).

fof('$_prop_120959',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__120959___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_120960',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__120960___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).

fof('$_prop_120961',axiom,
    ! [V0__S,V1__x,V2__y] :
      ( p(c_24__prop__120961___24a3(V0__S,V1__x,V2__y))
    <=> V1__x = V2__y ) ).

fof('$_prop_120963',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__120963___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_121001',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__121001___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_121027',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__121027___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_88464',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__88464___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vv__CANONICAL__0) ) ).

fof('$_type_1',axiom,
    ! [Vvar__2] :
      ( c_24__type__1___24t(Vvar__2)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2ead___24t(happ(Vvar__2,Vv__CANONICAL__0)) ) ) ).

fof('$_type_100949',axiom,
    ! [Vvar__100950] :
      ( c_24__type__100949___24t(Vvar__100950)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__100950,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_100966',axiom,
    ! [Vvar__100967] :
      ( c_24__type__100966___24t(Vvar__100967)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__100967,Vv__CANONICAL__0)) ) ) ).

fof('$_type_101300',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__101301] :
      ( c_24__type__101300___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__101301)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__101301,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_101311',axiom,
    ! [Vvar__101312] :
      ( c_24__type__101311___24t(Vvar__101312)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__101312,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102300',axiom,
    ! [Vvar__102301] :
      ( c_24__type__102300___24t(Vvar__102301)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__102301,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102342',axiom,
    ! [Vvar__102343] :
      ( c_24__type__102342___24t(Vvar__102343)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_24__lam__102345___24a1(Vv__CANONICAL__0)),c_24__prop__102346___24a1(Vv__CANONICAL__0),happ(Vvar__102343,Vv__CANONICAL__0)) ) ) ).

fof('$_type_102383',axiom,
    ! [Vvar__102384] :
      ( c_24__type__102383___24t(Vvar__102384)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__102384,Vv__CANONICAL__0)) ) ) ).

fof('$_type_102388',axiom,
    ! [Vvar__102389] :
      ( c_24__type__102388___24t(Vvar__102389)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__102389,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102441',axiom,
    ! [Vvar__102442] :
      ( c_24__type__102441___24t(Vvar__102442)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
                 => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__102442,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_102490',axiom,
    ! [Vvar__102491] :
      ( c_24__type__102490___24t(Vvar__102491)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__102491,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102564',axiom,
    ! [Vvar__102565] :
      ( c_24__type__102564___24t(Vvar__102565)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__102565,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102686',axiom,
    ! [Vvar__102687] :
      ( c_24__type__102686___24t(Vvar__102687)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__102687,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102703',axiom,
    ! [Vvar__102704] :
      ( c_24__type__102703___24t(Vvar__102704)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__102704,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_102722',axiom,
    ! [Vvar__102723] :
      ( c_24__type__102722___24t(Vvar__102723)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__102723,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_102727',axiom,
    ! [Vvar__102728] :
      ( c_24__type__102727___24t(Vvar__102728)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__102728,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_103920',axiom,
    ! [Vvar__103921] :
      ( c_24__type__103920___24t(Vvar__103921)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__156___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
                                 => t(happ(happ(happ(happ(happ(happ(happ(Vvar__103921,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).

fof('$_type_104017',axiom,
    ! [Vvar__104018] :
      ( c_24__type__104017___24t(Vvar__104018)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__104018,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_104032',axiom,
    ! [Vvar__104033] :
      ( c_24__type__104032___24t(Vvar__104033)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__104033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_104039',axiom,
    ! [Vvar__104040] :
      ( c_24__type__104039___24t(Vvar__104040)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__104040,Vv__CANONICAL__0)) ) ) ).

fof('$_type_104052',axiom,
    ! [Vvar__104053] :
      ( c_24__type__104052___24t(Vvar__104053)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__104053,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_104057',axiom,
    ! [Vvar__104058] :
      ( c_24__type__104057___24t(Vvar__104058)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__104058,Vv__CANONICAL__0)) ) ) ).

fof('$_type_104062',axiom,
    ! [Vvar__104063] :
      ( c_24__type__104062___24t(Vvar__104063)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__104063,Vv__CANONICAL__0)) ) ) ).

fof('$_type_104071',axiom,
    ! [Vvar__104072] :
      ( c_24__type__104071___24t(Vvar__104072)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
             => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__104072,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_104074',axiom,
    ! [Vvar__104075] :
      ( c_24__type__104074___24t(Vvar__104075)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__104075,Vv__CANONICAL__0)) ) ) ).

fof('$_type_104080',axiom,
    ! [Vvar__104081] :
      ( c_24__type__104080___24t(Vvar__104081)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__104081,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105437',axiom,
    ! [Vvar__105438] :
      ( c_24__type__105437___24t(Vvar__105438)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__105438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_105475',axiom,
    ! [Vvar__105476] :
      ( c_24__type__105475___24t(Vvar__105476)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__105476,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_105545',axiom,
    ! [Vvar__105546] :
      ( c_24__type__105545___24t(Vvar__105546)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__375___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ( ! [Vv__CANONICAL__3] :
                        ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                       => ! [Vv__CANONICAL__4] :
                            ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                           => ( happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) )
                   => cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(happ(happ(happ(Vvar__105546,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_105630',axiom,
    ! [Vvar__105631] :
      ( c_24__type__105630___24t(Vvar__105631)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__105631,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_105636',axiom,
    ! [Vvar__105637] :
      ( c_24__type__105636___24t(Vvar__105637)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__105637,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105639',axiom,
    ! [Vvar__105640] :
      ( c_24__type__105639___24t(Vvar__105640)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__105640,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_105655',axiom,
    ! [Vvar__105656] :
      ( c_24__type__105655___24t(Vvar__105656)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__105656,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_105674',axiom,
    ! [Vvar__105675] :
      ( c_24__type__105674___24t(Vvar__105675)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__105675,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_105766',axiom,
    ! [Vvar__105767] :
      ( c_24__type__105766___24t(Vvar__105767)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__105767,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105789',axiom,
    ! [Vvar__105790] :
      ( c_24__type__105789___24t(Vvar__105790)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__105790,Vv__CANONICAL__0)) ) ) ).

fof('$_type_105823',axiom,
    ! [Vvar__105824] :
      ( c_24__type__105823___24t(Vvar__105824)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__105829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__105841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__105824,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_105829',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105830] :
      ( c_24__type__105829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105830)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__105830,Vv__CANONICAL__2)) ) ) ).

fof('$_type_105841',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105842] :
      ( c_24__type__105841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__105842)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
           => t(happ(Vvar__105842,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexist___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ).

fof('$_type_107',axiom,
    ! [Vvar__108] :
      ( c_24__type__107___24t(Vvar__108)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__108,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10724',axiom,
    ! [Vvar__10725] :
      ( c_24__type__10724___24t(Vvar__10725)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__10725,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_10866',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10867] :
      ( c_24__type__10866___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10867)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__10867,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_10916',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10917] :
      ( c_24__type__10916___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10917)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__10917,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_10966',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10967] :
      ( c_24__type__10966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10967)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__10967,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_11008',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11009] :
      ( c_24__type__11008___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11009)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__11009,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_11058',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11059] :
      ( c_24__type__11058___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__11059)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__11059,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_111336',axiom,
    ! [Vvar__111337] :
      ( c_24__type__111336___24t(Vvar__111337)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__0)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__111337,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_111341',axiom,
    ! [Vvar__111342] :
      ( c_24__type__111341___24t(Vvar__111342)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__111342,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_111346',axiom,
    ! [Vvar__111347] :
      ( c_24__type__111346___24t(Vvar__111347)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__11205___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__11205___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__111347,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111348',axiom,
    ! [Vvar__111349] :
      ( c_24__type__111348___24t(Vvar__111349)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__111349,Vv__CANONICAL__0)) ) ) ).

fof('$_type_111352',axiom,
    ! [Vvar__111353] :
      ( c_24__type__111352___24t(Vvar__111353)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__104039___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__104039___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__111353,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111448',axiom,
    ! [Vvar__111449] :
      ( c_24__type__111448___24t(Vvar__111449)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cA___24t(Vv__CANONICAL__1)
             => cM___24t(happ(happ(Vvar__111449,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111451',axiom,
    ! [Vvar__111452] :
      ( c_24__type__111451___24t(Vvar__111452)
    <=> ! [Vv__CANONICAL__0] :
          ( cM___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cM___24t(Vv__CANONICAL__1)
             => cM___24t(happ(happ(Vvar__111452,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111477',axiom,
    ! [Vvar__111478] :
      ( c_24__type__111477___24t(Vvar__111478)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__111480___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__2)
                 => cIntMap_2eMap_2eMap___24t(cB,happ(happ(happ(Vvar__111478,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_111480',axiom,
    ! [Vvar__111481] :
      ( c_24__type__111480___24t(Vvar__111481)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cA___24t(Vv__CANONICAL__1)
             => cIntMap_2eMap_2eMap___24t(cB,happ(happ(Vvar__111481,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111486',axiom,
    ! [Vvar__111487] :
      ( c_24__type__111486___24t(Vvar__111487)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__111487,Vv__CANONICAL__0)) ) ) ).

fof('$_type_111489',axiom,
    ! [Vvar__111490] :
      ( c_24__type__111489___24t(Vvar__111490)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
             => cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__111490,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11149',axiom,
    ! [Vvar__11150] :
      ( c_24__type__11149___24t(Vvar__11150)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__11150,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111509',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111510] :
      ( c_24__type__111509___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111510)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__111510,Vv__CANONICAL__3)) ) ) ).

fof('$_type_111517',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111518] :
      ( c_24__type__111517___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111518)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__111518,Vv__CANONICAL__3)) ) ) ).

fof('$_type_111553',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111554] :
      ( c_24__type__111553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111554)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__111554,Vv__CANONICAL__2)) ) ) ).

fof('$_type_111557',axiom,
    ! [Vvar__111558] :
      ( c_24__type__111557___24t(Vvar__111558)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__111558,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111560',axiom,
    ! [Vv__CANONICAL__0,Vvar__111561] :
      ( c_24__type__111560___24t(Vv__CANONICAL__0,Vvar__111561)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__111561,Vv__CANONICAL__1)) ) ) ).

fof('$_type_111577',axiom,
    ! [Vvar__111578] :
      ( c_24__type__111577___24t(Vvar__111578)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__111578,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_111596',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111597] :
      ( c_24__type__111596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111597)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__111597,Vv__CANONICAL__3)) ) ) ).

fof('$_type_111604',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111605] :
      ( c_24__type__111604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111605)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__111605,Vv__CANONICAL__3)) ) ) ).

fof('$_type_111626',axiom,
    ! [Vvar__111627] :
      ( c_24__type__111626___24t(Vvar__111627)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__111632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__111644___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__111627,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_111632',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111633] :
      ( c_24__type__111632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111633)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__111633,Vv__CANONICAL__2)) ) ) ).

fof('$_type_111644',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111645] :
      ( c_24__type__111644___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111645)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
             => t(happ(happ(Vvar__111645,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eexistT___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).

fof('$_type_111659',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111660] :
      ( c_24__type__111659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111660)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__111660,Vv__CANONICAL__3)) ) ) ).

fof('$_type_111685',axiom,
    ! [Vvar__111686] :
      ( c_24__type__111685___24t(Vvar__111686)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__111689___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__111696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__111703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__111686,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_111689',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111690] :
      ( c_24__type__111689___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111690)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__111690,Vv__CANONICAL__2)) ) ) ).

fof('$_type_111696',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111697] :
      ( c_24__type__111696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111697)
    <=> ( p(Vv__CANONICAL__0)
       => t(Vvar__111697,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_111703',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111704] :
      ( c_24__type__111703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111704)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__111704,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_11171',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11172] :
      ( c_24__type__11171___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11172)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__11172,Vv__CANONICAL__2)) ) ) ).

fof('$_type_11179',axiom,
    ! [Vvar__11180] :
      ( c_24__type__11179___24t(Vvar__11180)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__11181___24a1(Vv__CANONICAL__0),c_24__prop__11182___24a1(Vv__CANONICAL__0),happ(Vvar__11180,Vv__CANONICAL__0)) ) ) ).

fof('$_type_111845',axiom,
    ! [Vvar__111846] :
      ( c_24__type__111845___24t(Vvar__111846)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__4___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),happ(happ(Vvar__111846,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11187',axiom,
    ! [Vvar__11188] :
      ( c_24__type__11187___24t(Vvar__11188)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__11188,Vv__CANONICAL__0)) ) ) ).

fof('$_type_111880',axiom,
    ! [Vvar__111881] :
      ( c_24__type__111880___24t(Vvar__111881)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__4___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),happ(happ(happ(Vvar__111881,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_111888',axiom,
    ! [Vvar__111889] :
      ( c_24__type__111888___24t(Vvar__111889)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__4___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cA___24t(Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),happ(happ(happ(Vvar__111889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_111897',axiom,
    ! [Vvar__111898] :
      ( c_24__type__111897___24t(Vvar__111898)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__111448___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__1)
             => cM___24t(happ(happ(Vvar__111898,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111922',axiom,
    ! [Vvar__111923] :
      ( c_24__type__111922___24t(Vvar__111923)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__111448___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__2)
                 => cM___24t(happ(happ(happ(Vvar__111923,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_111927',axiom,
    ! [Vvar__111928] :
      ( c_24__type__111927___24t(Vvar__111928)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__111480___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(cA,Vv__CANONICAL__1)
             => cIntMap_2eMap_2eMap___24t(cB,happ(happ(Vvar__111928,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_111960',axiom,
    ! [Vvar__111961] :
      ( c_24__type__111960___24t(Vvar__111961)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
                                     => cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__111961,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_11197',axiom,
    ! [Vvar__11198] :
      ( c_24__type__11197___24t(Vvar__11198)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__11198,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11205',axiom,
    ! [Vvar__11206] :
      ( c_24__type__11205___24t(Vvar__11206)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11206,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11214',axiom,
    ! [Vvar__11215] :
      ( c_24__type__11214___24t(Vvar__11215)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__11215,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11249',axiom,
    ! [Vvar__11250] :
      ( c_24__type__11249___24t(Vvar__11250)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11250,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11280',axiom,
    ! [Vvar__11281] :
      ( c_24__type__11280___24t(Vvar__11281)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__11281,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_112935',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__112936] :
      ( c_24__type__112935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__112936)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__112936,Vv__CANONICAL__6)) ) ) ).

fof('$_type_112941',axiom,
    ! [Vvar__112942] :
      ( c_24__type__112941___24t(Vvar__112942)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__112942,Vv__CANONICAL__0)) ) ) ).

fof('$_type_112958',axiom,
    ! [Vvar__112959] :
      ( c_24__type__112958___24t(Vvar__112959)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__112959,Vv__CANONICAL__0)) ) ) ).

fof('$_type_11337',axiom,
    ! [Vvar__11338] :
      ( c_24__type__11337___24t(Vvar__11338)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__11338,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113411',axiom,
    ! [Vvar__113412] :
      ( c_24__type__113411___24t(Vvar__113412)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__113412,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_11343',axiom,
    ! [Vvar__11344] :
      ( c_24__type__11343___24t(Vvar__11344)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__11344,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113444',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113445] :
      ( c_24__type__113444___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113445)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113445,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113452',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113453] :
      ( c_24__type__113452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113453)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113453,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113460',axiom,
    ! [Vvar__113461] :
      ( c_24__type__113460___24t(Vvar__113461)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__113461,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113494',axiom,
    ! [Vvar__113495] :
      ( c_24__type__113494___24t(Vvar__113495)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
                       => ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
                         => cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__113495,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).

fof('$_type_113522',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113523] :
      ( c_24__type__113522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113523)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113523,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113530',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113531] :
      ( c_24__type__113530___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113531)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113531,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113538',axiom,
    ! [Vvar__113539] :
      ( c_24__type__113538___24t(Vvar__113539)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__113539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113572',axiom,
    ! [Vvar__113573] :
      ( c_24__type__113572___24t(Vvar__113573)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
                             => cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__113573,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_113590',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113591] :
      ( c_24__type__113590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113591)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113591,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113596',axiom,
    ! [Vvar__113597] :
      ( c_24__type__113596___24t(Vvar__113597)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__113597,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_113770',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113771] :
      ( c_24__type__113770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113771)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__113771,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113776',axiom,
    ! [Vvar__113777] :
      ( c_24__type__113776___24t(Vvar__113777)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__113777,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_116403',axiom,
    ! [Vvar__116404] :
      ( c_24__type__116403___24t(Vvar__116404)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__116404,Vv__CANONICAL__0)) ) ) ).

fof('$_type_116410',axiom,
    ! [Vvar__116411] :
      ( c_24__type__116410___24t(Vvar__116411)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__116411,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1170',axiom,
    ! [Vvar__1171] :
      ( c_24__type__1170___24t(Vvar__1171)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__1171,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_117138',axiom,
    ! [Vvar__117139] :
      ( c_24__type__117138___24t(Vvar__117139)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__117139,Vv__CANONICAL__0)) ) ) ).

fof('$_type_117162',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__117163] :
      ( c_24__type__117162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__117163)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__117163,Vv__CANONICAL__6)) ) ) ).

fof('$_type_117171',axiom,
    ! [Vvar__117172] :
      ( c_24__type__117171___24t(Vvar__117172)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cProp___24t(happ(happ(happ(happ(Vvar__117172,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_117180',axiom,
    ! [Vvar__117181] :
      ( c_24__type__117180___24t(Vvar__117181)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( Vv__CANONICAL__1 = Vv__CANONICAL__2
                   => cProp___24t(happ(happ(happ(Vvar__117181,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_117223',axiom,
    ! [Vvar__117224] :
      ( c_24__type__117223___24t(Vvar__117224)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__105789___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__105789___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__117224,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117257',axiom,
    ! [Vv__CANONICAL__0,Vvar__117258] :
      ( c_24__type__117257___24t(Vv__CANONICAL__0,Vvar__117258)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__117258,Vv__CANONICAL__1)) ) ) ).

fof('$_type_117270',axiom,
    ! [Vvar__117271] :
      ( c_24__type__117270___24t(Vvar__117271)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__112958___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117275___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__117271,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_117275',axiom,
    ! [Vv__CANONICAL__0,Vvar__117276] :
      ( c_24__type__117275___24t(Vv__CANONICAL__0,Vvar__117276)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
             => t(happ(happ(Vvar__117276,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_117277',axiom,
    ! [Vvar__117278] :
      ( c_24__type__117277___24t(Vvar__117278)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__117278,Vv__CANONICAL__0)) ) ) ).

fof('$_type_117302',axiom,
    ! [Vvar__117303] :
      ( c_24__type__117302___24t(Vvar__117303)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cProp___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
                     => cType___24t(happ(happ(happ(happ(Vvar__117303,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_117353',axiom,
    ! [Vvar__117354] :
      ( c_24__type__117353___24t(Vvar__117354)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117354,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117356',axiom,
    ! [Vvar__117357] :
      ( c_24__type__117356___24t(Vvar__117357)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117357,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117374',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__117375] :
      ( c_24__type__117374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__117375)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ( Vv__CANONICAL__1 = Vv__CANONICAL__2
           => cProp___24t(happ(Vvar__117375,Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_117384',axiom,
    ! [Vvar__117385] :
      ( c_24__type__117384___24t(Vvar__117385)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__111560___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
                     => cProp___24t(happ(happ(happ(happ(Vvar__117385,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_117388',axiom,
    ! [Vvar__117389] :
      ( c_24__type__117388___24t(Vvar__117389)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__117389,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117395',axiom,
    ! [Vvar__117396] :
      ( c_24__type__117395___24t(Vvar__117396)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__117399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__117396,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_117399',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__117400] :
      ( c_24__type__117399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__117400)
    <=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
       => cProp___24t(Vvar__117400) ) ) ).

fof('$_type_117420',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__117421] :
      ( c_24__type__117420___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__117421)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__1,Vv__CANONICAL__5))
             => t(happ(happ(Vvar__117421,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_117433',axiom,
    ! [Vvar__117434] :
      ( c_24__type__117433___24t(Vvar__117434)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117434,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117438',axiom,
    ! [Vvar__117439] :
      ( c_24__type__117438___24t(Vvar__117439)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__117439,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_117441',axiom,
    ! [Vvar__117442] :
      ( c_24__type__117441___24t(Vvar__117442)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__117442,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_117637',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117638] :
      ( c_24__type__117637___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117638)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__117638,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_117730',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117731] :
      ( c_24__type__117730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117731)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__117731,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_117823',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117824] :
      ( c_24__type__117823___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117824)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__117824,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_117905',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117906] :
      ( c_24__type__117905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117906)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__117906,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_117998',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117999] :
      ( c_24__type__117998___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__117999)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__117999,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_118080',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__118081] :
      ( c_24__type__118080___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__118081)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__118081,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_118173',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__118174] :
      ( c_24__type__118173___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__118174)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__118174,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_118204',axiom,
    ! [Vvar__118205] :
      ( c_24__type__118204___24t(Vvar__118205)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__118205,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_118293',axiom,
    ! [Vvar__118294] :
      ( c_24__type__118293___24t(Vvar__118294)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__98262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => t(happ(happ(happ(happ(happ(Vvar__118294,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_118336',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__118337] :
      ( c_24__type__118336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__118337)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__118337,Vv__CANONICAL__3)) ) ) ).

