TPTP Problem File: SEV663+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV663+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Poly Exercises Church.plus 2
% 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 : Poly.Exercises.Church.plus.2.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 3065 (1358 unt; 0 def)
% Number of atoms : 9292 (2968 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6366 ( 139 ~; 796 |;1727 &)
% (1141 <=>;2563 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 611 ( 610 usr; 0 prp; 1-23 aty)
% Number of functors : 1812 (1812 usr;1223 con; 0-22 aty)
% Number of variables : 8862 (8195 !; 667 ?)
% 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$136199',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136199___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
| ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136199___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$136204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136204___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136204___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$136210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136210___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
| ( cCoq_2eInit_2eDatatypes_2eandb___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136210___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$136221',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__1 )
| ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) )
| ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$136226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136226___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
| ( cCoq_2eInit_2eDatatypes_2enegb___24a1(Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136226___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$136231',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136231___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
| ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136231___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$102413',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102413___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__102414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102414)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__102414)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102413___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__102414)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$102435',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__102436] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102436)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__102436)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__102436)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$110919',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__110932___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__110924] :
( t(Vvar__2___24Anonymous__110924,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__110925] :
( t(Vvar__3___24Anonymous__110925,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__110924,Vvar__3___24Anonymous__110925)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_24110919___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__110924)),Vvar__3___24Anonymous__110925)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$102430',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__102431] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102431)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__102431)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__102431) )
| ? [Vvar__0___24Anonymous__102432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__102432)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__102432)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__102432) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$111803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__111804] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111804)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111804)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__111819__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__111804)) )
| ? [Vvar__0___24Anonymous__111811] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111811)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111811)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111811) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_var_6_p_91898_91901',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91897] : c_24__let__var__6__p__91898__91901___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91897) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91897) ).
fof('$_def_$_let_var_6_p_91900_91902',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91899] : c_24__let__var__6__p__91900__91902___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91899) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91899) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
& cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__74824] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74824)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74824)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__74825] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74825)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74825)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__74828] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74828)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74828)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__74825,Vvar__0___24Anonymous__74828) ) ) ) ) ) ) ) ) ).
fof('$_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.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
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('$_def_Coq.Arith.PeanoNat.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__191823] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__191823)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__191823)
& cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__191823 ) ) ) ).
fof('$_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__82206___24a1(V0__A)) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__191825] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__191825)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__191825)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__191828] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__191828)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__191828)
& cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(Vvar__0___24Anonymous__191825,Vvar__0___24Anonymous__191828) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.t',axiom,
! [Vvar__191822] :
( cCoq_2eArith_2ePeanoNat_2eNat_2et___24t(Vvar__191822)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__191822) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.zero',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__82087] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82087)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82087)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__82087,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b)) ) ).
fof('$_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.ifb',axiom,
! [V0__b1,V1__b2,V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).
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('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__82187] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82187)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82187)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.E.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__191788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191788)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191788)
& ( ? [Vvar__0___24Anonymous__191792] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191792)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191792)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__191788,Vvar__0___24Anonymous__191792) ) )
| ? [Vvar__0___24Anonymous__191793] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191793)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191793)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__191794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191794)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191794)
& ( ? [Vvar__0___24Anonymous__191798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191798)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191798)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__191799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191799)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191799)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__191794,Vvar__0___24Anonymous__191799) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__191800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191800)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191800)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__191801] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191801)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191801)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.E.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
! [Vvar__191786] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et___24t(Vvar__191786)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__191786) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
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.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__81761] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__81761)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__81761) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_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__81777] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__81777)
& ? [Vvar__1___24Anonymous__81778] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__81778)
& ? [Vvar__2___24Anonymous__81779] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__81779)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__81777,Vvar__1___24Anonymous__81778,Vvar__2___24Anonymous__81779)
& ( ? [Vvar__0___24Anonymous__81792] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81792)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__81792)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__81792,Vvar__2___24Anonymous__81779) )
| ? [Vvar__0___24Anonymous__81793] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81793)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__81793)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__81793,Vvar__0___24Anonymous__81777) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__81778 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__81775] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__81775)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__81775) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__104043] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__104043)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__104043,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_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__81978] :
( t(Vvar__1___24Anonymous__81978,V0__A)
& ? [Vvar__2___24Anonymous__81979] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__81979)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__81978,Vvar__2___24Anonymous__81979)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__81978,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__81979,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__89929] :
( t(Vvar__2___24Anonymous__89929,V0__A)
& ? [Vvar__3___24Anonymous__89930] :
( t(Vvar__3___24Anonymous__89930,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__89929,Vvar__3___24Anonymous__89930)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__89929 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.implb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
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__74652] :
( t(Vvar__1___24Anonymous__74652,V0__A)
& ? [Vvar__2___24Anonymous__74653] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__74653)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__74652,Vvar__2___24Anonymous__74653)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__74653)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__74607___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__74605] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74605)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74605)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__74605),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__74605)) ) ) ) ) ).
fof('$_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.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__81966] :
( t(Vvar__2___24Anonymous__81966,V0__A)
& ? [Vvar__3___24Anonymous__81967] :
( t(Vvar__3___24Anonymous__81967,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__81966,Vvar__3___24Anonymous__81967)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__81967 ) ) ) ) ) ).
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.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__11] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__11,V2__m)) ) ) ) ).
fof('$_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__75960] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75960)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75960)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__75961] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75961)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75961)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__75964] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75964)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75964)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__75961,Vvar__0___24Anonymous__75964) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__66885] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66885)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66885)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66885)
& ( ( Vvar__0___24Anonymous__66885 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__66888] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66888)
& Vvar__0___24Anonymous__66885 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66888)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__66888)) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__20] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__20,Vvar__0___24Anonymous__23) ) ) ) ) ) ) ) ).
fof('$_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__66876] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66876)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66876)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66876)
& ( ( Vvar__0___24Anonymous__66876 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__66879] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66879)
& Vvar__0___24Anonymous__66876 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66879)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__66879) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__75990] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75990)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75990)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75990)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75990)) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__66419] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66419)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66419)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__66422] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66422)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66422)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__66419,Vvar__0___24Anonymous__66422) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__76006] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76006)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76006)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__76006,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__76009] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76009)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76009)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__76006,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__76009) ) ) ) ) ) ) ) ).
fof('$_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__75969] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75969)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75969)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__75972] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75972)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75972)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__75969,Vvar__0___24Anonymous__75972)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__82054] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82054)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82054)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__82057] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82057)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82057)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__82054,Vvar__0___24Anonymous__82057)) ) ) ) ) ) ) ) ).
fof('$_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__16] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__16)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__16)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__16,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.odd',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) ).
fof('$_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__28] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28)
& 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__28)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__66868] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66868)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66868)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__66868 ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.square',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esquare___24a1(V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V0__n,V0__n) ).
fof('$_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__66870] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66870)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66870)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__66873] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__66873)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__66873)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__66870,Vvar__0___24Anonymous__66873) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__104727] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__104727)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__104727) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__82060] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82060)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82060)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__82060,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__31] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__31) ) ) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__104730] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__104730)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__104730)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__78593___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__78587] :
( t(Vvar__2__x__78587,V0__A)
& p(happ(V1__P,Vvar__2__x__78587))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__78587)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__78587 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__111328___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__111322] :
( t(Vvar__2__x__111322,V0__A)
& ? [Vvar__3___24Anonymous__111323] :
( t(Vvar__3___24Anonymous__111323,happ(V1__P,Vvar__2__x__111322))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__111322,Vvar__3___24Anonymous__111323)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__111322 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__75788] :
( t(Vvar__1___24Anonymous__75788,V0__A)
& ? [Vvar__2___24Anonymous__75789] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__75789)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__75788,Vvar__2___24Anonymous__75789)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__75788 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__75789) ) ) ) ) ) ) ) ).
