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) ) ) ) ).
%------------------------------------------------------------------------------