fof('$_type_118383',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118384] :
      ( c_24__type__118383___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118384)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__118384,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_118418',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__118419] :
      ( c_24__type__118418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__118419)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__118419,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_118496',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118497] :
      ( c_24__type__118496___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118497)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__118497,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_118515',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118516] :
      ( c_24__type__118515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__118516)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__118516,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_118535',axiom,
    ! [Vvar__118536] :
      ( c_24__type__118535___24t(Vvar__118536)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__161___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => cType___24t(happ(happ(happ(happ(happ(Vvar__118536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_118618',axiom,
    ! [Vv__CANONICAL__0,Vvar__118619] :
      ( c_24__type__118618___24t(Vv__CANONICAL__0,Vvar__118619)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => t(happ(happ(Vvar__118619,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_118622',axiom,
    ! [Vv__CANONICAL__0,Vvar__118623] :
      ( c_24__type__118622___24t(Vv__CANONICAL__0,Vvar__118623)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__118623,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_118631',axiom,
    ! [Vvar__118632] :
      ( c_24__type__118631___24t(Vvar__118632)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__118632,Vv__CANONICAL__0)) ) ) ).

fof('$_type_118635',axiom,
    ! [Vvar__118636] :
      ( c_24__type__118635___24t(Vvar__118636)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__118636,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_118661',axiom,
    ! [Vvar__118662] :
      ( c_24__type__118661___24t(Vvar__118662)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__118662,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_118718',axiom,
    ! [Vvar__118719] :
      ( c_24__type__118718___24t(Vvar__118719)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__118719,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_118977',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__118978] :
      ( c_24__type__118977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__118978)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__118978,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119040',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119041] :
      ( c_24__type__119040___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119041)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119041,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119103',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119104] :
      ( c_24__type__119103___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119104)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119104,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119157',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119158] :
      ( c_24__type__119157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119158)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__119158,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_119220',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119221] :
      ( c_24__type__119220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__119221)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__119221,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_119326',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119327] :
      ( c_24__type__119326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119327)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119327,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119349',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119350] :
      ( c_24__type__119349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119350)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119350,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119372',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119373] :
      ( c_24__type__119372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119373)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__119373,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_119395',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119396] :
      ( c_24__type__119395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119396)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119396,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119413',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119414] :
      ( c_24__type__119413___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119414)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__119414,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_119439',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119440] :
      ( c_24__type__119439___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119440)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119440,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119457',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119458] :
      ( c_24__type__119457___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__119458)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__119458,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_119715',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119716] :
      ( c_24__type__119715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119716)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119716,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119840',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119841] :
      ( c_24__type__119840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119841)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__119841,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_119965',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119966] :
      ( c_24__type__119965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__119966)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__119966,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_120090',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120091] :
      ( c_24__type__120090___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120091)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__120091,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_120215',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120216] :
      ( c_24__type__120215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120216)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__120216,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_120340',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120341] :
      ( c_24__type__120340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120341)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__120341,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_120451',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120452] :
      ( c_24__type__120451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__120452)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__120452,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_120694',axiom,
    ! [Vvar__120695] :
      ( c_24__type__120694___24t(Vvar__120695)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__161___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__120704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__120695,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_120704',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120705] :
      ( c_24__type__120704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__120705)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__120705,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_120743',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120744] :
      ( c_24__type__120743___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120744)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__120744,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_120778',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__120779] :
      ( c_24__type__120778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__120779)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__120779,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_120813',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__120814] :
      ( c_24__type__120813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__120814)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__120814,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_120843',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120844] :
      ( c_24__type__120843___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120844)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__120844,Vv__CANONICAL__4)) ) ) ).

fof('$_type_120852',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120853] :
      ( c_24__type__120852___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__120853)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__120853,Vv__CANONICAL__4)) ) ) ).

fof('$_type_120939',axiom,
    ! [Vvar__120940] :
      ( c_24__type__120939___24t(Vvar__120940)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__120940,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120957',axiom,
    ! [Vvar__120958] :
      ( c_24__type__120957___24t(Vvar__120958)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__120959___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__120960___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__120958,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120978',axiom,
    ! [Vvar__120979] :
      ( c_24__type__120978___24t(Vvar__120979)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__120979,Vv__CANONICAL__0)) ) ) ).

fof('$_type_120993',axiom,
    ! [Vvar__120994] :
      ( c_24__type__120993___24t(Vvar__120994)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__120998___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__120994,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_120998',axiom,
    ! [Vv__CANONICAL__0,Vvar__120999] :
      ( c_24__type__120998___24t(Vv__CANONICAL__0,Vvar__120999)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__120999,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_121002',axiom,
    ! [Vvar__121003] :
      ( c_24__type__121002___24t(Vvar__121003)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__121003,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121019',axiom,
    ! [Vvar__121020] :
      ( c_24__type__121019___24t(Vvar__121020)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__121024___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__121020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_121024',axiom,
    ! [Vv__CANONICAL__0,Vvar__121025] :
      ( c_24__type__121024___24t(Vv__CANONICAL__0,Vvar__121025)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__121025,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_121062',axiom,
    ! [Vvar__121063] :
      ( c_24__type__121062___24t(Vvar__121063)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__121063,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_121076',axiom,
    ! [Vvar__121077] :
      ( c_24__type__121076___24t(Vvar__121077)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__121077,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_121140',axiom,
    ! [Vvar__121141] :
      ( c_24__type__121140___24t(Vvar__121141)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__121141,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121152',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121153] :
      ( c_24__type__121152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__121153)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__121153,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_121158',axiom,
    ! [Vvar__121159] :
      ( c_24__type__121158___24t(Vvar__121159)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__121159,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_121163',axiom,
    ! [Vvar__121164] :
      ( c_24__type__121163___24t(Vvar__121164)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__121164,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_121183',axiom,
    ! [Vvar__121184] :
      ( c_24__type__121183___24t(Vvar__121184)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__121184,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121193',axiom,
    ! [Vvar__121194] :
      ( c_24__type__121193___24t(Vvar__121194)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__121194,Vv__CANONICAL__0)) ) ) ).

fof('$_type_121218',axiom,
    ! [Vvar__121219] :
      ( c_24__type__121218___24t(Vvar__121219)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__121219,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_121220',axiom,
    ! [Vvar__121221] :
      ( c_24__type__121220___24t(Vvar__121221)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__121221,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1424',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1425] :
      ( c_24__type__1424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1425)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1425,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1487',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1488] :
      ( c_24__type__1487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1488)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1488,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_150',axiom,
    ! [Vv__CANONICAL__0,Vvar__151] :
      ( c_24__type__150___24t(Vv__CANONICAL__0,Vvar__151)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__151,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1550',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1551] :
      ( c_24__type__1550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1551)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1551,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_156',axiom,
    ! [Vv__CANONICAL__0,Vvar__157] :
      ( c_24__type__156___24t(Vv__CANONICAL__0,Vvar__157)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__157,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_1604',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1605] :
      ( c_24__type__1604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1605)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__1605,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_161',axiom,
    ! [Vv__CANONICAL__0,Vvar__162] :
      ( c_24__type__161___24t(Vv__CANONICAL__0,Vvar__162)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__162,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_1667',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1668] :
      ( c_24__type__1667___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__1668)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__1668,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_1809',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1810] :
      ( c_24__type__1809___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1810)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1810,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1839',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1840] :
      ( c_24__type__1839___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1840)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1840,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1863',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1864] :
      ( c_24__type__1863___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1864)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__1864,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_1893',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1894] :
      ( c_24__type__1893___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1894)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__1894,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_1923',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1924] :
      ( c_24__type__1923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1924)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1924,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1947',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1948] :
      ( c_24__type__1947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1948)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__1948,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_1980',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1981] :
      ( c_24__type__1980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1981)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1981,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_2004',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2005] :
      ( c_24__type__2004___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2005)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__2005,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_2031',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2032] :
      ( c_24__type__2031___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2032)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__2032,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_23',axiom,
    ! [Vvar__24] :
      ( c_24__type__23___24t(Vvar__24)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__24,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2430',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2431] :
      ( c_24__type__2430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2431)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__2431,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_2643',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2644] :
      ( c_24__type__2643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2644)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__2644,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_2856',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2857] :
      ( c_24__type__2856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__2857)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__2857,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_3051',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3052] :
      ( c_24__type__3051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3052)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__3052,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_3264',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3265] :
      ( c_24__type__3264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3265)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__3265,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_3477',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3478] :
      ( c_24__type__3477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3478)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__3478,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_35',axiom,
    ! [Vvar__36] :
      ( c_24__type__35___24t(Vvar__36)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__36,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_3690',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3691] :
      ( c_24__type__3690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3691)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__3691,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_37',axiom,
    ! [Vvar__38] :
      ( c_24__type__37___24t(Vvar__38)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__38,Vv__CANONICAL__0)) ) ) ).

fof('$_type_375',axiom,
    ! [Vv__CANONICAL__0,Vvar__376] :
      ( c_24__type__375___24t(Vv__CANONICAL__0,Vvar__376)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__376,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_386',axiom,
    ! [Vvar__387] :
      ( c_24__type__386___24t(Vvar__387)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__387,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_3903',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3904] :
      ( c_24__type__3903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3904)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__3904,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_4',axiom,
    ! [Vvar__5] :
      ( c_24__type__4___24t(Vvar__5)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cA___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4098',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4099] :
      ( c_24__type__4098___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4099)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__4099,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_4311',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4312] :
      ( c_24__type__4311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4312)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4312,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_440',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__441] :
      ( c_24__type__440___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__441)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__441,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_4506',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4507] :
      ( c_24__type__4506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4507)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__4507,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_454',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__455] :
      ( c_24__type__454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__455)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__455,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_4583',axiom,
    ! [Vvar__4584] :
      ( c_24__type__4583___24t(Vvar__4584)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__4584,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4596',axiom,
    ! [Vvar__4597] :
      ( c_24__type__4596___24t(Vvar__4597)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__4597,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4599',axiom,
    ! [Vvar__4600] :
      ( c_24__type__4599___24t(Vvar__4600)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4600,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4601',axiom,
    ! [Vvar__4602] :
      ( c_24__type__4601___24t(Vvar__4602)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4602,Vv__CANONICAL__0)) ) ) ).

fof('$_type_461',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__462] :
      ( c_24__type__461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__462)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__462,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_465',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__466] :
      ( c_24__type__465___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__466)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__466,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_4653',axiom,
    ! [Vvar__4654] :
      ( c_24__type__4653___24t(Vvar__4654)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__4654,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4684',axiom,
    ! [Vvar__4685] :
      ( c_24__type__4684___24t(Vvar__4685)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__4685,Vv__CANONICAL__0)) ) ) ).

fof('$_type_47',axiom,
    ! [Vvar__48] :
      ( c_24__type__47___24t(Vvar__48)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__48,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4909',axiom,
    ! [Vvar__4910] :
      ( c_24__type__4909___24t(Vvar__4910)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__150___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__4910,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_4941',axiom,
    ! [Vvar__4942] :
      ( c_24__type__4941___24t(Vvar__4942)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__4942,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5123',axiom,
    ! [Vvar__5124] :
      ( c_24__type__5123___24t(Vvar__5124)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5124,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_5154',axiom,
    ! [Vvar__5155] :
      ( c_24__type__5154___24t(Vvar__5155)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__5155,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5161',axiom,
    ! [Vvar__5162] :
      ( c_24__type__5161___24t(Vvar__5162)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5162,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5168',axiom,
    ! [Vvar__5169] :
      ( c_24__type__5168___24t(Vvar__5169)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__5169,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5173',axiom,
    ! [Vvar__5174] :
      ( c_24__type__5173___24t(Vvar__5174)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__5174,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_5176',axiom,
    ! [Vv__CANONICAL__0,Vvar__5177] :
      ( c_24__type__5176___24t(Vv__CANONICAL__0,Vvar__5177)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__5177,Vv__CANONICAL__1)) ) ) ).

fof('$_type_63',axiom,
    ! [Vvar__64] :
      ( c_24__type__63___24t(Vvar__64)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
                     => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__64,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_6908',axiom,
    ! [Vvar__6909] :
      ( c_24__type__6908___24t(Vvar__6909)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__6909,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_6911',axiom,
    ! [Vvar__6912] :
      ( c_24__type__6911___24t(Vvar__6912)
    <=> ! [Vv__CANONICAL__0] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eFset_2eFSet___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6912,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6925',axiom,
    ! [Vvar__6926] :
      ( c_24__type__6925___24t(Vvar__6926)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cIntMap_2eFset_2eFSet___24t(happ(happ(Vvar__6926,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6950',axiom,
    ! [Vvar__6951] :
      ( c_24__type__6950___24t(Vvar__6951)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__6951,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_6952',axiom,
    ! [Vvar__6953] :
      ( c_24__type__6952___24t(Vvar__6953)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(Vvar__6953,Vv__CANONICAL__0)) ) ) ).

fof('$_type_6957',axiom,
    ! [Vvar__6958] :
      ( c_24__type__6957___24t(Vvar__6958)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__6958,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_6962',axiom,
    ! [Vvar__6963] :
      ( c_24__type__6962___24t(Vvar__6963)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__6963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_6965',axiom,
    ! [Vv__CANONICAL__0,Vvar__6966] :
      ( c_24__type__6965___24t(Vv__CANONICAL__0,Vvar__6966)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__6966,Vv__CANONICAL__1)) ) ) ).

fof('$_type_7046',axiom,
    ! [Vvar__7047] :
      ( c_24__type__7046___24t(Vvar__7047)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7047,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_7153',axiom,
    ! [Vvar__7154] :
      ( c_24__type__7153___24t(Vvar__7154)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__7154,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_7248',axiom,
    ! [Vvar__7249] :
      ( c_24__type__7248___24t(Vvar__7249)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
                 => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7249,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_75',axiom,
    ! [Vvar__76] :
      ( c_24__type__75___24t(Vvar__76)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__76,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_82791',axiom,
    ! [Vvar__82792] :
      ( c_24__type__82791___24t(Vvar__82792)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__82792,Vv__CANONICAL__0)) ) ) ).

fof('$_type_82805',axiom,
    ! [Vvar__82806] :
      ( c_24__type__82805___24t(Vvar__82806)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__82806,Vv__CANONICAL__0)) ) ) ).

fof('$_type_82807',axiom,
    ! [Vvar__82808] :
      ( c_24__type__82807___24t(Vvar__82808)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__82808,Vv__CANONICAL__0)) ) ) ).

fof('$_type_82901',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82902] :
      ( c_24__type__82901___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82902)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__82902,Vv__CANONICAL__3)) ) ) ).

fof('$_type_82922',axiom,
    ! [Vvar__82923] :
      ( c_24__type__82922___24t(Vvar__82923)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__82926___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__82937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__82923,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_82926',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82927] :
      ( c_24__type__82926___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82927)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__82927,Vv__CANONICAL__2)) ) ) ).

fof('$_type_82937',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82938] :
      ( c_24__type__82937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__82938)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__82938,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).

fof('$_type_83001',axiom,
    ! [Vvar__83002] :
      ( c_24__type__83001___24t(Vvar__83002)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__83002,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_83013',axiom,
    ! [Vvar__83014] :
      ( c_24__type__83013___24t(Vvar__83014)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__83014,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_83034',axiom,
    ! [Vv__CANONICAL__0,Vvar__83035] :
      ( c_24__type__83034___24t(Vv__CANONICAL__0,Vvar__83035)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__83035,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_83055',axiom,
    ! [Vvar__83056] :
      ( c_24__type__83055___24t(Vvar__83056)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__83056,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_83063',axiom,
    ! [Vvar__83064] :
      ( c_24__type__83063___24t(Vvar__83064)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__83064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_85281',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85282] :
      ( c_24__type__85281___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85282)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85282,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85374',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85375] :
      ( c_24__type__85374___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85375)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85375,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85467',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85468] :
      ( c_24__type__85467___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85468)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85468,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85549',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85550] :
      ( c_24__type__85549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85550)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__85550,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_85642',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85643] :
      ( c_24__type__85642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85643)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__85643,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_85724',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85725] :
      ( c_24__type__85724___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85725)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__85725,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_85817',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85818] :
      ( c_24__type__85817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__85818)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__85818,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_86556',axiom,
    ! [Vvar__86557] :
      ( c_24__type__86556___24t(Vvar__86557)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__86557,Vv__CANONICAL__0)) ) ) ).

fof('$_type_86559',axiom,
    ! [Vvar__86560] :
      ( c_24__type__86559___24t(Vvar__86560)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__86560,Vv__CANONICAL__0)) ) ) ).

fof('$_type_87',axiom,
    ! [Vvar__88] :
      ( c_24__type__87___24t(Vvar__88)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__88,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_87891',axiom,
    ! [Vvar__87892] :
      ( c_24__type__87891___24t(Vvar__87892)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__87892,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_88068',axiom,
    ! [Vvar__88069] :
      ( c_24__type__88068___24t(Vvar__88069)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__88069,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_88089',axiom,
    ! [Vvar__88090] :
      ( c_24__type__88089___24t(Vvar__88090)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__88090,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_88137',axiom,
    ! [Vvar__88138] :
      ( c_24__type__88137___24t(Vvar__88138)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__88141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__88138,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_88141',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88142] :
      ( c_24__type__88141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88142)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__88142,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_88167',axiom,
    ! [Vvar__88168] :
      ( c_24__type__88167___24t(Vvar__88168)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__88174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__88168,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_88174',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88175] :
      ( c_24__type__88174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88175)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88175,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88334',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88335] :
      ( c_24__type__88334___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88335)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__88335,Vv__CANONICAL__2)) ) ) ).

fof('$_type_88381',axiom,
    ! [Vvar__88382] :
      ( c_24__type__88381___24t(Vvar__88382)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__88384___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM0___24a1(Vv__CANONICAL__0)))
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__88392___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__88409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__88382,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__1,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_88384',axiom,
    ! [Vv__CANONICAL__0,Vvar__88385] :
      ( c_24__type__88384___24t(Vv__CANONICAL__0,Vvar__88385)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__88385,Vv__CANONICAL__1)) ) ) ).

fof('$_type_88392',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88393] :
      ( c_24__type__88392___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88393)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88393,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ).

fof('$_type_88409',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88410] :
      ( c_24__type__88409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__88410)
    <=> ! [Vv__CANONICAL__2] :
          ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
             => ! [Vv__CANONICAL__4] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                 => ! [Vv__CANONICAL__5] :
                      ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__1,Vv__CANONICAL__4))
                     => t(happ(happ(happ(happ(Vvar__88410,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__1,cIntMap_2eMap_2eM2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ) ) ) ) ).

fof('$_type_88459',axiom,
    ! [Vvar__88460] :
      ( c_24__type__88459___24t(Vvar__88460)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(Vv__CANONICAL__0,c_24__lam__88463___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__88464___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__88460,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_88474',axiom,
    ! [Vvar__88475] :
      ( c_24__type__88474___24t(Vvar__88475)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__88477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__88477___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__88475,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_88477',axiom,
    ! [Vv__CANONICAL__0,Vvar__88478] :
      ( c_24__type__88477___24t(Vv__CANONICAL__0,Vvar__88478)
    <=> ! [Vv__CANONICAL__1] :
          ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__88478,Vv__CANONICAL__1)) ) ) ).

fof('$_type_88563',axiom,
    ! [Vvar__88564] :
      ( c_24__type__88563___24t(Vvar__88564)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cIntMap_2eMap_2ead___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__5)
                             => cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__88564,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_88817',axiom,
    ! [Vvar__88818] :
      ( c_24__type__88817___24t(Vvar__88818)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__88818,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_88965',axiom,
    ! [Vvar__88966] :
      ( c_24__type__88965___24t(Vvar__88966)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__88966,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_88976',axiom,
    ! [Vvar__88977] :
      ( c_24__type__88976___24t(Vvar__88977)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cIntMap_2eMap_2eMap___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__88977,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_88981',axiom,
    ! [Vvar__88982] :
      ( c_24__type__88981___24t(Vvar__88982)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__88982,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_89415',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89416] :
      ( c_24__type__89415___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89416)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89416,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89516',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89517] :
      ( c_24__type__89516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89517)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89517,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89617',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89618] :
      ( c_24__type__89617___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89618)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89618,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89707',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89708] :
      ( c_24__type__89707___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89708)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__89708,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_89808',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89809] :
      ( c_24__type__89808___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89809)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__89809,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_89909',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89910] :
      ( c_24__type__89909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__89910)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__89910,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90010',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__90011] :
      ( c_24__type__90010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__90011)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__90011,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90385',axiom,
    ! [Vv__CANONICAL__0,Vvar__90386] :
      ( c_24__type__90385___24t(Vv__CANONICAL__0,Vvar__90386)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__90386,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_90395',axiom,
    ! [Vvar__90396] :
      ( c_24__type__90395___24t(Vvar__90396)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__90396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_90414',axiom,
    ! [Vvar__90415] :
      ( c_24__type__90414___24t(Vvar__90415)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cProp___24t(Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__90415,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_90417',axiom,
    ! [Vv__CANONICAL__0,Vvar__90418] :
      ( c_24__type__90417___24t(Vv__CANONICAL__0,Vvar__90418)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__90418,Vv__CANONICAL__1)) ) ) ).