fof('$_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__75882] :
( t(Vvar__1___24Anonymous__75882,V1__B)
& ? [Vvar__2___24Anonymous__75883] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__75883)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__75882,Vvar__2___24Anonymous__75883)
& 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__75883,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__75882)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__75917] :
( t(Vvar__1___24Anonymous__75917,V1__B)
& ? [Vvar__2___24Anonymous__75918] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__75918)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__75917,Vvar__2___24Anonymous__75918)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__75917),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__75918)) ) ) ) ) ) ) ).
fof('$_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__91462] :
( t(Vvar__1___24Anonymous__91462,V0__A)
& ? [Vvar__2___24Anonymous__91463] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__91463)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__91462,Vvar__2___24Anonymous__91463)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__91462 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__104585] :
( t(Vvar__1___24Anonymous__104585,V0__A)
& ? [Vvar__2___24Anonymous__104586] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__104586)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__104586)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__104585,Vvar__2___24Anonymous__104586)
& ( ( Vvar__2___24Anonymous__104586 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__104585 )
| ? [Vvar__1___24Anonymous__104597] :
( t(Vvar__1___24Anonymous__104597,V0__A)
& ? [Vvar__2___24Anonymous__104598] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__104598)
& Vvar__2___24Anonymous__104586 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__104597,Vvar__2___24Anonymous__104598)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__104586,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__123894] :
( t(Vvar__1___24Anonymous__123894,V0__A)
& ? [Vvar__2___24Anonymous__123895] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__123895)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__123894,Vvar__2___24Anonymous__123895)
& 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__123894),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__123895)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__82001] :
( t(Vvar__1___24Anonymous__82001,V0__A)
& ? [Vvar__2___24Anonymous__82002] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__82002)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__82001,Vvar__2___24Anonymous__82002)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__82001 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__82004] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82004)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82004)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__82011] :
( t(Vvar__1___24Anonymous__82011,V0__A)
& ? [Vvar__2___24Anonymous__82012] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__82012)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__82011,Vvar__2___24Anonymous__82012)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__82004,Vvar__2___24Anonymous__82012,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__91473] :
( t(Vvar__1___24Anonymous__91473,V0__A)
& ? [Vvar__2___24Anonymous__91474] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__91474)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__91473,Vvar__2___24Anonymous__91474)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__91474 ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__78464___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__76718___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).
fof('$_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('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K_____24a1(V0__U)
<=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__89942___24t(V0__U,V1__x,V2__P)
=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P) ) ) ) ).
fof('$_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.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('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
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('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_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__111642___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNat.N.t',axiom,
! [Vvar__191820] :
( cCoq_2eNArith_2eBinNat_2eN_2et___24t(Vvar__191820)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__191820) ) ).
fof('$_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__731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__731)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__731)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__734)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__734)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__731,Vvar__0___24Anonymous__734)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__81484] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81484)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__81484)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__81485] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81485)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__81485)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__81488] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81488)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__81488)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__81485,Vvar__0___24Anonymous__81488) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__83140] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83140)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83140)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__83140)
& ( ? [Vvar__0___24Anonymous__83144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83144)
& Vvar__0___24Anonymous__83140 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__83144)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__83144) )
| ? [Vvar__0___24Anonymous__83145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83145)
& Vvar__0___24Anonymous__83140 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__83145)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__83145) )
| ( Vvar__0___24Anonymous__83140 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_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__66904] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66904)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66904)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__66904)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__744)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__744)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__745)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__745)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__748] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__748)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__748)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__745,Vvar__0___24Anonymous__748) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__111618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111618)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111618)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111618)
& ( ? [Vvar__0___24Anonymous__111622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111622)
& Vvar__0___24Anonymous__111618 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111622)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__111623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111623)
& Vvar__0___24Anonymous__111618 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111623)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__111618 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__111624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111624)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111624)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__111627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111627)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111627)
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__111624,Vvar__0___24Anonymous__111627) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.ldiff',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__111630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111630)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111630)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__111633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111633)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111633)
& cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff___24a2(Vvar__0___24Anonymous__111630,Vvar__0___24Anonymous__111633) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__111635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111635)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111635)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__111638] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111638)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111638)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__111635,Vvar__0___24Anonymous__111638) ) ) ) ) ) ) ) ).
fof('$_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.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__738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__738)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__738)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__741)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__741)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__738,Vvar__0___24Anonymous__741)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__759] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__759)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__759)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__759)) ) ) ) ).
fof('$_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__98192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98192)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__98192)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__98195] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98195)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__98195)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__98195,Vvar__0___24Anonymous__98192)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__111603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111603)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111603)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__111603) ) ) ) ).
fof('$_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__111607] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111607)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111607)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__111612] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111612)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111607)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111612)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111612)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__111607,Vvar__0___24Anonymous__111612) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__111615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111615)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__111607,Vvar__0___24Anonymous__111612) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__111615)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111615) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__111607,Vvar__0___24Anonymous__111612) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__82194] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82194)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__82194)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__82194)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__111604] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111604)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111604)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__111604) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__111602] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__111602)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__111602) ) ).
fof('$_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__98199] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98199)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__98199)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__98199,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__66905] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66905)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__66905)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__66905) ) ) ) ).
fof('$_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('$_def_Coq.PArith.BinPos.Pos.eq',axiom,
cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.PArith.BinPos.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__191839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191839)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191839)
& cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__191839),Vvar__0___24Anonymous__191839)) )
| ? [Vvar__0___24Anonymous__191840] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191840)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191840)
& cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__191840),Vvar__0___24Anonymous__191840) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__191849] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191849)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191849)
& cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__191849,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__191850] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191850)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191850)
& cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__191850,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_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('$_def_Coq.PArith.BinPos.Pos.t',axiom,
! [Vvar__191831] :
( cCoq_2ePArith_2eBinPos_2ePos_2et___24t(Vvar__191831)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__191831) ) ).
fof('$_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.compare_cont',axiom,
! [V1__r,V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__111698] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111698)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111698)
& ( ? [Vvar__0___24Anonymous__111702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111702)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111702)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__111698,Vvar__0___24Anonymous__111702) )
| ? [Vvar__0___24Anonymous__111703] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111703)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111703)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eGt,Vvar__0___24Anonymous__111698,Vvar__0___24Anonymous__111703) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__111704] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111704)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111704)
& ( ? [Vvar__0___24Anonymous__111708] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111708)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111708)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eLt,Vvar__0___24Anonymous__111704,Vvar__0___24Anonymous__111708) )
| ? [Vvar__0___24Anonymous__111709] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111709)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111709)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__111704,Vvar__0___24Anonymous__111709) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__111710] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111710)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111710)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__111711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111711)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111711)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = V1__r ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__137557] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__137557)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__137557)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__137557 )
| ? [Vvar__0___24Anonymous__137558] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__137558)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__137558)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__137558 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__191860] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191860)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191860)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__191860) )
| ? [Vvar__0___24Anonymous__191861] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191861)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191861)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = Vvar__0___24Anonymous__191861 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__111719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111719)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111719)
& ( ? [Vvar__0___24Anonymous__111723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111723)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111723)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__111719,Vvar__0___24Anonymous__111723) )
| ? [Vvar__0___24Anonymous__111724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111724)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111724)
& 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__111725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111725)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111725)
& ( ? [Vvar__0___24Anonymous__111729] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111729)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111729)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__111730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111730)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111730)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__111725,Vvar__0___24Anonymous__111730) )
| ( 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__111731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111731)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111731)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__111732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111732)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111732)
& 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__98205] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98205)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__98205)
& 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__98205),Vvar__0___24Anonymous__98205)) )
| ? [Vvar__0___24Anonymous__98206] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98206)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__98206)
& 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__98206),Vvar__0___24Anonymous__98206) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__81734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81734)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__81734)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__81734,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__81735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81735)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__81735)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__81735,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_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__83286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83286)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__83286)
& 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__83286,V2__y))) )
| ? [Vvar__0___24Anonymous__83287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83287)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__83287)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__83287,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__81751] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81751)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81751)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81751)
& ( ( Vvar__0___24Anonymous__81751 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__81754] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81754)
& Vvar__0___24Anonymous__81751 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81754)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__81751)) ) ) ) ) ) ) ) ).