fof('$_type_90442',axiom,
    ! [Vvar__90443] :
      ( c_24__type__90442___24t(Vvar__90443)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__90443,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_91205',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91206] :
      ( c_24__type__91205___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91206)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91206,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91551',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91552] :
      ( c_24__type__91551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91552)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91552,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91897',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91898] :
      ( c_24__type__91897___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__91898)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91898,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_92220',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92221] :
      ( c_24__type__92220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92221)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__92221,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_92566',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92567] :
      ( c_24__type__92566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92567)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__92567,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_92912',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92913] :
      ( c_24__type__92912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__92913)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__92913,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_93258',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93259] :
      ( c_24__type__93258___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93259)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__93259,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_93604',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93605] :
      ( c_24__type__93604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93605)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__93605,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_93950',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93951] :
      ( c_24__type__93950___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__93951)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__93951,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_94273',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94274] :
      ( c_24__type__94273___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94274)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__94274,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_94619',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94620] :
      ( c_24__type__94619___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94620)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__94620,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_94965',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94966] :
      ( c_24__type__94965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__94966)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__94966,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_95288',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95289] :
      ( c_24__type__95288___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95289)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__95289,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_95611',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95612] :
      ( c_24__type__95611___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95612)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__95612,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_95957',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95958] :
      ( c_24__type__95957___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__95958)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__95958,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_97141',axiom,
    ! [Vvar__97142] :
      ( c_24__type__97141___24t(Vvar__97142)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__97142,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_97146',axiom,
    ! [Vvar__97147] :
      ( c_24__type__97146___24t(Vvar__97147)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__97147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_97155',axiom,
    ! [Vvar__97156] :
      ( c_24__type__97155___24t(Vvar__97156)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__97156,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_97964',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97965] :
      ( c_24__type__97964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97965)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__97965,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_97983',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97984] :
      ( c_24__type__97983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97984)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__97984,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_97997',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97998] :
      ( c_24__type__97997___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__97998)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__97998,Vv__CANONICAL__4)) ) ) ).

fof('$_type_98',axiom,
    ! [Vvar__99] :
      ( c_24__type__98___24t(Vvar__99)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__99,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_98119',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98120] :
      ( c_24__type__98119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98120)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__98120,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_98163',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98164] :
      ( c_24__type__98163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98164)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__98164,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_98199',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98200] :
      ( c_24__type__98199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98200)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__98200,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_98243',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98244] :
      ( c_24__type__98243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__98244)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__98244,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_98262',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98263] :
      ( c_24__type__98262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98263)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__98263,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_98317',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__98318] :
      ( c_24__type__98317___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__98318)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__98318,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_98358',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98359] :
      ( c_24__type__98358___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98359)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__98359,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_98515',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98516] :
      ( c_24__type__98515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98516)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__98516,Vv__CANONICAL__2)) ) ) ).

fof('$_type_98519',axiom,
    ! [Vvar__98520] :
      ( c_24__type__98519___24t(Vvar__98520)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__98520,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_98537',axiom,
    ! [Vvar__98538] :
      ( c_24__type__98537___24t(Vvar__98538)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                   => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__98538,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_98544',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98545] :
      ( c_24__type__98544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98545)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__98545,Vv__CANONICAL__2)) ) ) ).

fof('$_type_98558',axiom,
    ! [Vvar__98559] :
      ( c_24__type__98558___24t(Vvar__98559)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__98559,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_98581',axiom,
    ! [Vvar__98582] :
      ( c_24__type__98581___24t(Vvar__98582)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__98582,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_98586',axiom,
    ! [Vvar__98587] :
      ( c_24__type__98586___24t(Vvar__98587)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__98587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_98601',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98602] :
      ( c_24__type__98601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98602)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__98602,Vv__CANONICAL__3)) ) ) ).

fof('$_type_98627',axiom,
    ! [Vvar__98628] :
      ( c_24__type__98627___24t(Vvar__98628)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__98631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__98638___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__98645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__98628,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_98631',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98632] :
      ( c_24__type__98631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98632)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__98632,Vv__CANONICAL__2)) ) ) ).

fof('$_type_98638',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98639] :
      ( c_24__type__98638___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98639)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => t(happ(Vvar__98639,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einleft___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).

fof('$_type_98645',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98646] :
      ( c_24__type__98645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__98646)
    <=> ( p(Vv__CANONICAL__1)
       => t(Vvar__98646,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2einright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).

fof('$_type_98649',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98650] :
      ( c_24__type__98649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__98650)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__98650,Vv__CANONICAL__2)) ) ) ).

fof('$_type_98663',axiom,
    ! [Vvar__98664] :
      ( c_24__type__98663___24t(Vvar__98664)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__98664,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_98828',axiom,
    ! [Vvar__98829] :
      ( c_24__type__98828___24t(Vvar__98829)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => cType___24t(happ(happ(happ(happ(Vvar__98829,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_99223',axiom,
    ! [Vvar__99224] :
      ( c_24__type__99223___24t(Vvar__99224)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__99224,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_99258',axiom,
    ! [Vvar__99259] :
      ( c_24__type__99258___24t(Vvar__99259)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
                             => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__99259,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_9974',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9975] :
      ( c_24__type__9974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9975)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__9975,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_typeof_A',axiom,
    cType___24t(cA) ).

fof('$_typeof_B',axiom,
    cType___24t(cB) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__90395___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.Even',axiom,
    c_24__type__82807___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eEven) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    c_24__type__111348___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__90395___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__111352___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
    c_24__type__90395___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__121019___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__82791___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__4599___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.leb',axiom,
    c_24__type__102686___24t(cCoq_2eBool_2eBool_2eleb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__102703___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
    c_24__type__112958___24t(cCoq_2eBool_2eBvector_2eBvector) ).

fof('$_typeof_Coq.Bool.Sumbool.sumbool_of_bool',axiom,
    c_24__type__11179___24t(cCoq_2eBool_2eSumbool_2esumbool__of__bool) ).

fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
    c_24__type__104039___24t(cCoq_2eBool_2eZerob_2ezerob) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__102564___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    c_24__type__102441___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    c_24__type__102490___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).

fof('$_typeof_Coq.Init.Byte.byte',axiom,
    cType___24t(cCoq_2eInit_2eByte_2ebyte) ).

fof('$_typeof_Coq.Init.Byte.x00',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).

fof('$_typeof_Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).

fof('$_typeof_Coq.Init.Byte.x02',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).

fof('$_typeof_Coq.Init.Byte.x03',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).

fof('$_typeof_Coq.Init.Byte.x04',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).

fof('$_typeof_Coq.Init.Byte.x05',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).

fof('$_typeof_Coq.Init.Byte.x06',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).

fof('$_typeof_Coq.Init.Byte.x07',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).

fof('$_typeof_Coq.Init.Byte.x08',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).

fof('$_typeof_Coq.Init.Byte.x09',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).

fof('$_typeof_Coq.Init.Byte.x0a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).

fof('$_typeof_Coq.Init.Byte.x0b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).

fof('$_typeof_Coq.Init.Byte.x0c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).

fof('$_typeof_Coq.Init.Byte.x0d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).

fof('$_typeof_Coq.Init.Byte.x0e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).

fof('$_typeof_Coq.Init.Byte.x0f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).

fof('$_typeof_Coq.Init.Byte.x10',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).

fof('$_typeof_Coq.Init.Byte.x11',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).

fof('$_typeof_Coq.Init.Byte.x12',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).

fof('$_typeof_Coq.Init.Byte.x13',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).

fof('$_typeof_Coq.Init.Byte.x14',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).

fof('$_typeof_Coq.Init.Byte.x15',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).

fof('$_typeof_Coq.Init.Byte.x16',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).

fof('$_typeof_Coq.Init.Byte.x17',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).

fof('$_typeof_Coq.Init.Byte.x18',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).

fof('$_typeof_Coq.Init.Byte.x19',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).

fof('$_typeof_Coq.Init.Byte.x1a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).

fof('$_typeof_Coq.Init.Byte.x1b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).

fof('$_typeof_Coq.Init.Byte.x1c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).

fof('$_typeof_Coq.Init.Byte.x1d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).

fof('$_typeof_Coq.Init.Byte.x1e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).

fof('$_typeof_Coq.Init.Byte.x1f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).

fof('$_typeof_Coq.Init.Byte.x20',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).

fof('$_typeof_Coq.Init.Byte.x21',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).

fof('$_typeof_Coq.Init.Byte.x22',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).

fof('$_typeof_Coq.Init.Byte.x23',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).

fof('$_typeof_Coq.Init.Byte.x24',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).

fof('$_typeof_Coq.Init.Byte.x25',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).

fof('$_typeof_Coq.Init.Byte.x26',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).

fof('$_typeof_Coq.Init.Byte.x27',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).

fof('$_typeof_Coq.Init.Byte.x28',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).

fof('$_typeof_Coq.Init.Byte.x29',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).

fof('$_typeof_Coq.Init.Byte.x2a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).

fof('$_typeof_Coq.Init.Byte.x2b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).

fof('$_typeof_Coq.Init.Byte.x2c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).

fof('$_typeof_Coq.Init.Byte.x2d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).

fof('$_typeof_Coq.Init.Byte.x2e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).

fof('$_typeof_Coq.Init.Byte.x2f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).

fof('$_typeof_Coq.Init.Byte.x30',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).

fof('$_typeof_Coq.Init.Byte.x31',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).

fof('$_typeof_Coq.Init.Byte.x32',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).

fof('$_typeof_Coq.Init.Byte.x33',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).

fof('$_typeof_Coq.Init.Byte.x34',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).

fof('$_typeof_Coq.Init.Byte.x35',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).

fof('$_typeof_Coq.Init.Byte.x36',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).

fof('$_typeof_Coq.Init.Byte.x37',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).

fof('$_typeof_Coq.Init.Byte.x38',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).

fof('$_typeof_Coq.Init.Byte.x39',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).

fof('$_typeof_Coq.Init.Byte.x3a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).

fof('$_typeof_Coq.Init.Byte.x3b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).

fof('$_typeof_Coq.Init.Byte.x3c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).

fof('$_typeof_Coq.Init.Byte.x3d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).

fof('$_typeof_Coq.Init.Byte.x3e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).

fof('$_typeof_Coq.Init.Byte.x3f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).

fof('$_typeof_Coq.Init.Byte.x40',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).

fof('$_typeof_Coq.Init.Byte.x41',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).

fof('$_typeof_Coq.Init.Byte.x42',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).

fof('$_typeof_Coq.Init.Byte.x43',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).

fof('$_typeof_Coq.Init.Byte.x44',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).

fof('$_typeof_Coq.Init.Byte.x45',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).

fof('$_typeof_Coq.Init.Byte.x46',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).

fof('$_typeof_Coq.Init.Byte.x47',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).

fof('$_typeof_Coq.Init.Byte.x48',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).

fof('$_typeof_Coq.Init.Byte.x49',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).

fof('$_typeof_Coq.Init.Byte.x4a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).

fof('$_typeof_Coq.Init.Byte.x4b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).

fof('$_typeof_Coq.Init.Byte.x4c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).

fof('$_typeof_Coq.Init.Byte.x4d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).

fof('$_typeof_Coq.Init.Byte.x4e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).

fof('$_typeof_Coq.Init.Byte.x4f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).

fof('$_typeof_Coq.Init.Byte.x50',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).

fof('$_typeof_Coq.Init.Byte.x51',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).

fof('$_typeof_Coq.Init.Byte.x52',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).

fof('$_typeof_Coq.Init.Byte.x53',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).

fof('$_typeof_Coq.Init.Byte.x54',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).

fof('$_typeof_Coq.Init.Byte.x55',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).

fof('$_typeof_Coq.Init.Byte.x56',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).

fof('$_typeof_Coq.Init.Byte.x57',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).

fof('$_typeof_Coq.Init.Byte.x58',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).

fof('$_typeof_Coq.Init.Byte.x59',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).

fof('$_typeof_Coq.Init.Byte.x5a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).

fof('$_typeof_Coq.Init.Byte.x5b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).

fof('$_typeof_Coq.Init.Byte.x5c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).

fof('$_typeof_Coq.Init.Byte.x5d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).

fof('$_typeof_Coq.Init.Byte.x5e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).

fof('$_typeof_Coq.Init.Byte.x5f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).

fof('$_typeof_Coq.Init.Byte.x60',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).

fof('$_typeof_Coq.Init.Byte.x61',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).

fof('$_typeof_Coq.Init.Byte.x62',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).

fof('$_typeof_Coq.Init.Byte.x63',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).

fof('$_typeof_Coq.Init.Byte.x64',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).

fof('$_typeof_Coq.Init.Byte.x65',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).

fof('$_typeof_Coq.Init.Byte.x66',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).

fof('$_typeof_Coq.Init.Byte.x67',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).

fof('$_typeof_Coq.Init.Byte.x68',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).

fof('$_typeof_Coq.Init.Byte.x69',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).

fof('$_typeof_Coq.Init.Byte.x6a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).

fof('$_typeof_Coq.Init.Byte.x6b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).

fof('$_typeof_Coq.Init.Byte.x6c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).

fof('$_typeof_Coq.Init.Byte.x6d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).

fof('$_typeof_Coq.Init.Byte.x6e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).

fof('$_typeof_Coq.Init.Byte.x6f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).

fof('$_typeof_Coq.Init.Byte.x70',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).

fof('$_typeof_Coq.Init.Byte.x71',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).

fof('$_typeof_Coq.Init.Byte.x72',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).

fof('$_typeof_Coq.Init.Byte.x73',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).

fof('$_typeof_Coq.Init.Byte.x74',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).

fof('$_typeof_Coq.Init.Byte.x75',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).

fof('$_typeof_Coq.Init.Byte.x76',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).

fof('$_typeof_Coq.Init.Byte.x77',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).

fof('$_typeof_Coq.Init.Byte.x78',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).

fof('$_typeof_Coq.Init.Byte.x79',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).

fof('$_typeof_Coq.Init.Byte.x7a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).

fof('$_typeof_Coq.Init.Byte.x7b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).

fof('$_typeof_Coq.Init.Byte.x7c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).

fof('$_typeof_Coq.Init.Byte.x7d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).

fof('$_typeof_Coq.Init.Byte.x7e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).

fof('$_typeof_Coq.Init.Byte.x7f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).

fof('$_typeof_Coq.Init.Byte.x80',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).

fof('$_typeof_Coq.Init.Byte.x81',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).

fof('$_typeof_Coq.Init.Byte.x82',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).

fof('$_typeof_Coq.Init.Byte.x83',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).

fof('$_typeof_Coq.Init.Byte.x84',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).

fof('$_typeof_Coq.Init.Byte.x85',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).

fof('$_typeof_Coq.Init.Byte.x86',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).

fof('$_typeof_Coq.Init.Byte.x87',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).

fof('$_typeof_Coq.Init.Byte.x88',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).

fof('$_typeof_Coq.Init.Byte.x89',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).

fof('$_typeof_Coq.Init.Byte.x8a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).

fof('$_typeof_Coq.Init.Byte.x8b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).

fof('$_typeof_Coq.Init.Byte.x8c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).

fof('$_typeof_Coq.Init.Byte.x8d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).

fof('$_typeof_Coq.Init.Byte.x8e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).

fof('$_typeof_Coq.Init.Byte.x8f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).

fof('$_typeof_Coq.Init.Byte.x90',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).

fof('$_typeof_Coq.Init.Byte.x91',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).

fof('$_typeof_Coq.Init.Byte.x92',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).

fof('$_typeof_Coq.Init.Byte.x93',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).

fof('$_typeof_Coq.Init.Byte.x94',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).

fof('$_typeof_Coq.Init.Byte.x95',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).

fof('$_typeof_Coq.Init.Byte.x96',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).

fof('$_typeof_Coq.Init.Byte.x97',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).

fof('$_typeof_Coq.Init.Byte.x98',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).

fof('$_typeof_Coq.Init.Byte.x99',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).

fof('$_typeof_Coq.Init.Byte.x9a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).

fof('$_typeof_Coq.Init.Byte.x9b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).

fof('$_typeof_Coq.Init.Byte.x9c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).

fof('$_typeof_Coq.Init.Byte.x9d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).

fof('$_typeof_Coq.Init.Byte.x9e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).

fof('$_typeof_Coq.Init.Byte.x9f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).

fof('$_typeof_Coq.Init.Byte.xa0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).

fof('$_typeof_Coq.Init.Byte.xa1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).

fof('$_typeof_Coq.Init.Byte.xa2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).

fof('$_typeof_Coq.Init.Byte.xa3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).

fof('$_typeof_Coq.Init.Byte.xa4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).

fof('$_typeof_Coq.Init.Byte.xa5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).

fof('$_typeof_Coq.Init.Byte.xa6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).

fof('$_typeof_Coq.Init.Byte.xa7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).

fof('$_typeof_Coq.Init.Byte.xa8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).

fof('$_typeof_Coq.Init.Byte.xa9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).

fof('$_typeof_Coq.Init.Byte.xaa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).

fof('$_typeof_Coq.Init.Byte.xab',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).

fof('$_typeof_Coq.Init.Byte.xac',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).

fof('$_typeof_Coq.Init.Byte.xad',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).

fof('$_typeof_Coq.Init.Byte.xae',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).

fof('$_typeof_Coq.Init.Byte.xaf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).

fof('$_typeof_Coq.Init.Byte.xb0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).

fof('$_typeof_Coq.Init.Byte.xb1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).

fof('$_typeof_Coq.Init.Byte.xb2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).

fof('$_typeof_Coq.Init.Byte.xb3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).

fof('$_typeof_Coq.Init.Byte.xb4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).

fof('$_typeof_Coq.Init.Byte.xb5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).

fof('$_typeof_Coq.Init.Byte.xb6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).

fof('$_typeof_Coq.Init.Byte.xb7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).

fof('$_typeof_Coq.Init.Byte.xb8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).

fof('$_typeof_Coq.Init.Byte.xb9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).

fof('$_typeof_Coq.Init.Byte.xba',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).

fof('$_typeof_Coq.Init.Byte.xbb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).

fof('$_typeof_Coq.Init.Byte.xbc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).

fof('$_typeof_Coq.Init.Byte.xbd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).

fof('$_typeof_Coq.Init.Byte.xbe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).

fof('$_typeof_Coq.Init.Byte.xbf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).

fof('$_typeof_Coq.Init.Byte.xc0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).

fof('$_typeof_Coq.Init.Byte.xc1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).

fof('$_typeof_Coq.Init.Byte.xc2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).

fof('$_typeof_Coq.Init.Byte.xc3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).

fof('$_typeof_Coq.Init.Byte.xc4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).

fof('$_typeof_Coq.Init.Byte.xc5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).

fof('$_typeof_Coq.Init.Byte.xc6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).

fof('$_typeof_Coq.Init.Byte.xc7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).

fof('$_typeof_Coq.Init.Byte.xc8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).

fof('$_typeof_Coq.Init.Byte.xc9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).

fof('$_typeof_Coq.Init.Byte.xca',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).

fof('$_typeof_Coq.Init.Byte.xcb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).

fof('$_typeof_Coq.Init.Byte.xcc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).

fof('$_typeof_Coq.Init.Byte.xcd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).

fof('$_typeof_Coq.Init.Byte.xce',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).

fof('$_typeof_Coq.Init.Byte.xcf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).

fof('$_typeof_Coq.Init.Byte.xd0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).

fof('$_typeof_Coq.Init.Byte.xd1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).

fof('$_typeof_Coq.Init.Byte.xd2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).

fof('$_typeof_Coq.Init.Byte.xd3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).

fof('$_typeof_Coq.Init.Byte.xd4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).

fof('$_typeof_Coq.Init.Byte.xd5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).

fof('$_typeof_Coq.Init.Byte.xd6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).

fof('$_typeof_Coq.Init.Byte.xd7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).

fof('$_typeof_Coq.Init.Byte.xd8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).

fof('$_typeof_Coq.Init.Byte.xd9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).

fof('$_typeof_Coq.Init.Byte.xda',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).

fof('$_typeof_Coq.Init.Byte.xdb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).

fof('$_typeof_Coq.Init.Byte.xdc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).

fof('$_typeof_Coq.Init.Byte.xdd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).

fof('$_typeof_Coq.Init.Byte.xde',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).

fof('$_typeof_Coq.Init.Byte.xdf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).

fof('$_typeof_Coq.Init.Byte.xe0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).

fof('$_typeof_Coq.Init.Byte.xe1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).

fof('$_typeof_Coq.Init.Byte.xe2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).

fof('$_typeof_Coq.Init.Byte.xe3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).

fof('$_typeof_Coq.Init.Byte.xe4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).

fof('$_typeof_Coq.Init.Byte.xe5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).

fof('$_typeof_Coq.Init.Byte.xe6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).

fof('$_typeof_Coq.Init.Byte.xe7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).

fof('$_typeof_Coq.Init.Byte.xe8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).

fof('$_typeof_Coq.Init.Byte.xe9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).

fof('$_typeof_Coq.Init.Byte.xea',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).

fof('$_typeof_Coq.Init.Byte.xeb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).

fof('$_typeof_Coq.Init.Byte.xec',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).

fof('$_typeof_Coq.Init.Byte.xed',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).

fof('$_typeof_Coq.Init.Byte.xee',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).

fof('$_typeof_Coq.Init.Byte.xef',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).

fof('$_typeof_Coq.Init.Byte.xf0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).

fof('$_typeof_Coq.Init.Byte.xf1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).

fof('$_typeof_Coq.Init.Byte.xf2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).

fof('$_typeof_Coq.Init.Byte.xf3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).

fof('$_typeof_Coq.Init.Byte.xf4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).

fof('$_typeof_Coq.Init.Byte.xf5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).

fof('$_typeof_Coq.Init.Byte.xf6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).

fof('$_typeof_Coq.Init.Byte.xf7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).

fof('$_typeof_Coq.Init.Byte.xf8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).

fof('$_typeof_Coq.Init.Byte.xf9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).

fof('$_typeof_Coq.Init.Byte.xfa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).

fof('$_typeof_Coq.Init.Byte.xfb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).

fof('$_typeof_Coq.Init.Byte.xfc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).

fof('$_typeof_Coq.Init.Byte.xfd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).

fof('$_typeof_Coq.Init.Byte.xfe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).

fof('$_typeof_Coq.Init.Byte.xff',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).

fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
    c_24__type__117277___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__117302___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).

fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).

fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).

fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
    cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).

fof('$_typeof_Coq.Init.Datatypes.None',axiom,
    c_24__type__37___24t(cCoq_2eInit_2eDatatypes_2eNone) ).

fof('$_typeof_Coq.Init.Datatypes.O',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_typeof_Coq.Init.Datatypes.S',axiom,
    c_24__type__82805___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__35___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__4599___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__83013___24t(cCoq_2eInit_2eDatatypes_2eapp) ).

fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).

fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).

fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
    c_24__type__5173___24t(cCoq_2eInit_2eDatatypes_2econs) ).

fof('$_typeof_Coq.Init.Datatypes.false',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).

fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
    c_24__type__75___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
    c_24__type__102722___24t(cCoq_2eInit_2eDatatypes_2einl) ).

fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
    c_24__type__102727___24t(cCoq_2eInit_2eDatatypes_2einr) ).

fof('$_typeof_Coq.Init.Datatypes.is_true',axiom,
    c_24__type__82791___24t(cCoq_2eInit_2eDatatypes_2eis__true) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__83001___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__23___24t(cCoq_2eInit_2eDatatypes_2elist) ).

fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).

fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
    c_24__type__117270___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__4601___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__5168___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__23___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__4599___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__63___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__47___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.prod_rect',axiom,
    c_24__type__82922___24t(cCoq_2eInit_2eDatatypes_2eprod__rect) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__87___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__47___24t(cCoq_2eInit_2eDatatypes_2esum) ).

fof('$_typeof_Coq.Init.Datatypes.true',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).

fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
    cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).

fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
    cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).

fof('$_typeof_Coq.Init.Datatypes.xorb',axiom,
    c_24__type__4599___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.compare',axiom,
    c_24__type__104032___24t(cCoq_2eInit_2eNat_2ecompare) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__82805___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__82805___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__104017___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__104039___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.gcd',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2egcd) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__82805___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
    c_24__type__82805___24t(cCoq_2eInit_2eNat_2esqrt) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__88981___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__104017___24t(cCoq_2eInit_2eNat_2etestbit) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__90395___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__90395___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__90395___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__98537___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.exist2',axiom,
    c_24__type__113494___24t(cCoq_2eInit_2eSpecif_2eexist2) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__111577___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.existT2',axiom,
    c_24__type__113572___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).

fof('$_typeof_Coq.Init.Specif.inleft',axiom,
    c_24__type__98581___24t(cCoq_2eInit_2eSpecif_2einleft) ).

fof('$_typeof_Coq.Init.Specif.inright',axiom,
    c_24__type__98586___24t(cCoq_2eInit_2eSpecif_2einright) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__111336___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
    c_24__type__113596___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).

fof('$_typeof_Coq.Init.Specif.projT1',axiom,
    c_24__type__113776___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__111341___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__98519___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__113460___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__111557___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__113538___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sigT_rect',axiom,
    c_24__type__111626___24t(cCoq_2eInit_2eSpecif_2esigT__rect) ).

fof('$_typeof_Coq.Init.Specif.sig_rec',axiom,
    c_24__type__105823___24t(cCoq_2eInit_2eSpecif_2esig__rec) ).

fof('$_typeof_Coq.Init.Specif.sig_rect',axiom,
    c_24__type__105823___24t(cCoq_2eInit_2eSpecif_2esig__rect) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__11149___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumbool_rect',axiom,
    c_24__type__111685___24t(cCoq_2eInit_2eSpecif_2esumbool__rect) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__98558___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Specif.sumor_rec',axiom,
    c_24__type__98627___24t(cCoq_2eInit_2eSpecif_2esumor__rec) ).

fof('$_typeof_Coq.Init.Specif.sumor_rect',axiom,
    c_24__type__98627___24t(cCoq_2eInit_2eSpecif_2esumor__rect) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__101311___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__88089___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__118293___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__88167___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__98___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.List.map',axiom,
    c_24__type__88137___24t(cCoq_2eLists_2eList_2emap) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__6950___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.List.tl',axiom,
    c_24__type__107___24t(cCoq_2eLists_2eList_2etl) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__120694___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__117138___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
    c_24__type__117171___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
    c_24__type__117384___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
    c_24__type__112941___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__) ).

fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
    c_24__type__117395___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__117180___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
    c_24__type__117388___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
    c_24__type__121002___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).

fof('$_typeof_Coq.NArith.BinNat.N.discr',axiom,
    c_24__type__102342___24t(cCoq_2eNArith_2eBinNat_2eN_2ediscr) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__105639___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__111346___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__105639___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.le_alt',axiom,
    c_24__type__105639___24t(cCoq_2eNArith_2eBinNat_2eN_2ele__alt) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__105639___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
    c_24__type__120993___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
    c_24__type__105630___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__11187___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__11187___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
    c_24__type__11197___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
    c_24__type__11205___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
    c_24__type__120978___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__11187___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
    c_24__type__88068___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__11187___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
    c_24__type__11187___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
    c_24__type__11197___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__105636___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).

fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
    c_24__type__111352___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).

fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).

fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).

fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
    c_24__type__5161___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).

fof('$_typeof_Coq.Numbers.BinNums.Z',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eZ) ).

fof('$_typeof_Coq.Numbers.BinNums.Z0',axiom,
    cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eNumbers_2eBinNums_2eZ0) ).

fof('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
    c_24__type__4596___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__4596___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).

fof('$_typeof_Coq.Numbers.BinNums.positive',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2epositive) ).

fof('$_typeof_Coq.Numbers.BinNums.xH',axiom,
    cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_typeof_Coq.Numbers.BinNums.xI',axiom,
    c_24__type__5154___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__5154___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__121140___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
    c_24__type__102300___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__102300___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    c_24__type__121158___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    c_24__type__102383___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
    c_24__type__11214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__102388___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.divide',axiom,
    c_24__type__102300___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2edivide) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    c_24__type__105674___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__105655___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__121076___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
    c_24__type__11214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__11214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__11214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    c_24__type__116410___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    c_24__type__116410___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
    c_24__type__5154___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    c_24__type__116403___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__11214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__5154___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    c_24__type__121062___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).

fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
    cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).

fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
    c_24__type__104062___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__104052___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__104057___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
    c_24__type__104074___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).

fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).

fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
    c_24__type__104080___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
    cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
    c_24__type__113411___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__113411___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__104074___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__113411___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__113411___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
    c_24__type__104071___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__104071___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__104074___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__104071___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__118631___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__118718___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
    c_24__type__118635___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__23___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__118635___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Antisymmetric',axiom,
    c_24__type__118661___24t(cCoq_2eSets_2eRelations__1_2eAntisymmetric) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__23___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__111960___24t(cCoq_2eStrings_2eAscii_2eAscii) ).

fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
    cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).

fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_typeof_Coq.Strings.String.String',axiom,
    c_24__type__98663___24t(cCoq_2eStrings_2eString_2eString) ).

fof('$_typeof_Coq.Strings.String.string',axiom,
    cType___24t(cCoq_2eStrings_2eString_2estring) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__118535___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
    c_24__type__90395___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__102300___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
    c_24__type__120957___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
    c_24__type__121163___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
    c_24__type__4583___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).

fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
    cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).

fof('$_typeof_Coq.Vectors.Fin.t',axiom,
    c_24__type__112958___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
    c_24__type__100966___24t(cCoq_2eVectors_2eVectorDef_2enil) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__100949___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Bezout',axiom,
    c_24__type__121218___24t(cCoq_2eZArith_2eBinInt_2eZ_2eBezout) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Even',axiom,
    c_24__type__4684___24t(cCoq_2eZArith_2eBinInt_2eZ_2eEven) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
    c_24__type__121220___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__117223___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__4583___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    c_24__type__86556___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    c_24__type__121183___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__11280___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__105789___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
    c_24__type__5123___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__105789___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__86559___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    c_24__type__105766___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__4941___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__11249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
    c_24__type__86556___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    c_24__type__121183___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__121193___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).

fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
    c_24__type__5123___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__4684___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__4684___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__11337___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
    c_24__type__90395___24t(cCoq_2eZArith_2eZnat_2eneq) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__118718___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__120939___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__23___24t(cCoq_2emicromega_2eEnv_2eEnv) ).

fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
    cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).

fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
    c_24__type__117356___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).

fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
    c_24__type__117353___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__23___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__83063___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__4653___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__83055___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__23___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).

fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
    cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__90442___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__90414___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).

fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
    c_24__type__23___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__23___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.Tauto.A',axiom,
    c_24__type__99258___24t(cCoq_2emicromega_2eTauto_2eA) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__98828___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
    c_24__type__99223___24t(cCoq_2emicromega_2eTauto_2eTT) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__47___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
    c_24__type__117433___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
    c_24__type__117441___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
    c_24__type__117438___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__23___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__23___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__23___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__118204___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__118204___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
    c_24__type__103920___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__97141___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__97146___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__10724___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__97146___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__97155___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__97146___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__23___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__386___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__23___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
    cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.Computational',axiom,
    c_24__type__105545___24t(cCoq_2esetoid__ring_2eRing__theory_2eComputational) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    c_24__type__105437___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__105437___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    c_24__type__105475___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__4909___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__1170___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).

fof('$_typeof_IntMap.Fset.FSet',axiom,
    cType___24t(cIntMap_2eFset_2eFSet) ).

fof('$_typeof_IntMap.Fset.FSetDelta',axiom,
    c_24__type__111489___24t(cIntMap_2eFset_2eFSetDelta) ).

fof('$_typeof_IntMap.Fset.FSetDiff',axiom,
    c_24__type__111489___24t(cIntMap_2eFset_2eFSetDiff) ).

fof('$_typeof_IntMap.Fset.FSetInter',axiom,
    c_24__type__111489___24t(cIntMap_2eFset_2eFSetInter) ).

fof('$_typeof_IntMap.Fset.FSetUnion',axiom,
    c_24__type__111489___24t(cIntMap_2eFset_2eFSetUnion) ).

fof('$_typeof_IntMap.Fset.MapDom',axiom,
    c_24__type__6925___24t(cIntMap_2eFset_2eMapDom) ).

fof('$_typeof_IntMap.Fset.MapDomRestrBy',axiom,
    c_24__type__87891___24t(cIntMap_2eFset_2eMapDomRestrBy) ).

fof('$_typeof_IntMap.Fset.MapDomRestrTo',axiom,
    c_24__type__87891___24t(cIntMap_2eFset_2eMapDomRestrTo) ).

fof('$_typeof_IntMap.Fset.in_FSet',axiom,
    c_24__type__6911___24t(cIntMap_2eFset_2ein__FSet) ).

fof('$_typeof_IntMap.Fset.in_dom',axiom,
    c_24__type__6908___24t(cIntMap_2eFset_2ein__dom) ).

fof('$_typeof_IntMap.Map.M0',axiom,
    c_24__type__6952___24t(cIntMap_2eMap_2eM0) ).

fof('$_typeof_IntMap.Map.M1',axiom,
    c_24__type__6957___24t(cIntMap_2eMap_2eM1) ).

fof('$_typeof_IntMap.Map.M2',axiom,
    c_24__type__6962___24t(cIntMap_2eMap_2eM2) ).

fof('$_typeof_IntMap.Map.Map',axiom,
    c_24__type__23___24t(cIntMap_2eMap_2eMap) ).

fof('$_typeof_IntMap.Map.MapCard',axiom,
    c_24__type__88817___24t(cIntMap_2eMap_2eMapCard) ).

fof('$_typeof_IntMap.Map.MapDelta',axiom,
    c_24__type__6962___24t(cIntMap_2eMap_2eMapDelta) ).

fof('$_typeof_IntMap.Map.MapEmptyp',axiom,
    c_24__type__88965___24t(cIntMap_2eMap_2eMapEmptyp) ).

fof('$_typeof_IntMap.Map.MapGet',axiom,
    c_24__type__7046___24t(cIntMap_2eMap_2eMapGet) ).

fof('$_typeof_IntMap.Map.MapMerge',axiom,
    c_24__type__6962___24t(cIntMap_2eMap_2eMapMerge) ).

fof('$_typeof_IntMap.Map.MapPut',axiom,
    c_24__type__7153___24t(cIntMap_2eMap_2eMapPut) ).

fof('$_typeof_IntMap.Map.MapPut1',axiom,
    c_24__type__88563___24t(cIntMap_2eMap_2eMapPut1) ).

fof('$_typeof_IntMap.Map.MapPut_behind',axiom,
    c_24__type__7153___24t(cIntMap_2eMap_2eMapPut__behind) ).

fof('$_typeof_IntMap.Map.MapRemove',axiom,
    c_24__type__7248___24t(cIntMap_2eMap_2eMapRemove) ).

fof('$_typeof_IntMap.Map.MapSingleton',axiom,
    c_24__type__6957___24t(cIntMap_2eMap_2eMapSingleton) ).

fof('$_typeof_IntMap.Map.Map_rec',axiom,
    c_24__type__88381___24t(cIntMap_2eMap_2eMap__rec) ).

fof('$_typeof_IntMap.Map.Map_rect',axiom,
    c_24__type__88381___24t(cIntMap_2eMap_2eMap__rect) ).

fof('$_typeof_IntMap.Map.ad',axiom,
    cType___24t(cIntMap_2eMap_2ead) ).

fof('$_typeof_IntMap.Map.eqm',axiom,
    c_24__type__88474___24t(cIntMap_2eMap_2eeqm) ).

fof('$_typeof_IntMap.Map.makeM2',axiom,
    c_24__type__6962___24t(cIntMap_2eMap_2emakeM2) ).

fof('$_typeof_IntMap.Map.newMap',axiom,
    c_24__type__6952___24t(cIntMap_2eMap_2enewMap) ).

fof('$_typeof_IntMap.Map.option_sum',axiom,
    c_24__type__88459___24t(cIntMap_2eMap_2eoption__sum) ).

fof('$_typeof_IntMap.Mapaxioms.eqmap',axiom,
    c_24__type__88976___24t(cIntMap_2eMapaxioms_2eeqmap) ).

fof('$_typeof_M',axiom,
    cType___24t(cM) ).

fof('$_typeof_Mapiter.MapIter.MapCollect',axiom,
    c_24__type__111927___24t(cMapiter_2eMapIter_2eMapCollect) ).

fof('$_typeof_Mapiter.MapIter.MapCollect1',axiom,
    c_24__type__111477___24t(cMapiter_2eMapIter_2eMapCollect1) ).

fof('$_typeof_Mapiter.MapIter.MapFoldDef.MapFold',axiom,
    c_24__type__111897___24t(cMapiter_2eMapIter_2eMapFoldDef_2eMapFold) ).

fof('$_typeof_Mapiter.MapIter.MapFoldDef.MapFold1',axiom,
    c_24__type__111922___24t(cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1) ).

fof('$_typeof_Mapiter.MapIter.MapSweep',axiom,
    c_24__type__111845___24t(cMapiter_2eMapIter_2eMapSweep) ).

fof('$_typeof_Mapiter.MapIter.MapSweep1',axiom,
    c_24__type__111880___24t(cMapiter_2eMapIter_2eMapSweep1) ).

fof('$_typeof_Mapiter.MapIter.MapSweep2',axiom,
    c_24__type__111888___24t(cMapiter_2eMapIter_2eMapSweep2) ).

fof('$_typeof_neutral',axiom,
    cM___24t(cneutral) ).

fof('$_typeof_op',axiom,
    c_24__type__111451___24t(cop) ).

fof('Coq.Arith.EqNat.eq_nat_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m)
           => V0__n = V1__m ) ) ) ).

fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
               => ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
                 => cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.add_cancel_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_cancel_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_dichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( ? [V2__p] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
                & cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = V1__m )
            | ? [V2__p] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
                & cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m) = V0__n ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.bits_inj',axiom,
    ! [V0__a] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
         => ( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(cCoq_2eInit_2eNat_2etestbit___24a1(V0__a),cCoq_2eInit_2eNat_2etestbit___24a1(V1__b))
           => V0__a = V1__b ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_0_gt_0_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( V0__n = cCoq_2eInit_2eDatatypes_2eO
        | cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__121027___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
    cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__90395,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__82807,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).

fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).

fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).

fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
          <=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_neq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
           => V0__n != V1__m ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_succ_pred',axiom,
    ! [V0__z] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
     => ! [V1__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n)
           => cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V1__n)) = V1__n ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.max_id',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2emax___24a2(V0__n,V0__n) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.max_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
           => cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.max_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.min_id',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2emin___24a2(V0__n,V0__n) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.min_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
           => cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.min_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
           => cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_1_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_1_r',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.neq_0',axiom,
    ~ ! [V0__n] :
        ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
       => V0__n = cCoq_2eInit_2eDatatypes_2eO ) ).

fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n != V1__m
           => V1__m != V0__n ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).

fof('Coq.Arith.PeanoNat.Nat.succ_inj',axiom,
    ! [V0__n1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
         => ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
           => V0__n1 = V1__n2 ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd',axiom,
    ! [V0__n1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
         => ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
          <=> V0__n1 = V1__n2 ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.two_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).

fof('Coq.Arith.PeanoNat.Nat.zero_or_succ',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( V0__n = cCoq_2eInit_2eDatatypes_2eO
        | ? [V1__m] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).

fof('Coq.Arith.Peano_dec.le_unique',axiom,
    ! [V0__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
     => ! [V1__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__m,V1__n)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__m,V1__n)
             => c_24Proof = c_24Proof ) ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( p(c_24False)
       => V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('Coq.Bool.Bool.andb_diag',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,V0__b) = V0__b ) ).

fof('Coq.Bool.Bool.andb_false_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('Coq.Bool.Bool.andb_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( t(V1__a,V0__A)
         => ! [V2__a_27] :
              ( t(V2__a_27,V0__A)
             => ! [V3__b] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
                 => ! [V4__b_27] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b_27)
                     => c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117232___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) ) ) ) ) ) ).

fof('Coq.Bool.Bool.andb_true_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).

fof('Coq.Bool.Bool.eq_iff_eq_true',axiom,
    ! [V0__b1] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ! [V1__b2] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = V1__b2
          <=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).

fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
    ! [V0__b1] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ! [V1__b2] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            <=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
           => V0__b1 = V1__b2 ) ) ) ).

fof('Coq.Bool.Bool.if_negb',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411350___24a4(V0__A,V1__b,V2__x,V3__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411355___24a4(V0__A,V1__b,V2__x,V3__y) ) ) ) ) ).

fof('Coq.Bool.Bool.negb_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( t(V1__a,V0__A)
         => ! [V2__a_27] :
              ( t(V2__a_27,V0__A)
             => ! [V3__b] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
                 => c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117248___24a4(V0__A,V1__a,V2__a_27,V3__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117253___24a4(V0__A,V1__a,V2__a_27,V3__b) ) ) ) ) ).

fof('Coq.Bool.Bool.negb_involutive',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) = V0__b ) ).

fof('Coq.Bool.Bool.negb_involutive_reverse',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => V0__b = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)) ) ).

fof('Coq.Bool.Bool.orb_diag',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,V0__b) = V0__b ) ).

fof('Coq.Bool.Bool.orb_false_l',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2efalse,V0__b) = V0__b ) ).

fof('Coq.Bool.Bool.orb_false_r',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = V0__b ) ).

fof('Coq.Bool.Bool.orb_true_l',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => cCoq_2eInit_2eDatatypes_2eorb___24a2(cCoq_2eInit_2eDatatypes_2etrue,V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.Bool.Bool.trans_eq_bool',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y = V2__z
                 => V0__x = V2__z ) ) ) ) ) ).

fof('Coq.Init.Datatypes.CompOpp_iff',axiom,
    ! [V0__c] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
     => ! [V1__c_27] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
         => ( cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__c) = V1__c_27
          <=> V0__c = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V1__c_27) ) ) ) ).

fof('Coq.Init.Datatypes.bool_ind',axiom,
    ! [V0__P] :
      ( c_24__type__82791___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2etrue))
       => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2efalse))
         => ! [V3__b] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
             => p(happ(V0__P,V3__b)) ) ) ) ) ).

fof('Coq.Init.Datatypes.list_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__5176___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( p(happ(V1__P,V4__l))
                       => p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
             => ! [V4__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                 => p(happ(V1__P,V4__l)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__82807___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ( p(happ(V0__P,V2__n))
               => p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
         => ! [V3__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Init.Datatypes.unit_ind',axiom,
    ! [V0__P] :
      ( c_24__type__111486___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2ett))
       => ! [V2__u] :
            ( cCoq_2eInit_2eDatatypes_2eunit___24t(V2__u)
           => p(happ(V0__P,V2__u)) ) ) ) ).