fof('$_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__82244] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82244)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82244)
& 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__82244)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__135735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135735)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__135735)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__135735)) )
| ? [Vvar__0___24Anonymous__135736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__135736)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__135736)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__135736)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__111695] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111695)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111695)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__111695)) )
| ? [Vvar__0___24Anonymous__111696] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111696)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111696)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__111696)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__81728] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81728)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__81728)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__81728)) )
| ? [Vvar__0___24Anonymous__81729] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81729)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__81729)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__81729)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_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__81723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81723)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__81723)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__81723 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__763)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__763)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__763)) )
| ? [Vvar__0___24Anonymous__764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__764)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__764)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__764) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__111693] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__111693)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__111693) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__111735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111735)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111735)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__111748___24a1(Vvar__0___24Anonymous__111735) )
| ? [Vvar__0___24Anonymous__111739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111739)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111739)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__111755___24a1(Vvar__0___24Anonymous__111739) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__111759 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__104736] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__104736)
& ? [Vvar__1__Qden__104737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__104737)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104736,Vvar__1__Qden__104737)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__104737 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__104731] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__104731)
& ? [Vvar__1__Qden__104732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__104732)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__104731,Vvar__1__Qden__104732)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__104731 ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__66432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66432)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66432)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__66432) )
| ? [Vvar__0___24Anonymous__66433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66433)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66433)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__66433)) ) ) ) ).
fof('$_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('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__75779___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__75779___24a1(V0__U) ).
fof('$_def_Coq.Structures.DecidableTypeEx.N_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
! [Vvar__191821] :
( cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et___24t(Vvar__191821)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__191821) ) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Nat_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
! [Vvar__191830] :
( cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et___24t(Vvar__191830)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__191830) ) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Positive_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
! [Vvar__191862] :
( cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et___24t(Vvar__191862)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__191862) ) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Z_as_DT.eq',axiom,
cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
! [Vvar__191887] :
( cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et___24t(Vvar__191887)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__191887) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__103985] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__103985)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__103985) ) ).
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.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__103993] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__103993)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__103993) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__111541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111541)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111541)
& ( ? [Vvar__0___24Anonymous__111545] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111545)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111545)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__111541,Vvar__0___24Anonymous__111545) ) )
| ? [Vvar__0___24Anonymous__111546] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111546)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111546)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__111547] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111547)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111547)
& ( ? [Vvar__0___24Anonymous__111551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111551)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111551)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__111552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111552)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111552)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__111547,Vvar__0___24Anonymous__111552) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__111553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111553)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111553)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__111554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111554)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111554)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
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.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__103951] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__103951)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__103951) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__103995] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__103995)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__103995) ) ).
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.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__111864] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__111864)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__111864) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__103997] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__103997)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__103997) ) ).
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('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_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.lnot',axiom,
! [V0__a] : cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(V0__a) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__a)) ).
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.Z.t',axiom,
! [Vvar__191886] :
( cCoq_2eZArith_2eBinInt_2eZ_2et___24t(Vvar__191886)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__191886) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.zero',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__82245] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82245)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82245)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82245) )
| ? [Vvar__0___24Anonymous__82246] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82246)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__82246)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82246) ) ) ) ).
fof('$_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__111885] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111885)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111885)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111885) )
| ? [Vvar__0___24Anonymous__111886] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111886)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111886)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__111886) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__82247] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82247)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82247)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__82247) )
| ? [Vvar__0___24Anonymous__82248] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82248)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__82248)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__82248) ) ) ) ).
fof('$_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__66756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66756)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66756)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__66760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66760)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66760)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__66756,Vvar__0___24Anonymous__66760)) )
| ? [Vvar__0___24Anonymous__66761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66761)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66761)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__66756,Vvar__0___24Anonymous__66761) ) ) ) ) )
| ? [Vvar__0___24Anonymous__66762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66762)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66762)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__66766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66766)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66766)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__66766,Vvar__0___24Anonymous__66762) )
| ? [Vvar__0___24Anonymous__66767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66767)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66767)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__66762,Vvar__0___24Anonymous__66767)) ) ) ) ) ) ) ) ).
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__83991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83991)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__83991)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__83992] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83992)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__83992)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__83993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83993)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__83993)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__83997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83997)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__83997)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__83993,Vvar__0___24Anonymous__83997) )
| ? [Vvar__0___24Anonymous__83998] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83998)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__83998)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__83999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83999)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__83999)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__84003] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84003)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__84003)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__84004] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84004)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__84004)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__83999,Vvar__0___24Anonymous__84004)) ) ) ) ) ) ) ) ).
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__98617] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__98617)
& ? [Vvar__3___24Anonymous__98618] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__98618)
& 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__98617,Vvar__3___24Anonymous__98618)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__98617 ) ) ) ) ).
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__98623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98623)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98623)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98623)
& ( ? [Vvar__0___24Anonymous__98627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98627)
& Vvar__0___24Anonymous__98623 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__98627)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__98628] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98628)
& Vvar__0___24Anonymous__98623 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__98628)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__98623 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__98629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98629)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98629)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98629)
& ( ? [Vvar__0___24Anonymous__98633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98633)
& Vvar__0___24Anonymous__98629 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__98633)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__98634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98634)
& Vvar__0___24Anonymous__98629 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__98634)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__98629 = 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('$_def_Coq.ZArith.BinIntDef.Z.log2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__111899] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111899)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111899)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111899)
& ( ? [Vvar__0___24Anonymous__111903] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111903)
& Vvar__0___24Anonymous__111899 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111903)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__111903)) )
| ? [Vvar__0___24Anonymous__111904] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111904)
& Vvar__0___24Anonymous__111899 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111904)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__111904)) )
| ( Vvar__0___24Anonymous__111899 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__111905] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111905)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111905)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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__84021] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__84021)
& ? [Vvar__3___24Anonymous__84022] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__84022)
& 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__84021,Vvar__3___24Anonymous__84022)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__84022 ) ) ) ) ).
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__66776] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66776)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66776)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__66780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66780)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66780)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__66776,Vvar__0___24Anonymous__66780)) )
| ? [Vvar__0___24Anonymous__66781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66781)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66781)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__66776,Vvar__0___24Anonymous__66781)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__66782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66782)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66782)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__66786] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66786)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66786)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__66782,Vvar__0___24Anonymous__66786)) )
| ? [Vvar__0___24Anonymous__66787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66787)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66787)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__66782,Vvar__0___24Anonymous__66787)) ) ) ) ) ) ) ) ).
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__111887] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111887)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111887)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111887)
& ( ? [Vvar__0___24Anonymous__111891] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111891)
& Vvar__0___24Anonymous__111887 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111891)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__111892] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111892)
& Vvar__0___24Anonymous__111887 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111892)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__111887 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__111893] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111893)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111893)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111893)
& ( ? [Vvar__0___24Anonymous__111897] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111897)
& Vvar__0___24Anonymous__111893 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111897)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__111898] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111898)
& Vvar__0___24Anonymous__111893 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111898)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__111893 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__98610] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98610)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__98610)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98610) ) ) ) ).
fof('$_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__81919] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81919)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81919)
& 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__81919)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__66771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66771)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66771)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66771) )
| ? [Vvar__0___24Anonymous__66772] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__66772)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__66772)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__66772) ) ) ) ).
fof('$_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__98602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98602)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98602)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__98602) )
| ? [Vvar__0___24Anonymous__98603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98603)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98603)
& 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('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__98605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98605)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98605)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__98606] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98606)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98606)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_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.t',axiom,
! [Vvar__111883] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__111883)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__111883) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__84009] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84009)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__84009)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__84009) )
| ? [Vvar__0___24Anonymous__84010] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84010)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__84010)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_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__82251] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82251)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__82251)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__82251) )
| ? [Vvar__0___24Anonymous__82252] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82252)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__82252)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__84013] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84013)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__84013)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__84013 )
| ? [Vvar__0___24Anonymous__84014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__84014)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__84014)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
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.Zdiv.eqm',axiom,
! [V0__N,V1__a,V2__b] :
( cCoq_2eZArith_2eZdiv_2eeqm___24a3(V0__N,V1__a,V2__b)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__a,V0__N) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V2__b,V0__N) ) ).
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__111483] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111483)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111483)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111483)
& ( ? [Vvar__0___24Anonymous__111487] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111487)
& Vvar__0___24Anonymous__111483 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111487)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__111488] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111488)
& Vvar__0___24Anonymous__111483 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111488)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__111483 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__111489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111489)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111489)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111489)
& ( ? [Vvar__0___24Anonymous__111493] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111493)
& Vvar__0___24Anonymous__111489 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111493)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__111494] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111494)
& Vvar__0___24Anonymous__111489 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111494)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__111489 = 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__98029] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98029)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98029)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__98029)
& ( ? [Vvar__0___24Anonymous__98033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98033)
& Vvar__0___24Anonymous__98029 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__98033)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__98034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98034)
& Vvar__0___24Anonymous__98029 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__98034)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__98029 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__98035] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98035)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98035)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__98035)
& ( ? [Vvar__0___24Anonymous__98039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98039)
& Vvar__0___24Anonymous__98035 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__98039)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__98040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__98040)
& Vvar__0___24Anonymous__98035 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__98040)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__98035 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__111499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111499)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111499)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__111500] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111500)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111500)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__111500) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__111496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111496)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111496)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__111496)) )
| ? [Vvar__0___24Anonymous__111497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111497)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111497)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__111497)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
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__99213___24a1(V0__D) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__104817] :
( t(Vvar__1___24Anonymous__104817,V1__A)
& ? [Vvar__2___24Anonymous__104818] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__104818)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__104818)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__104817,Vvar__2___24Anonymous__104818)
& ( ( Vvar__2___24Anonymous__104818 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__104817)) ) )
| ? [Vvar__1___24Anonymous__104829] :
( t(Vvar__1___24Anonymous__104829,V1__A)
& ? [Vvar__2___24Anonymous__104830] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__104830)
& Vvar__2___24Anonymous__104818 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__104829,Vvar__2___24Anonymous__104830)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__104817))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__104818) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__104798] :
( t(Vvar__1___24Anonymous__104798,V1__A)
& ? [Vvar__2___24Anonymous__104799] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__104799)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__104798,Vvar__2___24Anonymous__104799)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__104798))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__104799,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_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.micromega.ZMicromega.Vars.E.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__191805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191805)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191805)
& ( ? [Vvar__0___24Anonymous__191809] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191809)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191809)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__191805,Vvar__0___24Anonymous__191809) ) )
| ? [Vvar__0___24Anonymous__191810] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191810)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191810)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__191811] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191811)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191811)
& ( ? [Vvar__0___24Anonymous__191815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191815)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191815)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__191816] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191816)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191816)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__191811,Vvar__0___24Anonymous__191816) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__191817] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191817)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__191817)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__191818] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191818)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__191818)
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.E.eq',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eE_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.E.t',axiom,
! [Vvar__191803] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et___24t(Vvar__191803)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__191803) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).
fof('$_def_Coq.micromega.ZMicromega.Vars.elt',axiom,
! [Vvar__191863] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eelt___24t(Vvar__191863)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__191863) ) ).
fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__136326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136326)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__136326)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__136327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136327)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__136327)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__104573] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__104573)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__104573) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__136832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__136832)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__136832)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__136832) ) ) ) ) ).
fof('$_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__91346] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91346)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91346)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__91346)
& ( ? [Vvar__0___24Anonymous__91350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91350)
& Vvar__0___24Anonymous__91346 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__91350)
& 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__91346))) )
| ? [Vvar__0___24Anonymous__91351] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91351)
& Vvar__0___24Anonymous__91346 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__91351)
& 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__91346))) )
| ( Vvar__0___24Anonymous__91346 = 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__91352] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91352)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91352)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__91352)
& ( ? [Vvar__0___24Anonymous__91356] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91356)
& Vvar__0___24Anonymous__91352 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__91356)
& 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__91352)) )
| ? [Vvar__0___24Anonymous__91357] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91357)
& Vvar__0___24Anonymous__91352 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__91357)
& 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__91352)) )
| ( Vvar__0___24Anonymous__91352 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__91313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91313)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__91313)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__91313))) )
| ? [Vvar__0___24Anonymous__91314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91314)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__91314)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__91314)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_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__91380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91380)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__91380)
& 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__91380) )
| ? [Vvar__0___24Anonymous__91381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91381)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__91381)
& 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__91381)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
fof('$_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__66439] :
( t(Vvar__1___24Anonymous__66439,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__66439)
& ( ? [Vvar__1___24Anonymous__66449] :
( t(Vvar__1___24Anonymous__66449,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__66449)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__66439),Vvar__1___24Anonymous__66449) )
| ? [Vvar__1___24Anonymous__66451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66451)
& ? [Vvar__2___24Anonymous__66452] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__66452)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__66451,Vvar__2___24Anonymous__66452)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__66455] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66455)
& ? [Vvar__2___24Anonymous__66456] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66456)
& ? [Vvar__3___24Anonymous__66457] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__66457)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__66455,Vvar__2___24Anonymous__66456,Vvar__3___24Anonymous__66457)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__66462] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66462)
& ? [Vvar__2___24Anonymous__66463] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__66463)
& ( 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__66462,Vvar__2___24Anonymous__66463)
& ( ? [Vvar__1___24Anonymous__66483] :
( t(Vvar__1___24Anonymous__66483,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__66483)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__66485] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66485)
& ? [Vvar__2___24Anonymous__66486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__66486)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66462)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66485)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__66485,Vvar__2___24Anonymous__66486)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__66462,Vvar__1___24Anonymous__66485) = 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__66463,Vvar__2___24Anonymous__66486) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__66462,Vvar__1___24Anonymous__66485) = 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__66462,Vvar__1___24Anonymous__66485) = 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__66491] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66491)
& ? [Vvar__2___24Anonymous__66492] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66492)
& ? [Vvar__3___24Anonymous__66493] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__66493)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__66491,Vvar__2___24Anonymous__66492,Vvar__3___24Anonymous__66493)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__66498] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66498)
& ? [Vvar__2___24Anonymous__66499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66499)
& ? [Vvar__3___24Anonymous__66500] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__66500)
& ( 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__66498,Vvar__2___24Anonymous__66499,Vvar__3___24Anonymous__66500)
& ( ? [Vvar__1___24Anonymous__66533] :
( t(Vvar__1___24Anonymous__66533,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__66533)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__66535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66535)
& ? [Vvar__2___24Anonymous__66536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__66536)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__66535,Vvar__2___24Anonymous__66536)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__66539] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66539)
& ? [Vvar__2___24Anonymous__66540] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66540)
& ? [Vvar__3___24Anonymous__66541] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__66541)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66499)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__66540)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__66539,Vvar__2___24Anonymous__66540,Vvar__3___24Anonymous__66541)
& ( ( cType___24t(V0__C)
=> ( c_24__type__716___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66498)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__66539)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__66499,Vvar__2___24Anonymous__66540) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__66498,Vvar__1___24Anonymous__66539) = 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__66500,Vvar__3___24Anonymous__66541) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__66498,Vvar__1___24Anonymous__66539) = 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__66499,Vvar__2___24Anonymous__66540) = 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__66499,Vvar__2___24Anonymous__66540) = 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('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__110314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__110314)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__110314)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__110314),V4__x,Vvar__0___24Anonymous__110314) )
| ? [Vvar__0___24Anonymous__110315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__110315)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__110315)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__110315),V4__x,Vvar__0___24Anonymous__110315) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_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.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__77014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__77014)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__77014)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__77014) ) ) ) ) ).