fof('Coq.Init.Peano.f_equal2_nat',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__f] :
          ( c_24__type__118618___24t(V0__B,V1__f)
         => ! [V2__x1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x1)
             => ! [V3__y1] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y1)
                 => ! [V4__x2] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x2)
                     => ! [V5__y2] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y2)
                         => ( V2__x1 = V3__y1
                           => ( V4__x2 = V5__y2
                             => happ(happ(V1__f,V2__x1),V4__x2) = happ(happ(V1__f,V3__y1),V5__y2) ) ) ) ) ) ) ) ) ).

fof('Coq.Init.Peano.f_equal_nat',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__f] :
          ( c_24__type__90385___24t(V0__B,V1__f)
         => ! [V2__x] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
             => ! [V3__y] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
                 => ( V2__x = V3__y
                   => happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).

fof('Coq.Init.Peano.le_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Init.Peano.n_Sn',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).

fof('Coq.Init.Peano.plus_n_O',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).

fof('Coq.Init.Specif.sig_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__90417___24t(V0__A,V1__P)
         => ! [V2__P] :
              ( c_24__type__98544___24t(V0__A,V1__P,V2__P)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ( p(happ(V1__P,V3__x))
                     => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,V3__x))) ) )
               => ! [V4__s] :
                    ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V4__s)
                   => p(happ(V2__P,V4__s)) ) ) ) ) ) ).

fof('Coq.Init.Specif.sumbool_ind',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__11171___24t(V0__A,V1__B,V2__P)
             => ( ( p(V0__A)
                 => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
               => ( ( p(V1__B)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
                 => ! [V5__s] :
                      ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
                     => p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).

fof('Coq.Init.Specif.sumor_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__98649___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,V3__a))) )
               => ( ( p(V1__B)
                   => p(happ(V2__P,cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B))) )
                 => ! [V5__s] :
                      ( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
                     => p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.dec_not_not',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
       => ( ( ~ p(V0__P)
           => p(c_24False) )
         => p(V0__P) ) ) ) ).

fof('Coq.Logic.Decidable.not_or_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                | p(V1__B) )
             => p(c_24False) )
          <=> ( ( p(V0__A)
               => p(c_24False) )
              & ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.eq_dep_non_dep',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( cType___24t(V1__P)
         => ! [V2__p] :
              ( t(V2__p,V0__U)
             => ! [V3__q] :
                  ( t(V3__q,V0__U)
                 => ! [V4__x] :
                      ( t(V4__x,V1__P)
                     => ! [V5__y] :
                          ( t(V5__y,V1__P)
                         => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,c_24__lam__117405___24a2(V0__U,V1__P),V2__p,V4__x,V3__q,V5__y)
                           => V4__x = V5__y ) ) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.eq_indd',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ! [V2__P] :
              ( c_24__type__117374___24t(V0__A,V1__x,V2__P)
             => ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
               => ! [V4__y] :
                    ( t(V4__y,V0__A)
                   => ( V1__x = V4__y
                     => p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.f_eq_dep_non_dep',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( c_24__type__111560___24t(V0__U,V1__P)
         => ! [V2__R] :
              ( cType___24t(V2__R)
             => ! [V3__p] :
                  ( t(V3__p,V0__U)
                 => ! [V4__q] :
                      ( t(V4__q,V0__U)
                     => ! [V5__x] :
                          ( t(V5__x,happ(V1__P,V3__p))
                         => ! [V6__y] :
                              ( t(V6__y,happ(V1__P,V4__q))
                             => ! [V7__f] :
                                  ( c_24__type__117420___24t(V0__U,V1__P,V2__R,V3__p,V4__q,V7__f)
                                 => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V3__p,V5__x,V4__q,V6__y)
                                   => happ(happ(V7__f,V3__p),V5__x) = happ(happ(V7__f,V4__q),V6__y) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ( V1__x = V2__y
               => V2__y = V1__x ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.K_dec',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ( ! [V1__x] :
            ( t(V1__x,V0__A)
           => ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) ) )
       => ! [V2__x] :
            ( t(V2__x,V0__A)
           => ! [V3__P] :
                ( c_24__type__117399___24t(V0__A,V2__x,V3__P)
               => ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
                 => ( V2__x = V2__x
                   => p(V3__P) ) ) ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.K_dec_on',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ( ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) )
           => ! [V3__P] :
                ( c_24__type__117399___24t(V0__A,V1__x,V3__P)
               => ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
                 => ( V1__x = V1__x
                   => p(V3__P) ) ) ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ( ! [V1__x] :
            ( t(V1__x,V0__A)
           => ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) ) )
       => ! [V2__x] :
            ( t(V2__x,V0__A)
           => ! [V3__y] :
                ( t(V3__y,V0__A)
               => ( V2__x = V3__y
                 => ( V2__x = V3__y
                   => c_24Proof = c_24Proof ) ) ) ) ) ) ).

fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( t(V1__x,V0__A)
         => ( ! [V2__y] :
                ( t(V2__y,V0__A)
               => ( V1__x = V2__y
                  | V1__x != V2__y ) )
           => ! [V3__y] :
                ( t(V3__y,V0__A)
               => ( V1__x = V3__y
                 => ( V1__x = V3__y
                   => c_24Proof = c_24Proof ) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
               => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
                 => cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
           => cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.NArith.BinNat.N.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).

fof('Coq.NArith.BinNat.N.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).

fof('Coq.NArith.BinNat.N.add_cancel_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.NArith.BinNat.N.add_cancel_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V2__p) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.NArith.BinNat.N.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.NArith.BinNat.N.add_dichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( ? [V2__p] :
                ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
                & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V0__n) = V1__m )
            | ? [V2__p] :
                ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
                & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V2__p,V1__m) = V0__n ) ) ) ) ).

fof('Coq.NArith.BinNat.N.bits_inj',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
         => ( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V1__b))
           => V0__a = V1__b ) ) ) ).

fof('Coq.NArith.BinNat.N.div2_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = V0__n ) ).

fof('Coq.NArith.BinNat.N.div2_succ_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = V0__n ) ).

fof('Coq.NArith.BinNat.N.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.NArith.BinNat.N.eq_0_gt_0_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
        | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ) ).

fof('Coq.NArith.BinNat.N.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__121001___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).

fof('Coq.NArith.BinNat.N.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.eqb_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.NArith.BinNat.N.eqb_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__x,V1__y) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__y,V0__x) ) ) ).

fof('Coq.NArith.BinNat.N.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_wd',axiom,
    cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__105639,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__11343,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
    cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
    cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).

fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
          <=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_neq',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
           => V0__n != V1__m ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lxor_eq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V1__a_27) = cCoq_2eNumbers_2eBinNums_2eN0
           => V0__a = V1__a_27 ) ) ) ).

fof('Coq.NArith.BinNat.N.lxor_nilpotent',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('Coq.NArith.BinNat.N.mul_1_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).

fof('Coq.NArith.BinNat.N.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.NArith.BinNat.N.neq_0',axiom,
    ~ ! [V0__n] :
        ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
       => V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ).

fof('Coq.NArith.BinNat.N.neq_sym',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( V0__n != V1__m
           => V1__m != V0__n ) ) ) ).

fof('Coq.NArith.BinNat.N.pred_succ',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).

fof('Coq.NArith.BinNat.N.succ_inj',axiom,
    ! [V0__n1] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
           => V0__n1 = V1__n2 ) ) ) ).

fof('Coq.NArith.BinNat.N.succ_inj_wd',axiom,
    ! [V0__n1] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n2)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__n2)
          <=> V0__n1 = V1__n2 ) ) ) ).

fof('Coq.NArith.Ndec.Nbit0_neq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2efalse
           => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
             => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('Coq.NArith.Ndec.Ndiv2_bit_neq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2efalse
           => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__a) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a_27)
             => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('Coq.NArith.Ndec.Ndiv2_eq',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ! [V1__a_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__a_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__a,V1__a_27) = cCoq_2eInit_2eDatatypes_2etrue
           => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__a),cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a_27)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('Coq.NArith.Ndec.Neqb_complete',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__n_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2etrue
           => V0__n = V1__n_27 ) ) ) ).

fof('Coq.NArith.Ndec.Nxor_eq_false',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__n_27] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__n_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p)
               => cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('Coq.NArith.Ndigits.Ndiv2_double',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNArith_2eNdigits_2eNeven___24a1(V0__n)
       => cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).

fof('Coq.NArith.Ndigits.Ndiv2_double_plus_one',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( cCoq_2eNArith_2eNdigits_2eNodd___24a1(V0__n)
       => cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n)) = V0__n ) ) ).

fof('Coq.NArith.Ndigits.Ndouble_bit0',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2efalse ) ).

fof('Coq.NArith.Ndigits.Ndouble_plus_one_bit0',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('Coq.Numbers.BinNums.N_ind',axiom,
    ! [V0__P] :
      ( c_24__type__11343___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
       => ( ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V2__p))) )
         => ! [V3__n] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Numbers.BinNums.positive_ind',axiom,
    ! [V0__P] :
      ( c_24__type__11337___24t(V0__P)
     => ( ! [V1__p] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
           => ( p(happ(V0__P,V1__p))
             => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
       => ( ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
             => ( p(happ(V0__P,V2__p))
               => p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
         => ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
           => ! [V4__p] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
               => p(happ(V0__P,V4__p)) ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).

fof('Coq.PArith.BinPos.Pos.add_reg_r',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => ! [V2__r] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__r)
             => ( cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V2__r) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V2__r)
               => V0__p = V1__q ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__88141___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__121152___24t(V0__A,V1__B,V3__g)
                 => ! [V4__h] :
                      ( c_24__type__454___24t(V0__A,V1__B,V4__h)
                     => ( ! [V5__a] :
                            ( t(V5__a,V0__A)
                           => happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
                       => ! [V6__p] :
                            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
                           => ! [V7__a] :
                                ( t(V7__a,V0__A)
                               => happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.le_antisym',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V1__q)
           => ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__q,V0__p)
             => V0__p = V1__q ) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.lt_total',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q)
            | V0__p = V1__q
            | cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p) ) ) ) ).

fof('Coq.PArith.BinPos.Pos.mul_comm',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__q] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__q,V0__p) ) ) ).

fof('Coq.Reals.RIneq.Req_dec',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( V0__r1 = V1__r2
            | V0__r1 != V1__r2 ) ) ) ).

fof('Coq.Reals.RIneq.Req_le_sym',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( V1__r2 = V0__r1
           => cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).

fof('Coq.Reals.RIneq.Rge_antisym',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
           => ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)
             => V0__r1 = V1__r2 ) ) ) ) ).

fof('Coq.Reals.RIneq.Rle_antisym',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
           => ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)
             => V0__r1 = V1__r2 ) ) ) ) ).

fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
           => V0__r1 != V1__r2 ) ) ) ).

fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
    ! [V0__r] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
     => cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).

fof('Coq.Reals.RIneq.f_equal_R',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__f] :
          ( c_24__type__118622___24t(V0__B,V1__f)
         => ! [V2__x] :
              ( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
             => ! [V3__y] :
                  ( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
                 => ( V2__x = V3__y
                   => happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).

fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
    ! [V0__r1] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
     => ! [V1__r2] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
         => cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).

fof('Coq.Relations.Relations.inverse_image_of_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__88141___24t(V0__A,V1__B,V2__f)
             => cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__118656___24a3(V0__A,V1__B,V2__f)) ) ) ) ).

fof('Coq.Setoids.Setoid.gen_st',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,c_3d___24a1(V0__A)) ) ).

fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Structures.OrderedTypeEx.Z_as_OT.lt_not_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
           => V0__x != V1__y ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_BootStrap.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.Private_BootStrap.opp_inj',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
           => V0__n = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.IsTotal.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V1__y != V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_neq_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( V0__x != V1__y
             => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x != V1__y
               => ( V1__y = V2__z
                 => V0__x != V2__z ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x != V1__y
           => V1__y != V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ ( V0__x != V1__y )
           => V0__x = V1__y ) ) ) ).

fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
       => cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = V0__n ) ) ).

fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
              <=> V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.ZArith.BinInt.Z.add_reg_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p)
               => V1__m = V2__p ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.bits_inj\'',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
         => ( ! [V2__n] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n))
                 => cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n) ) )
           => V0__a = V1__b ) ) ) ).

fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__11310___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).

fof('Coq.ZArith.BinInt.Z.eq_opp_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m
          <=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_opp_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
          <=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
          <=> V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
             => V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
    cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).

fof('Coq.ZArith.BinInt.Z.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
    cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4583,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4684,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
    p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).

fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
    p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).

fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
          <=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
           => V0__n != V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_succ_pred',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ! [V1__n] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__z,V1__n))
           => cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V1__n)) = V1__n ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.max_id',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.max_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
           => cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).

fof('Coq.ZArith.BinInt.Z.max_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.max_spec',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
              & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
            | ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
              & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.min_id',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.min_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).

fof('Coq.ZArith.BinInt.Z.min_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
           => cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).

fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).

fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.ZArith.BinInt.Z.neq_sym',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( V0__n != V1__m
           => V1__m != V0__n ) ) ) ).

fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
           => V0__n = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.opp_inj_wd',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
          <=> V0__n = V1__m ) ) ) ).

fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.pred_succ',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.sub_0_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).

fof('Coq.ZArith.BinInt.Z.succ_inj',axiom,
    ! [V0__n1] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
           => V0__n1 = V1__n2 ) ) ) ).

fof('Coq.ZArith.BinInt.Z.succ_inj_wd',axiom,
    ! [V0__n1] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
          <=> V0__n1 = V1__n2 ) ) ) ).

fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).

fof('Coq.ZArith.Zmin.Zmin_irreducible',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n
            | cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).

fof('Coq.ZArith.Zorder.Zle_lt_or_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
              | V0__n = V1__m ) ) ) ) ).

fof('Coq.ZArith.Zorder.Ztrichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__120963___24a2(V0__x,V1__y)) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_Prop',axiom,
    ! [V0__S] :
      ( cType___24t(V0__S)
     => ! [V1__x] :
          ( t(V1__x,V0__S)
         => ! [V2__y] :
              ( t(V2__y,V0__S)
             => cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(c_24__prop__120961___24a3(V0__S,V1__x,V2__y)) ) ) ) ).

fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_refl_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( V0__x = V0__x
      <=> p(c_24True) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
             => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.new_var',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ? [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
          & V0__x = V1__y ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
                                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                     => ! [V10__x] :
                                          ( t(V10__x,V0__R)
                                         => p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => ! [V11__z] :
                                                ( t(V11__z,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__radd] :
          ( c_24__type__150___24t(V0__R,V1__radd)
         => ! [V2__rmul] :
              ( c_24__type__150___24t(V0__R,V2__rmul)
             => ! [V3__ropp] :
                  ( c_24__type__156___24t(V0__R,V3__ropp)
                 => cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__radd] :
          ( c_24__type__150___24t(V0__R,V1__radd)
         => ! [V2__rmul] :
              ( c_24__type__150___24t(V0__R,V2__rmul)
             => cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).

fof('Coq.setoid_ring.Ring_theory.mkmorph',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__150___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__150___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__150___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__156___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__161___24t(V0__R,V7__req)
                                 => ! [V8__C] :
                                      ( cType___24t(V8__C)
                                     => ! [V9__cO] :
                                          ( t(V9__cO,V8__C)
                                         => ! [V10__cI] :
                                              ( t(V10__cI,V8__C)
                                             => ! [V11__cadd] :
                                                  ( c_24__type__440___24t(V0__R,V8__C,V11__cadd)
                                                 => ! [V12__cmul] :
                                                      ( c_24__type__440___24t(V0__R,V8__C,V12__cmul)
                                                     => ! [V13__csub] :
                                                          ( c_24__type__440___24t(V0__R,V8__C,V13__csub)
                                                         => ! [V14__copp] :
                                                              ( c_24__type__454___24t(V0__R,V8__C,V14__copp)
                                                             => ! [V15__ceqb] :
                                                                  ( c_24__type__461___24t(V0__R,V8__C,V15__ceqb)
                                                                 => ! [V16__phi] :
                                                                      ( c_24__type__465___24t(V0__R,V8__C,V16__phi)
                                                                     => ( p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO))
                                                                       => ( p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI))
                                                                         => ( ! [V19__x] :
                                                                                ( t(V19__x,V8__C)
                                                                               => ! [V20__y] :
                                                                                    ( t(V20__y,V8__C)
                                                                                   => p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V19__x),V20__y))),happ(happ(V3__radd,happ(V16__phi,V19__x)),happ(V16__phi,V20__y)))) ) )
                                                                           => ( ! [V20__x] :
                                                                                  ( t(V20__x,V8__C)
                                                                                 => ! [V21__y] :
                                                                                      ( t(V21__y,V8__C)
                                                                                     => p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V20__x),V21__y))),happ(happ(V5__rsub,happ(V16__phi,V20__x)),happ(V16__phi,V21__y)))) ) )
                                                                             => ( ! [V21__x] :
                                                                                    ( t(V21__x,V8__C)
                                                                                   => ! [V22__y] :
                                                                                        ( t(V22__y,V8__C)
                                                                                       => p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V21__x),V22__y))),happ(happ(V4__rmul,happ(V16__phi,V21__x)),happ(V16__phi,V22__y)))) ) )
                                                                               => ( ! [V22__x] :
                                                                                      ( t(V22__x,V8__C)
                                                                                     => p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V22__x))),happ(V6__ropp,happ(V16__phi,V22__x)))) )
                                                                                 => ( ! [V23__x] :
                                                                                        ( t(V23__x,V8__C)
                                                                                       => ! [V24__y] :
                                                                                            ( t(V24__y,V8__C)
                                                                                           => ( happ(happ(V15__ceqb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                             => p(happ(happ(V7__req,happ(V16__phi,V23__x)),happ(V16__phi,V24__y))) ) ) )
                                                                                   => cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Fset.MapDomRestrBy_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,V3__m_27)),c_24__lam__88030___24a4(V0__A,V1__B,V2__m,V3__m_27)) ) ) ) ) ).

fof('IntMap.Fset.MapDomRestrTo_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V1__B,V3__m_27)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eFset_2eMapDomRestrTo___24a4(V0__A,V1__B,V2__m,V3__m_27)),c_24__lam__87907___24a4(V0__A,V1__B,V2__m,V3__m_27)) ) ) ) ) ).

fof('IntMap.Fset.in_FSet_inter',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetInter___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2eandb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27)) ) ) ) ).

fof('IntMap.Fset.in_FSet_union',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eFset_2ein__FSet___24a2(V2__a,cIntMap_2eFset_2eFSetUnion___24a2(V0__s,V1__s_27)) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s),cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27)) ) ) ) ).

fof('IntMap.Fset.in_dom_M0',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,cIntMap_2eMap_2eM0___24a1(V0__A)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('IntMap.Fset.in_dom_M1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a0,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y)) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,V2__a0) ) ) ) ) ).

fof('IntMap.Fset.in_dom_M1_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => cIntMap_2eFset_2ein__dom___24a3(V0__A,V1__a,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y)) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('IntMap.Fset.in_dom_M1_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a0] :
              ( cIntMap_2eMap_2ead___24t(V2__a0)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a0,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y)) = cCoq_2eInit_2eDatatypes_2etrue
                   => V1__a = V2__a0 ) ) ) ) ) ).

fof('IntMap.Fset.in_dom_none',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ( cIntMap_2eFset_2ein__dom___24a3(V0__A,V2__a,V1__m) = cCoq_2eInit_2eDatatypes_2efalse
               => cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V2__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ).

fof('IntMap.Map.M1_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V1__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__y) ) ) ) ).

fof('IntMap.Map.M1_semantics_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__a,V2__a_27) = cCoq_2eInit_2eDatatypes_2efalse
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y),V2__a_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)),c_24__lam__88939___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_1_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a0] :
                      ( cIntMap_2eMap_2ead___24t(V4__a0)
                     => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                       => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m_27,V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                         => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V3__m_27),V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_2_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a0] :
                      ( cIntMap_2eMap_2ead___24t(V4__a0)
                     => ! [V5__y0] :
                          ( t(V5__y0,V0__A)
                         => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                           => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m_27,V4__a0) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y0)
                             => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V3__m_27),V4__a0) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y0) ) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_2_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a0] :
                      ( cIntMap_2eMap_2ead___24t(V4__a0)
                     => ! [V5__y0] :
                          ( t(V5__y0,V0__A)
                         => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V4__a0) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y0)
                           => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m_27,V4__a0) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                             => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V3__m_27),V4__a0) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y0) ) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_3_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a0] :
          ( cIntMap_2eMap_2ead___24t(V1__a0)
         => ! [V2__y0] :
              ( t(V2__y0,V0__A)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ! [V6__y_27] :
                              ( t(V6__y_27,V0__A)
                             => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a0,V2__y0),V4__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y)
                               => ( cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m_27,V4__a) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V6__y_27)
                                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a0,V2__y0),V3__m_27),V4__a) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapDelta_semantics_comm',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapDelta___24a3(V0__A,V2__m_27,V1__m))) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_0',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2efalse
           => ! [V3__m] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V3__m,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ( cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V1__a) = cCoq_2eInit_2eDatatypes_2etrue
           => ! [V3__m] :
                ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m)
               => ! [V4__m_27] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m_27)
                   => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V3__m,V4__m_27),V1__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V4__m_27,cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V1__a)) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_M2_bit_0_if',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27),V3__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_247052___24a4(V0__A,V1__m,V2__m_27,V3__a) ) ) ) ) ).

fof('IntMap.Map.MapGet_if_commute',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__b] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__m_27] :
                  ( cIntMap_2eMap_2eMap___24t(V0__A,V3__m_27)
                 => ! [V4__a] :
                      ( cIntMap_2eMap_2ead___24t(V4__a)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488569___24a4(V0__A,V1__b,V2__m,V3__m_27),V4__a) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488575___24a5(V0__A,V1__b,V2__m,V3__m_27,V4__a) ) ) ) ) ) ).

fof('IntMap.Map.MapGet_if_same',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__b] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__b)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488579___24a3(V0__A,V1__m,V2__b),V3__a) = cIntMap_2eMap_2eMapGet___24a3(V0__A,V1__m,V3__a) ) ) ) ) ).

fof('IntMap.Map.MapMerge_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,V2__m_27)),c_24__lam__88905___24a3(V0__A,V1__m,V2__m_27)) ) ) ) ).

fof('IntMap.Map.MapPut1_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__p] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__a_27] :
                  ( cIntMap_2eMap_2ead___24t(V3__a_27)
                 => ! [V4__y] :
                      ( t(V4__y,V0__A)
                     => ! [V5__y_27] :
                          ( t(V5__y_27,V0__A)
                         => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V2__a,V3__a_27) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V1__p)
                           => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapPut1___24a6(V0__A,V2__a,V4__y,V3__a_27,V5__y_27,V1__p)),c_24__lam__88603___24a5(V0__A,V2__a,V3__a_27,V4__y,V5__y_27)) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapPut_behind_as_before_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__a0] :
                  ( cIntMap_2eMap_2ead___24t(V3__a0)
                 => ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V2__a_27,V3__a0) = cCoq_2eInit_2eDatatypes_2efalse
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => ! [V6__y_27] :
                            ( t(V6__y_27,V0__A)
                           => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V5__y),V2__a_27,V6__y_27),V3__a0) = cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V5__y),V2__a_27,V6__y_27),V3__a0) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapPut_behind_new',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),V2__a) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2488776___24a4(V0__A,V1__m,V2__a,V3__y) ) ) ) ) ).

fof('IntMap.Map.MapPut_behind_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y)),c_24__lam__88800___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y)),c_24__lam__7164___24a4(V0__A,V1__m,V2__a,V3__y)) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ! [V3__a0] :
                  ( cIntMap_2eMap_2ead___24t(V3__a0)
                 => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM0___24a1(V0__A),V1__a,V2__y),V3__a0) = cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V3__a0) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__y_27] :
                      ( t(V4__y_27,V0__A)
                     => ! [V5__a0] :
                          ( cIntMap_2eMap_2ead___24t(V5__a0)
                         => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y),V2__a_27,V4__y_27),V5__a0) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(V0__A,V1__a,V2__a_27,V3__y,V4__y_27,V5__a0) ) ) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics_2_1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( t(V2__y,V0__A)
             => ! [V3__y_27] :
                  ( t(V3__y_27,V0__A)
                 => ! [V4__a0] :
                      ( cIntMap_2eMap_2ead___24t(V4__a0)
                     => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V2__y),V1__a,V3__y_27),V4__a0) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488626___24a4(V0__A,V1__a,V3__y_27,V4__a0) ) ) ) ) ) ).

fof('IntMap.Map.MapPut_semantics_2_2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__a_27] :
              ( cIntMap_2eMap_2ead___24t(V2__a_27)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__y_27] :
                      ( t(V4__y_27,V0__A)
                     => ! [V5__a0] :
                          ( cIntMap_2eMap_2ead___24t(V5__a0)
                         => ! [V6__a_27_27] :
                              ( cIntMap_2eMap_2ead___24t(V6__a_27_27)
                             => ( cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V1__a,V2__a_27) = V6__a_27_27
                               => cIntMap_2eMap_2eMapGet___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V1__a,V3__y),V2__a_27,V4__y_27),V5__a0) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(V0__A,V1__a,V2__a_27,V3__y,V4__y_27,V5__a0) ) ) ) ) ) ) ) ) ).

fof('IntMap.Map.MapRemove_semantics',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V2__a)),c_24__lam__7257___24a3(V0__A,V1__m,V2__a)) ) ) ) ).

fof('IntMap.Map.Map_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__6965___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cIntMap_2eMap_2eM0___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__a] :
                      ( t(V4__a,V0__A)
                     => p(happ(V1__P,cIntMap_2eMap_2eM1___24a3(V0__A,V3__a,V4__a))) ) )
             => ( ! [V4__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V4__m)
                   => ( p(happ(V1__P,V4__m))
                     => ! [V6__m] :
                          ( cIntMap_2eMap_2eMap___24t(V0__A,V6__m)
                         => ( p(happ(V1__P,V6__m))
                           => p(happ(V1__P,cIntMap_2eMap_2eM2___24a3(V0__A,V4__m,V6__m))) ) ) ) )
               => ! [V5__m] :
                    ( cIntMap_2eMap_2eMap___24t(V0__A,V5__m)
                   => p(happ(V1__P,V5__m)) ) ) ) ) ) ) ).

fof('IntMap.Map.makeM2_M2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => cIntMap_2eMap_2eeqm___24a3(V0__A,cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2emakeM2___24a3(V0__A,V1__m,V2__m_27)),cIntMap_2eMap_2eMapGet___24a2(V0__A,cIntMap_2eMap_2eM2___24a3(V0__A,V1__m,V2__m_27))) ) ) ) ).

fof('IntMap.Mapaxioms.FSet_ext',axiom,
    ! [V0__s] :
      ( cIntMap_2eFset_2eFSet___24t(V0__s)
     => ! [V1__s_27] :
          ( cIntMap_2eFset_2eFSet___24t(V1__s_27)
         => ( ! [V2__a] :
                ( cIntMap_2eMap_2ead___24t(V2__a)
               => cIntMap_2eFset_2ein__FSet___24a2(V2__a,V0__s) = cIntMap_2eFset_2ein__FSet___24a2(V2__a,V1__s_27) )
           => cIntMap_2eMapaxioms_2eeqmap___24a3(cCoq_2eInit_2eDatatypes_2eunit,V0__s,V1__s_27) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_as_Merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V2__a,V3__y),cIntMap_2eMap_2eMapMerge___24a3(V0__A,V1__m,cIntMap_2eMap_2eM1___24a3(V0__A,V2__a,V3__y))) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_behind_as_Merge',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V2__a,V3__y),cIntMap_2eMap_2eMapMerge___24a3(V0__A,cIntMap_2eMap_2eM1___24a3(V0__A,V2__a,V3__y),V1__m)) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_behind_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V1__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut__behind___24a4(V0__A,V2__m_27,V4__a,V5__y)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapPut_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => ! [V5__y] :
                        ( t(V5__y,V0__A)
                       => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapPut___24a4(V0__A,V1__m,V4__a,V5__y),cIntMap_2eMap_2eMapPut___24a4(V0__A,V2__m_27,V4__a,V5__y)) ) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapRemove_as_RestrBy',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__m] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V2__m,V3__a),cIntMap_2eFset_2eMapDomRestrBy___24a4(V0__A,V1__B,V2__m,cIntMap_2eMap_2eM1___24a3(V1__B,V3__a,V4__y))) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.MapRemove_ext',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(V0__A,V1__m)
         => ! [V2__m_27] :
              ( cIntMap_2eMap_2eMap___24t(V0__A,V2__m_27)
             => ( cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,V1__m,V2__m_27)
               => ! [V4__a] :
                    ( cIntMap_2eMap_2ead___24t(V4__a)
                   => cIntMap_2eMapaxioms_2eeqmap___24a3(V0__A,cIntMap_2eMap_2eMapRemove___24a3(V0__A,V1__m,V4__a),cIntMap_2eMap_2eMapRemove___24a3(V0__A,V2__m_27,V4__a)) ) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqm_refl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__88477___24t(V0__A,V1__f)
         => cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V1__f) ) ) ).

fof('IntMap.Mapaxioms.eqm_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__88477___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__88477___24t(V0__A,V2__f_27)
             => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V2__f_27)
               => cIntMap_2eMap_2eeqm___24a3(V0__A,V2__f_27,V1__f) ) ) ) ) ).

fof('IntMap.Mapaxioms.eqm_trans',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__88477___24t(V0__A,V1__f)
         => ! [V2__f_27] :
              ( c_24__type__88477___24t(V0__A,V2__f_27)
             => ! [V3__f_27_27] :
                  ( c_24__type__88477___24t(V0__A,V3__f_27_27)
                 => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V2__f_27)
                   => ( cIntMap_2eMap_2eeqm___24a3(V0__A,V2__f_27,V3__f_27_27)
                     => cIntMap_2eMap_2eeqm___24a3(V0__A,V1__f,V3__f_27_27) ) ) ) ) ) ) ).

fof('Mapiter.MapIter.MapFoldDef.MapFold_empty',axiom,
    ! [V0__f] :
      ( c_24__type__111448___24t(V0__f)
     => cMapiter_2eMapIter_2eMapFoldDef_2eMapFold___24a2(V0__f,cIntMap_2eMap_2eM0___24a1(cA)) = cneutral ) ).

fof('Mapiter.MapIter.MapSweep_semantics_1',axiom,
    ! [V0__f] :
      ( c_24__type__4___24t(V0__f)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m)
         => ! [V2__a] :
              ( cIntMap_2eMap_2ead___24t(V2__a)
             => ! [V3__y] :
                  ( cA___24t(V3__y)
                 => ( cMapiter_2eMapIter_2eMapSweep___24a2(V0__f,V1__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,cA,V2__a,V3__y))
                   => happ(happ(V0__f,V2__a),V3__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).

fof('Mapiter.MapIter.MapSweep_semantics_1_1',axiom,
    ! [V0__f] :
      ( c_24__type__4___24t(V0__f)
     => ! [V1__m] :
          ( cIntMap_2eMap_2eMap___24t(cA,V1__m)
         => ! [V2__pf] :
              ( c_24__type__1___24t(V2__pf)
             => ! [V3__a] :
                  ( cIntMap_2eMap_2ead___24t(V3__a)
                 => ! [V4__y] :
                      ( cA___24t(V4__y)
                     => ( cMapiter_2eMapIter_2eMapSweep1___24a3(V0__f,V2__pf,V1__m) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cIntMap_2eMap_2ead,cA),cCoq_2eInit_2eDatatypes_2epair___24a4(cIntMap_2eMap_2ead,cA,V3__a,V4__y))
                       => happ(happ(V0__f,V3__a),V4__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$adef_IntMap.Map.M0_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM0,V_24X1) = cIntMap_2eMap_2eM0___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinInt.Z.Even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eBinInt_2eZ_2eEven,V_24X1))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eEven___24a1(V_24X1) ) ).

fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_117215_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117215,V_24X1),V_24X2),V_24X3) = c_24__prop__117215___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_$_prop_11310_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__11310,V_24X1),V_24X2) = c_24__prop__11310___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88880_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__88880,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__88880___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_102335_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(c_24__lam__102335,V_24X1))
    <=> c_24__lam__102335___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88626_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488626,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488626___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88939_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__88939,V_24X1),V_24X2),V_24X3) = c_24__lam__88939___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_11182_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__11182,V_24X1) = c_24__prop__11182___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).

fof('$adef_IntMap.Fset.MapDomRestrBy_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2eMapDomRestrBy,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2eMapDomRestrBy___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sig_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_120959_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__120959,V_24X1),V_24X2) = c_24__prop__120959___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_7036_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7036,V_24X1),V_24X2),V_24X3) = c_24__lam__7036___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_117216_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117216,V_24X1),V_24X2),V_24X3) = c_24__prop__117216___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumor_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumor__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_7103_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7103,V_24X1),V_24X2),V_24X3) = c_24__lam__7103___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_102338_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__102338,V_24X1) = c_24__lam__102338___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.le_alt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_7103_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7103,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7103___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).

fof('$adef_$_lam_88030_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88030,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88030___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapDelta_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapDelta,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapDelta___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$117232_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117232,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117232___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_$_lam_7244_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7244,V_24X1),V_24X2),V_24X3) = c_24__lam__7244___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_88712_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88712,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88712___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapPut_behind_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut__behind___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2edivide,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPosDef_2ePos_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_120960_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__120960,V_24X1),V_24X2) = c_24__prop__120960___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_102339_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__102339,V_24X1) = c_24__prop__102339___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Map.MapPut_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2) = cIntMap_2eMap_2eMapPut___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumor_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumor__rec___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_117219_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__117219,V_24X1),V_24X2) = c_24__prop__117219___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.makeM2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2emakeM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2emakeM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_7354_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7354,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7354___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Mapiter.MapIter.MapCollect1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cMapiter_2eMapIter_2eMapCollect1,V_24X1),V_24X2),V_24X3) = cMapiter_2eMapIter_2eMapCollect1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_121055_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__121055,V_24X1),V_24X2) = c_24__lam__121055___24a2(V_24X1,V_24X2) ).

fof('$adef_$_let_var_6_p_1156_1159_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__1156__1159,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__1156__1159___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).

fof('$adef_$_lam_7304_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7304,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7304___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.hd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).

fof('$adef_$_lam_467_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__467,V_24X1) = c_24__lam__467___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).

fof('$adef_$_lam_88905_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__88905,V_24X1),V_24X2),V_24X3) = c_24__lam__88905___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).

fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
    <=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).

fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).

fof('$adef_$_lam_118656_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__118656,V_24X1),V_24X2),V_24X3) = c_24__lam__118656___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_7244_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7244,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7244___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumor_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumor__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumor__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_let_var_8_m_88537_88540_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__var__8__m__88537__88540,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__var__8__m__88537__88540___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_7140_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7140,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7140___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_7236_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7236,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7236___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_fix_121137_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__121137__v__CANONICAL__0,V_24X1) = c_24__fix__121137__v__CANONICAL__0___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a1(V_24X1) ).

fof('$adef_$_lam_7236_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7236,V_24X1),V_24X2),V_24X3) = c_24__lam__7236___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.Map_rect_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMap__rect,V_24X1),V_24X2) = cIntMap_2eMap_2eMap__rect___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_88464_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__88464,V_24X1),V_24X2) = c_24__prop__88464___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88030_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__88030,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__88030___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_IntMap.Map.M1_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eM1,V_24X1) = cIntMap_2eMap_2eM1___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88939_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88939,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88939___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88569_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488569,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488569___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_88603_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__88603,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__88603___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_IntMap.Map.M1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM1,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eis__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eis__true___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_7257_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7257,V_24X1),V_24X2),V_24X3) = c_24__lam__7257___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).

fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapPut1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMap_2eMapPut1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMap_2eMapPut1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapRemove_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapRemove,V_24X1),V_24X2) = cIntMap_2eMap_2eMapRemove___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Sets.Relations_1.Antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSets_2eRelations__1_2eAntisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_$_lam_87793_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__87793,V_24X1),V_24X2),V_24X3) = c_24__lam__87793___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).

fof('$adef_$_lam_7228_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__7228,V_24X1),V_24X2) = c_24__lam__7228___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_$_lam_7164_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7164,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7164___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
    <=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).

fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).

fof('$adef_$_lam_117405_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__117405,V_24X1),V_24X2),V_24X3) = c_24__lam__117405___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Fset.MapDomRestrBy_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eFset_2eMapDomRestrBy,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eFset_2eMapDomRestrBy___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$121121_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24121121___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_121059_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__121059,V_24X1) = c_24__lam__121059___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_111471_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__111471,V_24X1) = c_24__lam__111471___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.Add_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_88800_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__88800,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__88800___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sig_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig__rec___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_87866_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__87866,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__87866___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$118689_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24118689,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24118689___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).

fof('$adef_IntMap.Map.MapDelta_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapDelta,V_24X1),V_24X2) = cIntMap_2eMap_2eMapDelta___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$117248_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117248,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117248___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Map.M2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eM2,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eM2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_7009_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7009,V_24X1),V_24X2),V_24X3) = c_24__lam__7009___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_fix_102347_1_add_carry_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__102347__1__add__carry,V_24X1),V_24X2) = c_24__fix__102347__1__add__carry___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Fset.MapDomRestrTo_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eFset_2eMapDomRestrTo,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eFset_2eMapDomRestrTo___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.prod$11121_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411121,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
    <=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2411121___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).

fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Bool.Sumbool.sumbool_of_bool_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eSumbool_2esumbool__of__bool,V_24X1) = cCoq_2eBool_2eSumbool_2esumbool__of__bool___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.land_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_$_lam_7140_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7140,V_24X1),V_24X2),V_24X3) = c_24__lam__7140___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_121055_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__121055,V_24X1) = c_24__lam__121055___24a1(V_24X1) ).

fof('$adef_$_lam_7292_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__7292,V_24X1),V_24X2) = c_24__lam__7292___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88603_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__88603,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__88603___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Init.Nat.sqrt_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2esqrt,V_24X1) = cCoq_2eInit_2eNat_2esqrt___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.In_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_IntMap.Map.MapPut_behind_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut__behind,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut__behind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_87957_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__87957,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__87957___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_87907_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__87907,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__87907___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_111469_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__111469,V_24X1) = c_24__lam__111469___24a1(V_24X1) ).

fof('$adef_Coq.Init.Peano.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.exist_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Logic.EqdepFacts.Streicher_K__$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__,V_24X1))
    <=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K_____24a1(V_24X1) ) ).

fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Even.even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
    <=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Mapiter.MapIter.MapCollect_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cMapiter_2eMapIter_2eMapCollect,V_24X1),V_24X2) = cMapiter_2eMapIter_2eMapCollect___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapSingleton_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMapSingleton,V_24X1) = cIntMap_2eMap_2eMapSingleton___24a1(V_24X1) ).

fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
    <=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).

fof('$adef_IntMap.Mapaxioms.eqmap_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cIntMap_2eMapaxioms_2eeqmap,V_24X1),V_24X2),V_24X3))
    <=> cIntMap_2eMapaxioms_2eeqmap___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Fset.in_dom_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eFset_2ein__dom,V_24X1) = cIntMap_2eFset_2ein__dom___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Map.MapMerge_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapMerge___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Mapiter.MapIter.MapSweep1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cMapiter_2eMapIter_2eMapSweep1,V_24X1),V_24X2),V_24X3) = cMapiter_2eMapIter_2eMapSweep1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.List.nth_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.NArith.BinNat.N.discr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2ediscr,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2ediscr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
    <=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).

fof('$adef_$_let_var_6_p_1158_1160_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__1158__1160,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__1158__1160___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_7228_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__7228,V_24X1) = c_24__lam__7228___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).

fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$117253_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117253,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117253___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_7001_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__7001,V_24X1) = c_24__lam__7001___24a1(V_24X1) ).

fof('$adef_$_lam_102345_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__102345,V_24X1),V_24X2))
    <=> c_24__lam__102345___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).

fof('$adef_IntMap.Fset.in_FSet_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2ein__FSet,V_24X1),V_24X2) = cIntMap_2eFset_2ein__FSet___24a2(V_24X1,V_24X2) ).

fof('$adef_Mapiter.MapIter.MapFoldDef.MapFold1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1,V_24X1),V_24X2),V_24X3) = cMapiter_2eMapIter_2eMapFoldDef_2eMapFold1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_120981_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__120981,V_24X1) = c_24__lam__120981___24a1(V_24X1) ).

fof('$adef_$_lam_113374_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__113374,V_24X1) = c_24__lam__113374___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_87808_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__87808,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__87808___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Mapiter.MapIter.MapSweep_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cMapiter_2eMapIter_2eMapSweep,V_24X1),V_24X2) = cMapiter_2eMapIter_2eMapSweep___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88575_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488575,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488575___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.Init.Specif.sigT_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esigT__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_Mapiter.MapIter.MapSweep2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cMapiter_2eMapIter_2eMapSweep2,V_24X1),V_24X2),V_24X3) = cMapiter_2eMapIter_2eMapSweep2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$117243_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24117243___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).

fof('$adef_$_prop_121001_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__121001,V_24X1),V_24X2) = c_24__prop__121001___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).

fof('$adef_$_lam_7001_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__7001,V_24X1),V_24X2) = c_24__lam__7001___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_121027_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__121027,V_24X1),V_24X2) = c_24__prop__121027___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_87866_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__87866,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__87866___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.gcd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
    <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).

fof('$adef_$_lam_7036_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7036,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7036___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Map.Map_rec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMap__rec,V_24X1),V_24X2) = cIntMap_2eMap_2eMap__rec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sig_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esig__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eSpecif_2esig__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_IntMap.Map.MapCard_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapCard,V_24X1),V_24X2) = cIntMap_2eMap_2eMapCard___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapEmptyp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapEmptyp,V_24X1),V_24X2) = cIntMap_2eMap_2eMapEmptyp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88880_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88880,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88880___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$7052_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_247052,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_247052___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_87793_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__87793,V_24X1),V_24X2) = c_24__lam__87793___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.Even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eEven,V_24X1))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eEven___24a1(V_24X1) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88547_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488547,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488547___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_lam_88463_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__88463,V_24X1),V_24X2) = c_24__lam__88463___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88712_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__88712,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__88712___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).