fof('$_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__91897] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91897)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__91897)
& 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__91898__91901___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91897)),c_24__let__var__6__p__91898__91901___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91897))) )
| ? [Vvar__0___24Anonymous__91899] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__91899)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__91899)
& 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__91900__91902___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91899)),c_24__let__var__6__p__91900__91902___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__91899)) )
| ( 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('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_LF.Basics.andb',axiom,
! [V0__b1,V1__b2] :
( cLF_2eBasics_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cLF_2eBasics_2etrue
& cLF_2eBasics_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cLF_2eBasics_2efalse
& cLF_2eBasics_2eandb___24a2(V0__b1,V1__b2) = cLF_2eBasics_2efalse ) ) ) ).
fof('$_def_LF.Basics.minustwo',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cLF_2eBasics_2eminustwo___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__81923] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81923)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81923)
=> ( V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81923)
& ( ( Vvar__0___24Anonymous__81923 = cCoq_2eInit_2eDatatypes_2eO
& cLF_2eBasics_2eminustwo___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__81926] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81926)
& Vvar__0___24Anonymous__81923 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81926)
& cLF_2eBasics_2eminustwo___24a1(V0__n) = Vvar__0___24Anonymous__81926 ) ) ) ) ) ) ) ).
fof('$_def_LF.Basics.orb',axiom,
! [V0__b1,V1__b2] :
( cLF_2eBasics_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cLF_2eBasics_2etrue
& cLF_2eBasics_2eorb___24a2(V0__b1,V1__b2) = cLF_2eBasics_2etrue )
| ( V0__b1 = cLF_2eBasics_2efalse
& cLF_2eBasics_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).
fof('$_def_LF.Lists.NatList.bag',axiom,
! [Vvar__81685] :
( cLF_2eLists_2eNatList_2ebag___24t(Vvar__81685)
<=> cLF_2eLists_2eNatList_2enatlist___24t(Vvar__81685) ) ).
fof('$_def_LF.Lists.NatList.fst',axiom,
! [V0__p] :
( cLF_2eLists_2eNatList_2enatprod___24t(V0__p)
=> ? [Vvar__0__n1__111674] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__111674)
& ? [Vvar__1__n2__111675] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__111675)
& V0__p = cLF_2eLists_2eNatList_2epair___24a2(Vvar__0__n1__111674,Vvar__1__n2__111675)
& cLF_2eLists_2eNatList_2efst___24a1(V0__p) = Vvar__0__n1__111674 ) ) ) ).
fof('$_def_LF.Lists.NatList.hd',axiom,
! [V0__default,V1__l] :
( cLF_2eLists_2eNatList_2enatlist___24t(V1__l)
=> ( ( V1__l = cLF_2eLists_2eNatList_2enil
& cLF_2eLists_2eNatList_2ehd___24a2(V0__default,V1__l) = V0__default )
| ? [Vvar__0__n__81674] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__81674)
& ? [Vvar__1__l__81675] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vvar__1__l__81675)
& V1__l = cLF_2eLists_2eNatList_2econs___24a2(Vvar__0__n__81674,Vvar__1__l__81675)
& cLF_2eLists_2eNatList_2ehd___24a2(V0__default,V1__l) = Vvar__0__n__81674 ) ) ) ) ).
fof('$_def_LF.Lists.NatList.option_elim',axiom,
! [V0__d,V1__o] :
( cLF_2eLists_2eNatList_2enatoption___24t(V1__o)
=> ( ? [Vvar__0__n__137553] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__137553)
& V1__o = cLF_2eLists_2eNatList_2eSome___24a1(Vvar__0__n__137553)
& cLF_2eLists_2eNatList_2eoption__elim___24a2(V0__d,V1__o) = Vvar__0__n__137553 )
| ( V1__o = cLF_2eLists_2eNatList_2eNone
& cLF_2eLists_2eNatList_2eoption__elim___24a2(V0__d,V1__o) = V0__d ) ) ) ).
fof('$_def_LF.Lists.NatList.snd',axiom,
! [V0__p] :
( cLF_2eLists_2eNatList_2enatprod___24t(V0__p)
=> ? [Vvar__0__n1__111679] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__111679)
& ? [Vvar__1__n2__111680] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__111680)
& V0__p = cLF_2eLists_2eNatList_2epair___24a2(Vvar__0__n1__111679,Vvar__1__n2__111680)
& cLF_2eLists_2eNatList_2esnd___24a1(V0__p) = Vvar__1__n2__111680 ) ) ) ).
fof('$_def_Poly.Exercises.Church.cnat',axiom,
! [Vvar__191701] :
( cPoly_2eExercises_2eChurch_2ecnat___24t(Vvar__191701)
<=> ! [V0__X] :
( cType___24t(V0__X)
=> ! [V1___24Anonymous] :
( c_24__type__711___24t(V0__X,V1___24Anonymous)
=> ! [V2___24Anonymous] :
( t(V2___24Anonymous,V0__X)
=> t(happ(happ(happ(Vvar__191701,V0__X),V1___24Anonymous),V2___24Anonymous),V0__X) ) ) ) ) ).
fof('$_def_Poly.Exercises.Church.one',axiom,
! [V0__X,V1__f,V2__x] : cPoly_2eExercises_2eChurch_2eone___24a3(V0__X,V1__f,V2__x) = happ(V1__f,V2__x) ).
fof('$_def_Poly.Exercises.Church.three',axiom,
cPoly_2eExercises_2eChurch_2ethree = cPoly_2edoit3times ).
fof('$_def_Poly.Exercises.Church.two',axiom,
! [V0__X,V1__f,V2__x] : cPoly_2eExercises_2eChurch_2etwo___24a3(V0__X,V1__f,V2__x) = happ(V1__f,happ(V1__f,V2__x)) ).
fof('$_def_Poly.Exercises.Church.zero',axiom,
! [V0__X,V1__f,V2__x] : cPoly_2eExercises_2eChurch_2ezero___24a3(V0__X,V1__f,V2__x) = V2__x ).
fof('$_def_Poly.constfun',axiom,
! [V0__X,V1__x,V2__k] : cPoly_2econstfun___24a3(V0__X,V1__x,V2__k) = V1__x ).
fof('$_def_Poly.doit3times',axiom,
! [V0__X,V1__f,V2__n] : cPoly_2edoit3times___24a3(V0__X,V1__f,V2__n) = happ(V1__f,happ(V1__f,happ(V1__f,V2__n))) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__99172,Vvar__1___24Anonymous__99173,Vvar__0__P__99174,Vvar__1___24Anonymous__99175] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__99172) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__99174) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__81766,Vvar__1___24Anonymous__81767,Vvar__2___24Anonymous__81768] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__81766,Vvar__1___24Anonymous__81767,Vvar__2___24Anonymous__81768) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__82763,Vvar__1__Plt__82764,Vvar__2__Pgt__82765,Vvar__3___24Anonymous__82766,Vvar__0__Peq__82767,Vvar__1__Plt__82768,Vvar__2__Pgt__82769,Vvar__3___24Anonymous__82770] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82763,Vvar__1__Plt__82764,Vvar__2__Pgt__82765) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82767,Vvar__1__Plt__82768,Vvar__2__Pgt__82769) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__66343,Vvar__1___24Anonymous__66344,Vvar__0__A__66345] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__66343,Vvar__1___24Anonymous__66344) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__66345) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__99194,Vvar__1__B__99195,Vvar__2___24Anonymous__99196,Vvar__0__A__99197,Vvar__1__B__99198,Vvar__2___24Anonymous__99199] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__99194,Vvar__1__B__99195,Vvar__2___24Anonymous__99196) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__99197,Vvar__1__B__99198,Vvar__2___24Anonymous__99199) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__66399,Vvar__0__A__66400,Vvar__1___24Anonymous__66401,Vvar__2___24Anonymous__66402] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66399) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66400,Vvar__1___24Anonymous__66401,Vvar__2___24Anonymous__66402) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__104059,Vvar__1__f__104060,Vvar__0__i__104061,Vvar__1__f__104062,Vvar__2__e__104063] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__104059,Vvar__1__f__104060) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__104061,Vvar__1__f__104062,Vvar__2__e__104063) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__74787] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__74787) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__104047,Vvar__0__d__104048] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__104047) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__104048) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__78699,Vvar__1__B__78700,Vvar__2___24Anonymous__78701,Vvar__0__A__78702,Vvar__1__B__78703,Vvar__2___24Anonymous__78704] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__78699,Vvar__1__B__78700,Vvar__2___24Anonymous__78701) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__78702,Vvar__1__B__78703) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__78615,Vvar__1__B__78616,Vvar__2___24Anonymous__78617,Vvar__0__A__78618,Vvar__1__B__78619,Vvar__2___24Anonymous__78620] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__78615,Vvar__1__B__78616) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__78618,Vvar__1__B__78619) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__777] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__777) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__788] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__788) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__178,Vvar__0___24Anonymous__179] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__178) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__179) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.IsNul$Coq.PArith.BinPos.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__191835] : cCoq_2ePArith_2eBinPos_2ePos_2eIsNul != cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__191835) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__111822,Vvar__1___24Anonymous__111823] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__111822,Vvar__1___24Anonymous__111823) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__83213] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__83213) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__102455,Vvar__1___24Anonymous__102456,Vvar__0__x__102457,Vvar__1__n__102458,Vvar__2___24Anonymous__102459] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__102455) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__102457,Vvar__1__n__102458) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__82093,Vvar__1___24Anonymous__82094] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82093,Vvar__1___24Anonymous__82094) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__102193,Vvar__1__lt__102194,Vvar__2__eq__102195,Vvar__3__x__102196,Vvar__4__y__102197,Vvar__5___24Anonymous__102198,Vvar__0__X__102199,Vvar__1__lt__102200,Vvar__2__eq__102201,Vvar__3__x__102202,Vvar__4__y__102203,Vvar__5___24Anonymous__102204] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__102193,Vvar__1__lt__102194,Vvar__2__eq__102195,Vvar__3__x__102196,Vvar__4__y__102197) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__102199,Vvar__1__lt__102200,Vvar__2__eq__102201,Vvar__3__x__102202,Vvar__4__y__102203) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__74907,Vvar__0__n__74908,Vvar__1___24Anonymous__74909] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74907) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74908,Vvar__1___24Anonymous__74909) ).
fof('$_discrim_Coq.Vectors.Vector.nil$Coq.Vectors.Vector.cons',axiom,
! [Vvar__0__A__191771,Vvar__0__A__191772,Vvar__1__h__191773,Vvar__2__n__191774,Vvar__3___24Anonymous__191775] : cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__191771) != cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__191772,Vvar__1__h__191773,Vvar__2__n__191774,Vvar__3___24Anonymous__191775) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__78982,Vvar__0__A__78983,Vvar__1__h__78984,Vvar__2__n__78985,Vvar__3___24Anonymous__78986] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__78982) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__78983,Vvar__1__h__78984,Vvar__2__n__78985,Vvar__3___24Anonymous__78986) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__99339,Vvar__1___24Anonymous__99340,Vvar__0__C__99341,Vvar__1___24Anonymous__99342] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__99339,Vvar__1___24Anonymous__99340) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__99341,Vvar__1___24Anonymous__99342) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__99403,Vvar__1___24Anonymous__99404,Vvar__0__C__99405,Vvar__1___24Anonymous__99406,Vvar__2___24Anonymous__99407] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__99403,Vvar__1___24Anonymous__99404) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__99405,Vvar__1___24Anonymous__99406,Vvar__2___24Anonymous__99407) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__99437,Vvar__1___24Anonymous__99438] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__99437,Vvar__1___24Anonymous__99438) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_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.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__110254,Vvar__1___24Anonymous__110255,Vvar__0__C__110256,Vvar__1___24Anonymous__110257] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__110254,Vvar__1___24Anonymous__110255) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__110256,Vvar__1___24Anonymous__110257) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__103781,Vvar__1__TX__103782,Vvar__2__AA__103783,Vvar__3__AF__103784,Vvar__0__TA__103785,Vvar__1__TX__103786,Vvar__2__AA__103787,Vvar__3__AF__103788] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__103781,Vvar__1__TX__103782,Vvar__2__AA__103783,Vvar__3__AF__103784) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__103785,Vvar__1__TX__103786,Vvar__2__AA__103787,Vvar__3__AF__103788) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__111408,Vvar__0__A__111409,Vvar__1___24Anonymous__111410] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__111408) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__111409,Vvar__1___24Anonymous__111410) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__81127,Vvar__1___24Anonymous__81128] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__81127,Vvar__1___24Anonymous__81128) ).
fof('$_discrim_Coq.micromega.ZMicromega.Vars.Leaf$Coq.micromega.ZMicromega.Vars.Node',axiom,
! [Vvar__0___24Anonymous__191868,Vvar__1___24Anonymous__191869,Vvar__2___24Anonymous__191870] : cCoq_2emicromega_2eZMicromega_2eVars_2eLeaf != cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__191868,Vvar__1___24Anonymous__191869,Vvar__2___24Anonymous__191870) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__90242,Vvar__0__C__90243] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__90242) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__90243) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__435,Vvar__0__C__436] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__435) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__436) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__211,Vvar__1___24Anonymous__212,Vvar__0__C__213,Vvar__1___24Anonymous__214,Vvar__2___24Anonymous__215] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__211,Vvar__1___24Anonymous__212) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__213,Vvar__1___24Anonymous__214,Vvar__2___24Anonymous__215) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__245,Vvar__1___24Anonymous__246] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__245,Vvar__1___24Anonymous__246) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__83053,Vvar__1__req__83054,Vvar__2__reqb__83055,Vvar__3___24Anonymous__83056] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__83053,Vvar__1__req__83054,Vvar__2__reqb__83055) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_discrim_LF.Basics.B0$LF.Basics.B1',axiom,
cLF_2eBasics_2eB0 != cLF_2eBasics_2eB1 ).
fof('$_discrim_LF.Basics.NatPlayground.O$LF.Basics.NatPlayground.S',axiom,
! [Vvar__0__n__111684] : cLF_2eBasics_2eNatPlayground_2eO != cLF_2eBasics_2eNatPlayground_2eS___24a1(Vvar__0__n__111684) ).
fof('$_discrim_LF.Basics.NatPlayground.stop$LF.Basics.NatPlayground.tick',axiom,
! [Vvar__0__foo__111689] : cLF_2eBasics_2eNatPlayground_2estop != cLF_2eBasics_2eNatPlayground_2etick___24a1(Vvar__0__foo__111689) ).