fof('$adef_IntMap.Map.Map_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cIntMap_2eMap_2eMap__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cIntMap_2eMap_2eMap__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$118706_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24118706___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.Ndigits.Neven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eNArith_2eNdigits_2eNeven,V_24X1))
    <=> cCoq_2eNArith_2eNdigits_2eNeven___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Nat.testbit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2etestbit,V_24X1) = cCoq_2eInit_2eNat_2etestbit___24a1(V_24X1) ).

fof('$adef_Coq.Logic.EqdepFacts.UIP_refl_on__$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1),V_24X2))
    <=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.prod_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_7164_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7164,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7164___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapGet_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2) = cIntMap_2eMap_2eMapGet___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.String.String_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_117214_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117214,V_24X1),V_24X2),V_24X3) = c_24__prop__117214___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.inright_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einright___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).

fof('$adef_$_lam_7354_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7354,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7354___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).

fof('$adef_$_lam_7009_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7009,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7009___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$11350_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411350,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411350___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_IntMap.Map.MapPut_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cIntMap_2eMap_2eMapPut,V_24X1),V_24X2),V_24X3),V_24X4) = cIntMap_2eMap_2eMapPut___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_op_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cop,V_24X1),V_24X2) = cop___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.MapMerge_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eMap_2eMapMerge,V_24X1),V_24X2) = cIntMap_2eMap_2eMapMerge___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_$_lam_88800_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88800,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88800___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
    <=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_87808_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__87808,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__87808___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_88749_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__88749,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__88749___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_IntMap.Map.MapRemove_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapRemove,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapRemove___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_121048_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__121048,V_24X1) = c_24__lam__121048___24a1(V_24X1) ).

fof('$adef_$_lam_117405_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__117405,V_24X1),V_24X2) = c_24__lam__117405___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_117213_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__117213,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__117213___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.FSetUnion_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetUnion,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetUnion___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_case_Coq.Init.Datatypes.option$88776_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eoption_2488776,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2eoption_2488776___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_111469_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__111469,V_24X1),V_24X2) = c_24__lam__111469___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_120961_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__120961,V_24X1),V_24X2),V_24X3) = c_24__prop__120961___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.newMap_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2enewMap,V_24X1) = cIntMap_2eMap_2enewMap___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_88905_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88905,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88905___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_87907_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__87907,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__87907___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.List.map_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).

fof('$adef_$_lam_102338_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__lam__102338,V_24X1),V_24X2))
    <=> c_24__lam__102338___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
    <=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88579_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488579,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488579___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.Ndigits.Nodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eNArith_2eNdigits_2eNodd,V_24X1))
    <=> cCoq_2eNArith_2eNdigits_2eNodd___24a1(V_24X1) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_$_lam_102345_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__102345,V_24X1) = c_24__lam__102345___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.sqrt_iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_7257_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7257,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7257___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).

fof('$adef_$_prop_117218_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117218,V_24X1),V_24X2),V_24X3) = c_24__prop__117218___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).

fof('$adef_$_lam_7292_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__7292,V_24X1) = c_24__lam__7292___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_7304_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7304,V_24X1),V_24X2),V_24X3) = c_24__lam__7304___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_88749_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__88749,V_24X1),V_24X2),V_24X3) = c_24__lam__88749___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_88848_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__88848,V_24X1),V_24X2),V_24X3) = c_24__lam__88848___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_87999_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__87999,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__87999___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_120963_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__120963,V_24X1),V_24X2) = c_24__prop__120963___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_IntMap.Fset.FSetInter_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetInter,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetInter___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_111471_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__111471,V_24X1),V_24X2) = c_24__lam__111471___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.FSetDiff_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetDiff,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetDiff___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_117217_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__117217,V_24X1),V_24X2),V_24X3) = c_24__prop__117217___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$118711_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24118711___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.left_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
    <=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).

fof('$adef_$_prop_102346_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__102346,V_24X1) = c_24__prop__102346___24a1(V_24X1) ).

fof('$adef_IntMap.Map.MapGet_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eMap_2eMapGet,V_24X1),V_24X2),V_24X3) = cIntMap_2eMap_2eMapGet___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_87999_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__87999,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__87999___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_$_lam_113374_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__113374,V_24X1),V_24X2) = c_24__lam__113374___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.tl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.leb_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eBool_2eBool_2eleb,V_24X1),V_24X2))
    <=> cCoq_2eBool_2eBool_2eleb___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_11181_$a1',axiom,
    ! [V_24X1] : happ(c_24__prop__11181,V_24X1) = c_24__prop__11181___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
    <=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_118656_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(c_24__lam__118656,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> c_24__lam__118656___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.le_alt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele__alt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele__alt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Specif.left_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Fset.MapDomRestrTo_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2eMapDomRestrTo,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2eMapDomRestrTo___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_88848_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__88848,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__88848___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_87957_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__87957,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__87957___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$11355_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411355,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2411355___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_121048_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__121048,V_24X1),V_24X2) = c_24__lam__121048___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.eqm_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cIntMap_2eMap_2eeqm,V_24X1),V_24X2),V_24X3))
    <=> cIntMap_2eMap_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Map.Map_$a1',axiom,
    ! [V_24X1] : happ(cIntMap_2eMap_2eMap,V_24X1) = cIntMap_2eMap_2eMap___24a1(V_24X1) ).

fof('$adef_Mapiter.MapIter.MapFoldDef.MapFold_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cMapiter_2eMapIter_2eMapFoldDef_2eMapFold,V_24X1),V_24X2) = cMapiter_2eMapIter_2eMapFoldDef_2eMapFold___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sumbool_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$88639_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2488639___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Specif.right_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_120981_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__120981,V_24X1),V_24X2) = c_24__lam__120981___24a2(V_24X1,V_24X2) ).

fof('$adef_IntMap.Fset.MapDom_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eMapDom,V_24X1),V_24X2) = cIntMap_2eFset_2eMapDom___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).

fof('$adef_$_lam_88463_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(c_24__lam__88463,V_24X1),V_24X2),V_24X3))
    <=> c_24__lam__88463___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).

fof('$adef_IntMap.Fset.FSetDelta_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cIntMap_2eFset_2eFSetDelta,V_24X1),V_24X2) = cIntMap_2eFset_2eFSetDelta___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_IntMap.Fset.in_dom_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cIntMap_2eFset_2ein__dom,V_24X1),V_24X2),V_24X3) = cIntMap_2eFset_2ein__dom___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$tdef_$_type_83001',axiom,
    ! [V_24Y] :
      ( c_24__type__83001___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83001) ) ).

fof('$tdef_$_type_88477',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__88477___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__88477___24a1(V_24X1)) ) ).

fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_113530',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113530___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113530___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_5176',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__5176___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__5176___24a1(V_24X1)) ) ).

fof('$tdef_$_type_111517',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111517___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111517___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_119395',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119395___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_111489',axiom,
    ! [V_24Y] :
      ( c_24__type__111489___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111489) ) ).

fof('$tdef_$_type_105823',axiom,
    ! [V_24Y] :
      ( c_24__type__105823___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105823) ) ).

fof('$tdef_$_type_119220',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__119220___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__119220___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_118173',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__118173___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__118173___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).

fof('$tdef_$_type_113452',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113452___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113452___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_98627',axiom,
    ! [V_24Y] :
      ( c_24__type__98627___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98627) ) ).

fof('$tdef_$_type_82791',axiom,
    ! [V_24Y] :
      ( c_24__type__82791___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82791) ) ).

fof('$tdef_$_type_104052',axiom,
    ! [V_24Y] :
      ( c_24__type__104052___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104052) ) ).

fof('$tdef_$_type_101311',axiom,
    ! [V_24Y] :
      ( c_24__type__101311___24t(V_24Y)
    <=> t(V_24Y,c_24__type__101311) ) ).

fof('$tdef_$_type_111553',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__111553___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__111553___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_89617',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89617___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89617___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).

fof('$tdef_$_type_99223',axiom,
    ! [V_24Y] :
      ( c_24__type__99223___24t(V_24Y)
    <=> t(V_24Y,c_24__type__99223) ) ).

fof('$tdef_$_type_117171',axiom,
    ! [V_24Y] :
      ( c_24__type__117171___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117171) ) ).

fof('$tdef_$_type_120998',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__120998___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__120998___24a1(V_24X1)) ) ).

fof('$tdef_$_type_9974',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__9974___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__9974___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_111477',axiom,
    ! [V_24Y] :
      ( c_24__type__111477___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111477) ) ).

fof('$tdef_$_type_113411',axiom,
    ! [V_24Y] :
      ( c_24__type__113411___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113411) ) ).

fof('$tdef_Coq.Init.Specif.sigT2',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_161',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__161___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__161___24a1(V_24X1)) ) ).

fof('$tdef_$_type_7153',axiom,
    ! [V_24Y] :
      ( c_24__type__7153___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7153) ) ).

fof('$tdef_$_type_119103',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__119103___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__119103___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_95957',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__95957___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__95957___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_94273',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__94273___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__94273___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_111509',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111509___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111509___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_23',axiom,
    ! [V_24Y] :
      ( c_24__type__23___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23) ) ).

fof('$tdef_$_type_121220',axiom,
    ! [V_24Y] :
      ( c_24__type__121220___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121220) ) ).

fof('$tdef_$_type_85467',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85467___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85467___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_11343',axiom,
    ! [V_24Y] :
      ( c_24__type__11343___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11343) ) ).

fof('$tdef_$_type_117637',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__117637___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__117637___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_118418',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__118418___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__118418___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_5173',axiom,
    ! [V_24Y] :
      ( c_24__type__5173___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5173) ) ).

fof('$tdef_$_type_111352',axiom,
    ! [V_24Y] :
      ( c_24__type__111352___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111352) ) ).

fof('$tdef_$_type_118977',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__118977___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__118977___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_93604',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__93604___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__93604___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_118336',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__118336___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__118336___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_IntMap.Map.Map',axiom,
    ! [V_24X1,V_24Y] :
      ( cIntMap_2eMap_2eMap___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2eMap___24a1(V_24X1)) ) ).

fof('$tdef_$_type_111560',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__111560___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__111560___24a1(V_24X1)) ) ).

fof('$tdef_$_type_3264',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__3264___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__3264___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_97146',axiom,
    ! [V_24Y] :
      ( c_24__type__97146___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97146) ) ).

fof('$tdef_Coq.Init.Datatypes.bool',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).

fof('$tdef_$_type_105766',axiom,
    ! [V_24Y] :
      ( c_24__type__105766___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105766) ) ).

fof('$tdef_Coq.Init.Datatypes.list',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).

fof('$tdef_$_type_98317',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__98317___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__98317___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_440',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__440___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__440___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_$_type_6911',axiom,
    ! [V_24Y] :
      ( c_24__type__6911___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6911) ) ).

fof('$tdef_$_type_111626',axiom,
    ! [V_24Y] :
      ( c_24__type__111626___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111626) ) ).

fof('$tdef_$_type_91551',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__91551___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__91551___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.option',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).

fof('$tdef_$_type_93258',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__93258___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__93258___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_92912',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__92912___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__92912___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_97155',axiom,
    ! [V_24Y] :
      ( c_24__type__97155___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97155) ) ).

fof('$tdef_$_type_37',axiom,
    ! [V_24Y] :
      ( c_24__type__37___24t(V_24Y)
    <=> t(V_24Y,c_24__type__37) ) ).

fof('$tdef_$_type_121218',axiom,
    ! [V_24Y] :
      ( c_24__type__121218___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121218) ) ).

fof('$tdef_$_type_86556',axiom,
    ! [V_24Y] :
      ( c_24__type__86556___24t(V_24Y)
    <=> t(V_24Y,c_24__type__86556) ) ).

fof('$tdef_$_type_104080',axiom,
    ! [V_24Y] :
      ( c_24__type__104080___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104080) ) ).

fof('$tdef_$_type_111448',axiom,
    ! [V_24Y] :
      ( c_24__type__111448___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111448) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).

fof('$tdef_$_type_105829',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__105829___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__105829___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_118080',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__118080___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__118080___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_4',axiom,
    ! [V_24Y] :
      ( c_24__type__4___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).

fof('$tdef_$_type_82901',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__82901___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__82901___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_117399',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__117399___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__117399___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_98243',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__98243___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__98243___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_120852',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__120852___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__120852___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).

fof('$tdef_$_type_82807',axiom,
    ! [V_24Y] :
      ( c_24__type__82807___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82807) ) ).

fof('$tdef_$_type_121140',axiom,
    ! [V_24Y] :
      ( c_24__type__121140___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121140) ) ).

fof('$tdef_$_type_11214',axiom,
    ! [V_24Y] :
      ( c_24__type__11214___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11214) ) ).

fof('$tdef_$_type_82937',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__82937___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__82937___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_117384',axiom,
    ! [V_24Y] :
      ( c_24__type__117384___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117384) ) ).

fof('$tdef_$_type_120743',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__120743___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__120743___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_88068',axiom,
    ! [V_24Y] :
      ( c_24__type__88068___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88068) ) ).

fof('$tdef_$_type_4941',axiom,
    ! [V_24Y] :
      ( c_24__type__4941___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4941) ) ).

fof('$tdef_$_type_102727',axiom,
    ! [V_24Y] :
      ( c_24__type__102727___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102727) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).

fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).

fof('$tdef_$_type_1487',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__1487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__1487___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_119372',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119372___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119372___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_11187',axiom,
    ! [V_24Y] :
      ( c_24__type__11187___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11187) ) ).

fof('$tdef_$_type_118515',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__118515___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__118515___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_113596',axiom,
    ! [V_24Y] :
      ( c_24__type__113596___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113596) ) ).

fof('$tdef_$_type_11149',axiom,
    ! [V_24Y] :
      ( c_24__type__11149___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11149) ) ).

fof('$tdef_$_type_82922',axiom,
    ! [V_24Y] :
      ( c_24__type__82922___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82922) ) ).

fof('$tdef_$_type_88981',axiom,
    ! [V_24Y] :
      ( c_24__type__88981___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88981) ) ).

fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.Numbers.BinNums.N',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).

fof('$tdef_$_type_386',axiom,
    ! [V_24Y] :
      ( c_24__type__386___24t(V_24Y)
    <=> t(V_24Y,c_24__type__386) ) ).

fof('$tdef_$_type_107',axiom,
    ! [V_24Y] :
      ( c_24__type__107___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107) ) ).

fof('$tdef_Coq.Init.Specif.sig2',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_82926',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82926___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82926___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_3477',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__3477___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__3477___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_1923',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1923___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1923___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Init.Specif.sumbool',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_97997',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__97997___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__97997___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_83034',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__83034___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__83034___24a1(V_24X1)) ) ).

fof('$tdef_$_type_113494',axiom,
    ! [V_24Y] :
      ( c_24__type__113494___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113494) ) ).

fof('$tdef_$_type_111644',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111644___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111644___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_98601',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__98601___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__98601___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).

fof('$tdef_$_type_117180',axiom,
    ! [V_24Y] :
      ( c_24__type__117180___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117180) ) ).

fof('$tdef_$_type_90385',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__90385___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__90385___24a1(V_24X1)) ) ).

fof('$tdef_$_type_118661',axiom,
    ! [V_24Y] :
      ( c_24__type__118661___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118661) ) ).

fof('$tdef_$_type_111557',axiom,
    ! [V_24Y] :
      ( c_24__type__111557___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111557) ) ).

fof('$tdef_$_type_105636',axiom,
    ! [V_24Y] :
      ( c_24__type__105636___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105636) ) ).

fof('$tdef_$_type_118204',axiom,
    ! [V_24Y] :
      ( c_24__type__118204___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118204) ) ).

fof('$tdef_$_type_88141',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__88141___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__88141___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_120978',axiom,
    ! [V_24Y] :
      ( c_24__type__120978___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120978) ) ).

fof('$tdef_$_type_94965',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__94965___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__94965___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_90395',axiom,
    ! [V_24Y] :
      ( c_24__type__90395___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90395) ) ).

fof('$tdef_$_type_117270',axiom,
    ! [V_24Y] :
      ( c_24__type__117270___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117270) ) ).

fof('$tdef_$_type_98515',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__98515___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__98515___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_98558',axiom,
    ! [V_24Y] :
      ( c_24__type__98558___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98558) ) ).

fof('$tdef_$_type_2643',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__2643___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__2643___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_461',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__461___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__461___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_121024',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__121024___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__121024___24a1(V_24X1)) ) ).

fof('$tdef_$_type_118718',axiom,
    ! [V_24Y] :
      ( c_24__type__118718___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118718) ) ).

fof('$tdef_$_type_92566',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__92566___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__92566___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_1863',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1863___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1863___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_90010',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__90010___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__90010___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_111604',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111604___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111604___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_119457',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119457___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119457___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_4909',axiom,
    ! [V_24Y] :
      ( c_24__type__4909___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4909) ) ).

fof('$tdef_$_type_4653',axiom,
    ! [V_24Y] :
      ( c_24__type__4653___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4653) ) ).

fof('$tdef_$_type_111703',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111703___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111703___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_111348',axiom,
    ! [V_24Y] :
      ( c_24__type__111348___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111348) ) ).

fof('$tdef_$_type_87891',axiom,
    ! [V_24Y] :
      ( c_24__type__87891___24t(V_24Y)
    <=> t(V_24Y,c_24__type__87891) ) ).

fof('$tdef_$_type_1',axiom,
    ! [V_24Y] :
      ( c_24__type__1___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_117388',axiom,
    ! [V_24Y] :
      ( c_24__type__117388___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117388) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).

fof('$tdef_$_type_111346',axiom,
    ! [V_24Y] :
      ( c_24__type__111346___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111346) ) ).

fof('$tdef_$_type_119965',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__119965___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__119965___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_118293',axiom,
    ! [V_24Y] :
      ( c_24__type__118293___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118293) ) ).

fof('$tdef_Coq.Init.Datatypes.unit',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).

fof('$tdef_$_type_7046',axiom,
    ! [V_24Y] :
      ( c_24__type__7046___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7046) ) ).

fof('$tdef_$_type_117223',axiom,
    ! [V_24Y] :
      ( c_24__type__117223___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117223) ) ).

fof('$tdef_$_type_102703',axiom,
    ! [V_24Y] :
      ( c_24__type__102703___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102703) ) ).

fof('$tdef_$_type_98119',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__98119___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__98119___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_82805',axiom,
    ! [V_24Y] :
      ( c_24__type__82805___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82805) ) ).

fof('$tdef_Coq.Init.Specif.sig',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_10966',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10966___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_95611',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__95611___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__95611___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_IntMap.Fset.FSet',axiom,
    ! [V_24Y] :
      ( cIntMap_2eFset_2eFSet___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eFset_2eFSet) ) ).

fof('$tdef_$_type_104062',axiom,
    ! [V_24Y] :
      ( c_24__type__104062___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104062) ) ).

fof('$tdef_Coq.Init.Datatypes.sum',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_111451',axiom,
    ! [V_24Y] :
      ( c_24__type__111451___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111451) ) ).

fof('$tdef_$_type_92220',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__92220___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__92220___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_120813',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__120813___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__120813___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_118383',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__118383___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__118383___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
    ! [V_24Y] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).

fof('$tdef_$_type_113770',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113770___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113770___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_104017',axiom,
    ! [V_24Y] :
      ( c_24__type__104017___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104017) ) ).

fof('$tdef_$_type_2430',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__2430___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__2430___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).

fof('$tdef_$_type_85817',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85817___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_98519',axiom,
    ! [V_24Y] :
      ( c_24__type__98519___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98519) ) ).

fof('$tdef_$_type_11171',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__11171___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__11171___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_88563',axiom,
    ! [V_24Y] :
      ( c_24__type__88563___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88563) ) ).

fof('$tdef_$_type_97964',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__97964___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__97964___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_11337',axiom,
    ! [V_24Y] :
      ( c_24__type__11337___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11337) ) ).

fof('$tdef_$_type_98663',axiom,
    ! [V_24Y] :
      ( c_24__type__98663___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98663) ) ).

fof('$tdef_$_type_120993',axiom,
    ! [V_24Y] :
      ( c_24__type__120993___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120993) ) ).

fof('$tdef_$_type_111689',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__111689___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__111689___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_104057',axiom,
    ! [V_24Y] :
      ( c_24__type__104057___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104057) ) ).

fof('$tdef_$_type_111596',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111596___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111596___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_119326',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119326___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119326___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_95288',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__95288___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__95288___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_88167',axiom,
    ! [V_24Y] :
      ( c_24__type__88167___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88167) ) ).

fof('$tdef_$_type_102564',axiom,
    ! [V_24Y] :
      ( c_24__type__102564___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102564) ) ).

fof('$tdef_$_type_6908',axiom,
    ! [V_24Y] :
      ( c_24__type__6908___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6908) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).

fof('$tdef_$_type_88137',axiom,
    ! [V_24Y] :
      ( c_24__type__88137___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88137) ) ).

fof('$tdef_$_type_120340',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__120340___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__120340___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_11197',axiom,
    ! [V_24Y] :
      ( c_24__type__11197___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11197) ) ).