fof('$_discrim_LF.Basics.Z$LF.Basics.A',axiom,
! [Vvar__0__n__104006] : cLF_2eBasics_2eZ != cLF_2eBasics_2eA___24a1(Vvar__0__n__104006) ).
fof('$_discrim_LF.Basics.black$LF.Basics.white',axiom,
cLF_2eBasics_2eblack != cLF_2eBasics_2ewhite ).
fof('$_discrim_LF.Basics.monday$LF.Basics.tuesday',axiom,
cLF_2eBasics_2emonday != cLF_2eBasics_2etuesday ).
fof('$_discrim_LF.Basics.red$LF.Basics.green',axiom,
cLF_2eBasics_2ered != cLF_2eBasics_2egreen ).
fof('$_discrim_LF.Basics.true$LF.Basics.false',axiom,
cLF_2eBasics_2etrue != cLF_2eBasics_2efalse ).
fof('$_discrim_LF.Lists.Baz1$LF.Lists.Baz2',axiom,
! [Vvar__0__x__82361,Vvar__0__y__82362,Vvar__1__b__82363] : cLF_2eLists_2eBaz1___24a1(Vvar__0__x__82361) != cLF_2eLists_2eBaz2___24a2(Vvar__0__y__82362,Vvar__1__b__82363) ).
fof('$_discrim_LF.Lists.NatList.Some$LF.Lists.NatList.None',axiom,
! [Vvar__0__n__66749] : cLF_2eLists_2eNatList_2eSome___24a1(Vvar__0__n__66749) != cLF_2eLists_2eNatList_2eNone ).
fof('$_discrim_LF.Lists.NatList.nil$LF.Lists.NatList.cons',axiom,
! [Vvar__0__n__43,Vvar__1__l__44] : cLF_2eLists_2eNatList_2enil != cLF_2eLists_2eNatList_2econs___24a2(Vvar__0__n__43,Vvar__1__l__44) ).
fof('$_discrim_LF.Lists.PartialMap.empty$LF.Lists.PartialMap.record',axiom,
! [Vvar__0__i__82454,Vvar__1__v__82455,Vvar__2__m__82456] : cLF_2eLists_2ePartialMap_2eempty != cLF_2eLists_2ePartialMap_2erecord___24a3(Vvar__0__i__82454,Vvar__1__v__82455,Vvar__2__m__82456) ).
fof('$_discrim_Poly.MumbleGrumble.a$Poly.MumbleGrumble.b',axiom,
! [Vvar__0__x__111578,Vvar__1__y__111579] : cPoly_2eMumbleGrumble_2ea != cPoly_2eMumbleGrumble_2eb___24a2(Vvar__0__x__111578,Vvar__1__y__111579) ).
fof('$_discrim_Poly.MumbleGrumble.d$Poly.MumbleGrumble.e',axiom,
! [Vvar__0__X__111590,Vvar__1__m__111591,Vvar__0__X__111592,Vvar__1__x__111593] : cPoly_2eMumbleGrumble_2ed___24a2(Vvar__0__X__111590,Vvar__1__m__111591) != cPoly_2eMumbleGrumble_2ee___24a2(Vvar__0__X__111592,Vvar__1__x__111593) ).
fof('$_discrim_Poly.OptionPlayground.Some$Poly.OptionPlayground.None',axiom,
! [Vvar__0__X__153809,Vvar__1__x__153810,Vvar__0__X__153811] : cPoly_2eOptionPlayground_2eSome___24a2(Vvar__0__X__153809,Vvar__1__x__153810) != cPoly_2eOptionPlayground_2eNone___24a1(Vvar__0__X__153811) ).
fof('$_discrim_Poly.bool_nil$Poly.bool_cons',axiom,
! [Vvar__0__b__82538,Vvar__1__l__82539] : cPoly_2ebool__nil != cPoly_2ebool__cons___24a2(Vvar__0__b__82538,Vvar__1__l__82539) ).
fof('$_discrim_Poly.nil$Poly.cons',axiom,
! [Vvar__0__X__154,Vvar__0__X__155,Vvar__1__x__156,Vvar__2__l__157] : cPoly_2enil___24a1(Vvar__0__X__154) != cPoly_2econs___24a3(Vvar__0__X__155,Vvar__1__x__156,Vvar__2__l__157) ).
fof('$_discrim_Poly.nil\'$Poly.cons\'',axiom,
! [Vvar__0__X__111919,Vvar__0__X__111920,Vvar__1__x__111921,Vvar__2__l__111922] : cPoly_2enil_27___24a1(Vvar__0__X__111919) != cPoly_2econs_27___24a3(Vvar__0__X__111920,Vvar__1__x__111921,Vvar__2__l__111922) ).
fof('$_fix_111819_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__111820] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111820)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111820)
& c_24__fix__111819__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__111819__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__111820)) )
| ? [Vvar__0___24Anonymous__111821] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111821)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__111821)
& c_24__fix__111819__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__111821) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__111819__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__99180,Vvar__0__P__99181,Vvar__1___24Anonymous__99182,Vvar__1___24Anonymous__99183] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__99180) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__99181)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__99180 = Vvar__0__P__99181 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__99176,Vvar__0__P__99177,Vvar__1___24Anonymous__99178,Vvar__1___24Anonymous__99179] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__99176) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__99177)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__99176 = Vvar__0__P__99177 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__81769,Vvar__0___24Anonymous__81770,Vvar__1___24Anonymous__81771,Vvar__1___24Anonymous__81772,Vvar__2___24Anonymous__81773,Vvar__2___24Anonymous__81774] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__81769,Vvar__1___24Anonymous__81771,Vvar__2___24Anonymous__81773) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__81770,Vvar__1___24Anonymous__81772,Vvar__2___24Anonymous__81774)
=> ( Vvar__2___24Anonymous__81773 = Vvar__2___24Anonymous__81774
& Vvar__1___24Anonymous__81771 = Vvar__1___24Anonymous__81772
& Vvar__0___24Anonymous__81769 = Vvar__0___24Anonymous__81770 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__82771,Vvar__0__Peq__82772,Vvar__1__Plt__82773,Vvar__1__Plt__82774,Vvar__2__Pgt__82775,Vvar__2__Pgt__82776,Vvar__3___24Anonymous__82777,Vvar__3___24Anonymous__82778] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82771,Vvar__1__Plt__82773,Vvar__2__Pgt__82775) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82772,Vvar__1__Plt__82774,Vvar__2__Pgt__82776)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82775 = Vvar__2__Pgt__82776
& Vvar__1__Plt__82773 = Vvar__1__Plt__82774
& Vvar__0__Peq__82771 = Vvar__0__Peq__82772 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__82787,Vvar__0__Peq__82788,Vvar__1__Plt__82789,Vvar__1__Plt__82790,Vvar__2__Pgt__82791,Vvar__2__Pgt__82792,Vvar__3___24Anonymous__82793,Vvar__3___24Anonymous__82794] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82787,Vvar__1__Plt__82789,Vvar__2__Pgt__82791) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82788,Vvar__1__Plt__82790,Vvar__2__Pgt__82792)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82791 = Vvar__2__Pgt__82792
& Vvar__1__Plt__82789 = Vvar__1__Plt__82790
& Vvar__0__Peq__82787 = Vvar__0__Peq__82788 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__82779,Vvar__0__Peq__82780,Vvar__1__Plt__82781,Vvar__1__Plt__82782,Vvar__2__Pgt__82783,Vvar__2__Pgt__82784,Vvar__3___24Anonymous__82785,Vvar__3___24Anonymous__82786] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82779,Vvar__1__Plt__82781,Vvar__2__Pgt__82783) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82780,Vvar__1__Plt__82782,Vvar__2__Pgt__82784)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__82783 = Vvar__2__Pgt__82784
& Vvar__1__Plt__82781 = Vvar__1__Plt__82782
& Vvar__0__Peq__82779 = Vvar__0__Peq__82780 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__66350,Vvar__0__A__66351] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__66350) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__66351)
=> Vvar__0__A__66350 = Vvar__0__A__66351 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4,Vvar__0___24Anonymous__5] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5)
=> Vvar__0___24Anonymous__4 = Vvar__0___24Anonymous__5 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__66346,Vvar__0__A__66347,Vvar__1___24Anonymous__66348,Vvar__1___24Anonymous__66349] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__66346,Vvar__1___24Anonymous__66348) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__66347,Vvar__1___24Anonymous__66349)
=> ( Vvar__1___24Anonymous__66348 = Vvar__1___24Anonymous__66349