fof('$tdef_Prop',axiom,
    ! [V_24Y] :
      ( cProp___24t(V_24Y)
    <=> t(V_24Y,cProp) ) ).

fof('$tdef_$_type_97141',axiom,
    ! [V_24Y] :
      ( c_24__type__97141___24t(V_24Y)
    <=> t(V_24Y,c_24__type__97141) ) ).

fof('$tdef_$_type_113522',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113522___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113522___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_102383',axiom,
    ! [V_24Y] :
      ( c_24__type__102383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102383) ) ).

fof('$tdef_$_type_88459',axiom,
    ! [V_24Y] :
      ( c_24__type__88459___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88459) ) ).

fof('$tdef_$_type_4583',axiom,
    ! [V_24Y] :
      ( c_24__type__4583___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4583) ) ).

fof('$tdef_$_type_85549',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85549___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_88334',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__88334___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__88334___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_90414',axiom,
    ! [V_24Y] :
      ( c_24__type__90414___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90414) ) ).

fof('$tdef_$_type_118622',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__118622___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__118622___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1604',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__1604___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__1604___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_117257',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__117257___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__117257___24a1(V_24X1)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).

fof('$tdef_$_type_98358',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__98358___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__98358___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_111897',axiom,
    ! [V_24Y] :
      ( c_24__type__111897___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111897) ) ).

fof('$tdef_$_type_105437',axiom,
    ! [V_24Y] :
      ( c_24__type__105437___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105437) ) ).

fof('$tdef_$_type_75',axiom,
    ! [V_24Y] :
      ( c_24__type__75___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75) ) ).

fof('$tdef_$_type_98199',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__98199___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__98199___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_Coq.Init.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

fof('$tdef_$_type_83013',axiom,
    ! [V_24Y] :
      ( c_24__type__83013___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83013) ) ).

fof('$tdef_$_type_116410',axiom,
    ! [V_24Y] :
      ( c_24__type__116410___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116410) ) ).

fof('$tdef_$_type_1839',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1839___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1839___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_120778',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__120778___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__120778___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117162',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__117162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__117162___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_98262',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__98262___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__98262___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_111480',axiom,
    ! [V_24Y] :
      ( c_24__type__111480___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111480) ) ).

fof('$tdef_$_type_98',axiom,
    ! [V_24Y] :
      ( c_24__type__98___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98) ) ).

fof('$tdef_$_type_2856',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__2856___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__2856___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_98645',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__98645___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__98645___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_113590',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113590___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113590___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_112941',axiom,
    ! [V_24Y] :
      ( c_24__type__112941___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112941) ) ).

fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Strings.String.string',axiom,
    ! [V_24Y] :
      ( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).

fof('$tdef_$_type_85374',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85374___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85374___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_6965',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__6965___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__6965___24a1(V_24X1)) ) ).

fof('$tdef_$_type_98163',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__98163___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__98163___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_117277',axiom,
    ! [V_24Y] :
      ( c_24__type__117277___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117277) ) ).

fof('$tdef_$_type_111927',axiom,
    ! [V_24Y] :
      ( c_24__type__111927___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111927) ) ).

fof('$tdef_$_type_6957',axiom,
    ! [V_24Y] :
      ( c_24__type__6957___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6957) ) ).

fof('$tdef_$_type_119349',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119349___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119349___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_94619',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__94619___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__94619___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_113444',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113444___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113444___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_120215',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__120215___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__120215___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_4506',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__4506___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__4506___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_IntMap.Map.ad',axiom,
    ! [V_24Y] :
      ( cIntMap_2eMap_2ead___24t(V_24Y)
    <=> t(V_24Y,cIntMap_2eMap_2ead) ) ).

fof('$tdef_$_type_118618',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__118618___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__118618___24a1(V_24X1)) ) ).

fof('$tdef_$_type_117420',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__117420___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__117420___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_4599',axiom,
    ! [V_24Y] :
      ( c_24__type__4599___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4599) ) ).

fof('$tdef_$_type_1947',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1947___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1947___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_91205',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__91205___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__91205___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_98586',axiom,
    ! [V_24Y] :
      ( c_24__type__98586___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98586) ) ).

fof('$tdef_$_type_111960',axiom,
    ! [V_24Y] :
      ( c_24__type__111960___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111960) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).

fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_117823',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__117823___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__117823___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Init.Specif.sigT',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105545',axiom,
    ! [V_24Y] :
      ( c_24__type__105545___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105545) ) ).

fof('$tdef_$_type_88089',axiom,
    ! [V_24Y] :
      ( c_24__type__88089___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88089) ) ).

fof('$tdef_$_type_97983',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__97983___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__97983___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_120451',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__120451___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__120451___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_5154',axiom,
    ! [V_24Y] :
      ( c_24__type__5154___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5154) ) ).

fof('$tdef_$_type_104039',axiom,
    ! [V_24Y] :
      ( c_24__type__104039___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104039) ) ).

fof('$tdef_$_type_98631',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__98631___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__98631___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_103920',axiom,
    ! [V_24Y] :
      ( c_24__type__103920___24t(V_24Y)
    <=> t(V_24Y,c_24__type__103920) ) ).

fof('$tdef_$_type_3690',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__3690___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__3690___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_A',axiom,
    ! [V_24Y] :
      ( cA___24t(V_24Y)
    <=> t(V_24Y,cA) ) ).

fof('$tdef_$_type_1980',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1980___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1980___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_116403',axiom,
    ! [V_24Y] :
      ( c_24__type__116403___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116403) ) ).

fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).

fof('$tdef_$_type_5161',axiom,
    ! [V_24Y] :
      ( c_24__type__5161___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5161) ) ).

fof('$tdef_$_type_113460',axiom,
    ! [V_24Y] :
      ( c_24__type__113460___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113460) ) ).

fof('$tdef_$_type_85642',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85642___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85642___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_98638',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__98638___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__98638___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_117374',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__117374___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__117374___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_89707',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89707___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89707___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_99258',axiom,
    ! [V_24Y] :
      ( c_24__type__99258___24t(V_24Y)
    <=> t(V_24Y,c_24__type__99258) ) ).

fof('$tdef_$_type_117438',axiom,
    ! [V_24Y] :
      ( c_24__type__117438___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117438) ) ).

fof('$tdef_$_type_112958',axiom,
    ! [V_24Y] :
      ( c_24__type__112958___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112958) ) ).

fof('$tdef_$_type_119715',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__119715___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__119715___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_101300',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__101300___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__101300___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_120694',axiom,
    ! [V_24Y] :
      ( c_24__type__120694___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120694) ) ).

fof('$tdef_$_type_105475',axiom,
    ! [V_24Y] :
      ( c_24__type__105475___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105475) ) ).

fof('$tdef_$_type_88392',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__88392___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__88392___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117730',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__117730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__117730___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_6950',axiom,
    ! [V_24Y] :
      ( c_24__type__6950___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6950) ) ).

fof('$tdef_$_type_156',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__156___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__156___24a1(V_24X1)) ) ).

fof('$tdef_$_type_4601',axiom,
    ! [V_24Y] :
      ( c_24__type__4601___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4601) ) ).

fof('$tdef_$_type_118535',axiom,
    ! [V_24Y] :
      ( c_24__type__118535___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118535) ) ).

fof('$tdef_$_type_119157',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__119157___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__119157___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_4311',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__4311___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__4311___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_10866',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10866___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10866___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_88474',axiom,
    ! [V_24Y] :
      ( c_24__type__88474___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88474) ) ).

fof('$tdef_$_type_121158',axiom,
    ! [V_24Y] :
      ( c_24__type__121158___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121158) ) ).

fof('$tdef_$_type_117356',axiom,
    ! [V_24Y] :
      ( c_24__type__117356___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117356) ) ).

fof('$tdef_$_type_113776',axiom,
    ! [V_24Y] :
      ( c_24__type__113776___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113776) ) ).

fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Init.Specif.sumor',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_98581',axiom,
    ! [V_24Y] :
      ( c_24__type__98581___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98581) ) ).

fof('$tdef_$_type_4684',axiom,
    ! [V_24Y] :
      ( c_24__type__4684___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4684) ) ).

fof('$tdef_$_type_120843',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__120843___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__120843___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_119439',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119439___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119439___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_105789',axiom,
    ! [V_24Y] :
      ( c_24__type__105789___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105789) ) ).

fof('$tdef_$_type_89516',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89516___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89516___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_11008',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11008___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11008___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_375',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__375___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__375___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).

fof('$tdef_$_type_1667',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__1667___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__1667___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_6925',axiom,
    ! [V_24Y] :
      ( c_24__type__6925___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6925) ) ).

fof('$tdef_$_type_121183',axiom,
    ! [V_24Y] :
      ( c_24__type__121183___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121183) ) ).

fof('$tdef_$_type_104032',axiom,
    ! [V_24Y] :
      ( c_24__type__104032___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104032) ) ).

fof('$tdef_$_type_465',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__465___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__465___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_11179',axiom,
    ! [V_24Y] :
      ( c_24__type__11179___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11179) ) ).

fof('$tdef_$_type_3903',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__3903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__3903___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_7248',axiom,
    ! [V_24Y] :
      ( c_24__type__7248___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7248) ) ).

fof('$tdef_$_type_4596',axiom,
    ! [V_24Y] :
      ( c_24__type__4596___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4596) ) ).

fof('$tdef_$_type_118635',axiom,
    ! [V_24Y] :
      ( c_24__type__118635___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118635) ) ).

fof('$tdef_$_type_104071',axiom,
    ! [V_24Y] :
      ( c_24__type__104071___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104071) ) ).

fof('$tdef_$_type_102300',axiom,
    ! [V_24Y] :
      ( c_24__type__102300___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102300) ) ).

fof('$tdef_Coq.Bool.Bool.reflect',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_121152',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__121152___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__121152___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2031',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__2031___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__2031___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_102490',axiom,
    ! [V_24Y] :
      ( c_24__type__102490___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102490) ) ).

fof('$tdef_$_type_90442',axiom,
    ! [V_24Y] :
      ( c_24__type__90442___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90442) ) ).

fof('$tdef_$_type_88381',axiom,
    ! [V_24Y] :
      ( c_24__type__88381___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88381) ) ).

fof('$tdef_$_type_2004',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__2004___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__2004___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_121163',axiom,
    ! [V_24Y] :
      ( c_24__type__121163___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121163) ) ).

fof('$tdef_$_type_120704',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__120704___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__120704___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_102342',axiom,
    ! [V_24Y] :
      ( c_24__type__102342___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102342) ) ).

fof('$tdef_$_type_89415',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89415___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89415___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).

fof('$tdef_$_type_98537',axiom,
    ! [V_24Y] :
      ( c_24__type__98537___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98537) ) ).

fof('$tdef_$_type_5123',axiom,
    ! [V_24Y] :
      ( c_24__type__5123___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5123) ) ).

fof('$tdef_$_type_90417',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__90417___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__90417___24a1(V_24X1)) ) ).

fof('$tdef_$_type_102722',axiom,
    ! [V_24Y] :
      ( c_24__type__102722___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102722) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_$_type_6952',axiom,
    ! [V_24Y] :
      ( c_24__type__6952___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6952) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).

fof('$tdef_$_type_86559',axiom,
    ! [V_24Y] :
      ( c_24__type__86559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__86559) ) ).

fof('$tdef_$_type_120090',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__120090___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__120090___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_119040',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__119040___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__119040___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.Init.Datatypes.nat',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).

fof('$tdef_$_type_111659',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111659___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111659___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1170',axiom,
    ! [V_24Y] :
      ( c_24__type__1170___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1170) ) ).

fof('$tdef_$_type_111486',axiom,
    ! [V_24Y] :
      ( c_24__type__111486___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111486) ) ).

fof('$tdef_$_type_105630',axiom,
    ! [V_24Y] :
      ( c_24__type__105630___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105630) ) ).

fof('$tdef_$_type_119840',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
      ( c_24__type__119840___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
    <=> t(V_24Y,c_24__type__119840___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_$_type_98544',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__98544___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__98544___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_105674',axiom,
    ! [V_24Y] :
      ( c_24__type__105674___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105674) ) ).

fof('$tdef_$_type_104074',axiom,
    ! [V_24Y] :
      ( c_24__type__104074___24t(V_24Y)
    <=> t(V_24Y,c_24__type__104074) ) ).

fof('$tdef_$_type_88174',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__88174___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__88174___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117138',axiom,
    ! [V_24Y] :
      ( c_24__type__117138___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117138) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).

fof('$tdef_$_type_102686',axiom,
    ! [V_24Y] :
      ( c_24__type__102686___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102686) ) ).

fof('$tdef_Coq.Init.Datatypes.prod',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117441',axiom,
    ! [V_24Y] :
      ( c_24__type__117441___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117441) ) ).

fof('$tdef_$_type_111880',axiom,
    ! [V_24Y] :
      ( c_24__type__111880___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111880) ) ).

fof('$tdef_$_type_102441',axiom,
    ! [V_24Y] :
      ( c_24__type__102441___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102441) ) ).

fof('$tdef_$_type_35',axiom,
    ! [V_24Y] :
      ( c_24__type__35___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).

fof('$tdef_$_type_119413',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__119413___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__119413___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_150',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__150___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__150___24a1(V_24X1)) ) ).

fof('$tdef_$_type_63',axiom,
    ! [V_24Y] :
      ( c_24__type__63___24t(V_24Y)
    <=> t(V_24Y,c_24__type__63) ) ).

fof('$tdef_$_type_111685',axiom,
    ! [V_24Y] :
      ( c_24__type__111685___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111685) ) ).

fof('$tdef_$_type_105639',axiom,
    ! [V_24Y] :
      ( c_24__type__105639___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105639) ) ).

fof('$tdef_$_type_11205',axiom,
    ! [V_24Y] :
      ( c_24__type__11205___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11205) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_83063',axiom,
    ! [V_24Y] :
      ( c_24__type__83063___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83063) ) ).

fof('$tdef_$_type_47',axiom,
    ! [V_24Y] :
      ( c_24__type__47___24t(V_24Y)
    <=> t(V_24Y,c_24__type__47) ) ).

fof('$tdef_$_type_85281',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85281___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85281___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_120957',axiom,
    ! [V_24Y] :
      ( c_24__type__120957___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120957) ) ).

fof('$tdef_$_type_4098',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__4098___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__4098___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_89808',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89808___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89808___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_117433',axiom,
    ! [V_24Y] :
      ( c_24__type__117433___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117433) ) ).

fof('$tdef_$_type_10724',axiom,
    ! [V_24Y] :
      ( c_24__type__10724___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10724) ) ).

fof('$tdef_$_type_1809',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1809___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1809___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_88976',axiom,
    ! [V_24Y] :
      ( c_24__type__88976___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88976) ) ).

fof('$tdef_$_type_87',axiom,
    ! [V_24Y] :
      ( c_24__type__87___24t(V_24Y)
    <=> t(V_24Y,c_24__type__87) ) ).

fof('$tdef_$_type_118631',axiom,
    ! [V_24Y] :
      ( c_24__type__118631___24t(V_24Y)
    <=> t(V_24Y,c_24__type__118631) ) ).

fof('$tdef_$_type_11280',axiom,
    ! [V_24Y] :
      ( c_24__type__11280___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11280) ) ).

fof('$tdef_$_type_5168',axiom,
    ! [V_24Y] :
      ( c_24__type__5168___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5168) ) ).

fof('$tdef_$_type_121019',axiom,
    ! [V_24Y] :
      ( c_24__type__121019___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121019) ) ).

fof('$tdef_$_type_117395',axiom,
    ! [V_24Y] :
      ( c_24__type__117395___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117395) ) ).

fof('$tdef_$_type_117353',axiom,
    ! [V_24Y] :
      ( c_24__type__117353___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117353) ) ).

fof('$tdef_$_type_1893',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__1893___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__1893___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_93950',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__93950___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__93950___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).

fof('$tdef_$_type_3051',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
      ( c_24__type__3051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
    <=> t(V_24Y,c_24__type__3051___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_$_type_88384',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__88384___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__88384___24a1(V_24X1)) ) ).

fof('$tdef_$_type_121062',axiom,
    ! [V_24Y] :
      ( c_24__type__121062___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121062) ) ).

fof('$tdef_$_type_111336',axiom,
    ! [V_24Y] :
      ( c_24__type__111336___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111336) ) ).

fof('$tdef_$_type_11058',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__11058___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__11058___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_111632',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__111632___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__111632___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_111888',axiom,
    ! [V_24Y] :
      ( c_24__type__111888___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111888) ) ).

fof('$tdef_Coq.Vectors.VectorDef.t',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_121002',axiom,
    ! [V_24Y] :
      ( c_24__type__121002___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121002) ) ).

fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_91897',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
      ( c_24__type__91897___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
    <=> t(V_24Y,c_24__type__91897___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_$_type_10916',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__10916___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__10916___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_6962',axiom,
    ! [V_24Y] :
      ( c_24__type__6962___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6962) ) ).

fof('$tdef_$_type_121193',axiom,
    ! [V_24Y] :
      ( c_24__type__121193___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121193) ) ).

fof('$tdef_$_type_111845',axiom,
    ! [V_24Y] :
      ( c_24__type__111845___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111845) ) ).

fof('$tdef_$_type_111341',axiom,
    ! [V_24Y] :
      ( c_24__type__111341___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111341) ) ).

fof('$tdef_$_type_98649',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__98649___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__98649___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_117302',axiom,
    ! [V_24Y] :
      ( c_24__type__117302___24t(V_24Y)
    <=> t(V_24Y,c_24__type__117302) ) ).

fof('$tdef_$_type_117275',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__117275___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__117275___24a1(V_24X1)) ) ).

fof('$tdef_M',axiom,
    ! [V_24Y] :
      ( cM___24t(V_24Y)
    <=> t(V_24Y,cM) ) ).

fof('$tdef_$_type_100966',axiom,
    ! [V_24Y] :
      ( c_24__type__100966___24t(V_24Y)
    <=> t(V_24Y,c_24__type__100966) ) ).

fof('$tdef_$_type_98828',axiom,
    ! [V_24Y] :
      ( c_24__type__98828___24t(V_24Y)
    <=> t(V_24Y,c_24__type__98828) ) ).

fof('$tdef_$_type_111922',axiom,
    ! [V_24Y] :
      ( c_24__type__111922___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111922) ) ).

fof('$tdef_$_type_117998',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__117998___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__117998___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_454',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__454___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__454___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).

fof('$tdef_$_type_85724',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__85724___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__85724___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_111577',axiom,
    ! [V_24Y] :
      ( c_24__type__111577___24t(V_24Y)
    <=> t(V_24Y,c_24__type__111577) ) ).

fof('$tdef_$_type_105655',axiom,
    ! [V_24Y] :
      ( c_24__type__105655___24t(V_24Y)
    <=> t(V_24Y,c_24__type__105655) ) ).

fof('$tdef_$_type_83055',axiom,
    ! [V_24Y] :
      ( c_24__type__83055___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83055) ) ).

fof('$tdef_Coq.Vectors.Fin.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).

fof('$tdef_$_type_121076',axiom,
    ! [V_24Y] :
      ( c_24__type__121076___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121076) ) ).

fof('$tdef_$_type_1424',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__1424___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__1424___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_118496',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__118496___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__118496___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_112935',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__112935___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__112935___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_88965',axiom,
    ! [V_24Y] :
      ( c_24__type__88965___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88965) ) ).

fof('$tdef_$_type_113538',axiom,
    ! [V_24Y] :
      ( c_24__type__113538___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113538) ) ).

fof('$tdef_$_type_105841',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__105841___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__105841___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_117905',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__117905___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__117905___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_100949',axiom,
    ! [V_24Y] :
      ( c_24__type__100949___24t(V_24Y)
    <=> t(V_24Y,c_24__type__100949) ) ).

fof('$tdef_$_type_120939',axiom,
    ! [V_24Y] :
      ( c_24__type__120939___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120939) ) ).

fof('$tdef_$_type_113572',axiom,
    ! [V_24Y] :
      ( c_24__type__113572___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113572) ) ).

fof('$tdef_$_type_88409',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__88409___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__88409___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_11249',axiom,
    ! [V_24Y] :
      ( c_24__type__11249___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11249) ) ).

fof('$tdef_$_type_88817',axiom,
    ! [V_24Y] :
      ( c_24__type__88817___24t(V_24Y)
    <=> t(V_24Y,c_24__type__88817) ) ).

fof('$tdef_$_type_111696',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__111696___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__111696___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1550',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__1550___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
    <=> t(V_24Y,c_24__type__1550___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_102388',axiom,
    ! [V_24Y] :
      ( c_24__type__102388___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102388) ) ).

fof('$tdef_$_type_89909',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
      ( c_24__type__89909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
    <=> t(V_24Y,c_24__type__89909___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__f] :
      ( c_24__type__111448___24t(V0__f)
     => ! [V1__a] :
          ( cIntMap_2eMap_2ead___24t(V1__a)
         => ! [V2__y] :
              ( cA___24t(V2__y)
             => cMapiter_2eMapIter_2eMapFoldDef_2eMapFold___24a2(V0__f,cIntMap_2eMap_2eM1___24a3(cA,V1__a,V2__y)) = happ(happ(V0__f,V1__a),V2__y) ) ) ) ).

%------------------------------------------------------------------------------