& Vvar__0__A__66346 = Vvar__0__A__66347 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__66405,Vvar__0__A__66406,Vvar__1___24Anonymous__66407,Vvar__1___24Anonymous__66408,Vvar__2___24Anonymous__66409,Vvar__2___24Anonymous__66410] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66405,Vvar__1___24Anonymous__66407,Vvar__2___24Anonymous__66409) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66406,Vvar__1___24Anonymous__66408,Vvar__2___24Anonymous__66410)
=> ( Vvar__2___24Anonymous__66409 = Vvar__2___24Anonymous__66410
& Vvar__1___24Anonymous__66407 = Vvar__1___24Anonymous__66408
& Vvar__0__A__66405 = Vvar__0__A__66406 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__99200,Vvar__0__A__99201,Vvar__1__B__99202,Vvar__1__B__99203,Vvar__2___24Anonymous__99204,Vvar__2___24Anonymous__99205] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__99200,Vvar__1__B__99202,Vvar__2___24Anonymous__99204) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__99201,Vvar__1__B__99203,Vvar__2___24Anonymous__99205)
=> ( Vvar__2___24Anonymous__99204 = Vvar__2___24Anonymous__99205
& Vvar__1__B__99202 = Vvar__1__B__99203
& Vvar__0__A__99200 = Vvar__0__A__99201 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__99206,Vvar__0__A__99207,Vvar__1__B__99208,Vvar__1__B__99209,Vvar__2___24Anonymous__99210,Vvar__2___24Anonymous__99211] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__99206,Vvar__1__B__99208,Vvar__2___24Anonymous__99210) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__99207,Vvar__1__B__99209,Vvar__2___24Anonymous__99211)
=> ( Vvar__2___24Anonymous__99210 = Vvar__2___24Anonymous__99211
& Vvar__1__B__99208 = Vvar__1__B__99209
& Vvar__0__A__99206 = Vvar__0__A__99207 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__66403,Vvar__0__A__66404] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66403) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66404)
=> Vvar__0__A__66403 = Vvar__0__A__66404 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__66385,Vvar__0__A__66386,Vvar__1__B__66387,Vvar__1__B__66388,Vvar__2___24Anonymous__66389,Vvar__2___24Anonymous__66390,Vvar__3___24Anonymous__66391,Vvar__3___24Anonymous__66392] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__66385,Vvar__1__B__66387,Vvar__2___24Anonymous__66389,Vvar__3___24Anonymous__66391) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__66386,Vvar__1__B__66388,Vvar__2___24Anonymous__66390,Vvar__3___24Anonymous__66392)
=> ( Vvar__3___24Anonymous__66391 = Vvar__3___24Anonymous__66392
& Vvar__2___24Anonymous__66389 = Vvar__2___24Anonymous__66390
& Vvar__1__B__66387 = Vvar__1__B__66388
& Vvar__0__A__66385 = Vvar__0__A__66386 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__74788,Vvar__0___24Anonymous__74789] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__74788) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__74789)
=> Vvar__0___24Anonymous__74788 = Vvar__0___24Anonymous__74789 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__74790,Vvar__0___24Anonymous__74791] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__74790) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__74791)
=> Vvar__0___24Anonymous__74790 = Vvar__0___24Anonymous__74791 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__74792,Vvar__0___24Anonymous__74793] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__74792) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__74793)
=> Vvar__0___24Anonymous__74792 = Vvar__0___24Anonymous__74793 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__74794,Vvar__0___24Anonymous__74795] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__74794) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__74795)
=> Vvar__0___24Anonymous__74794 = Vvar__0___24Anonymous__74795 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__74796,Vvar__0___24Anonymous__74797] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__74796) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__74797)
=> Vvar__0___24Anonymous__74796 = Vvar__0___24Anonymous__74797 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__74798,Vvar__0___24Anonymous__74799] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__74798) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__74799)
=> Vvar__0___24Anonymous__74798 = Vvar__0___24Anonymous__74799 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__74800,Vvar__0___24Anonymous__74801] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__74800) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__74801)
=> Vvar__0___24Anonymous__74800 = Vvar__0___24Anonymous__74801 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__74802,Vvar__0___24Anonymous__74803] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__74802) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__74803)
=> Vvar__0___24Anonymous__74802 = Vvar__0___24Anonymous__74803 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__74804,Vvar__0___24Anonymous__74805] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__74804) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__74805)
=> Vvar__0___24Anonymous__74804 = Vvar__0___24Anonymous__74805 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__74806,Vvar__0___24Anonymous__74807] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__74806) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__74807)
=> Vvar__0___24Anonymous__74806 = Vvar__0___24Anonymous__74807 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__104064,Vvar__0__i__104065,Vvar__1__f__104066,Vvar__1__f__104067] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__104064,Vvar__1__f__104066) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__104065,Vvar__1__f__104067)
=> ( Vvar__1__f__104066 = Vvar__1__f__104067
& Vvar__0__i__104064 = Vvar__0__i__104065 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__104068,Vvar__0__i__104069,Vvar__1__f__104070,Vvar__1__f__104071,Vvar__2__e__104072,Vvar__2__e__104073] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__104068,Vvar__1__f__104070,Vvar__2__e__104072) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__104069,Vvar__1__f__104071,Vvar__2__e__104073)
=> ( Vvar__2__e__104072 = Vvar__2__e__104073
& Vvar__1__f__104070 = Vvar__1__f__104071
& Vvar__0__i__104068 = Vvar__0__i__104069 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__104051,Vvar__0__d__104052] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__104051) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__104052)
=> Vvar__0__d__104051 = Vvar__0__d__104052 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__104049,Vvar__0__d__104050] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__104049) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__104050)
=> Vvar__0__d__104049 = Vvar__0__d__104050 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__78561,Vvar__0__A__78562,Vvar__1__P__78563,Vvar__1__P__78564,Vvar__2__x__78565,Vvar__2__x__78566,Vvar__3___24Anonymous__78567,Vvar__3___24Anonymous__78568] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78561,Vvar__1__P__78563,Vvar__2__x__78565) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78562,Vvar__1__P__78564,Vvar__2__x__78566)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__78565 = Vvar__2__x__78566
& Vvar__1__P__78563 = Vvar__1__P__78564
& Vvar__0__A__78561 = Vvar__0__A__78562 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__95307,Vvar__0__A__95308,Vvar__1__P__95309,Vvar__1__P__95310,Vvar__2__Q__95311,Vvar__2__Q__95312,Vvar__3__x__95313,Vvar__3__x__95314,Vvar__4___24Anonymous__95315,Vvar__4___24Anonymous__95316,Vvar__5___24Anonymous__95317,Vvar__5___24Anonymous__95318] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__95307,Vvar__1__P__95309,Vvar__2__Q__95311,Vvar__3__x__95313) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__95308,Vvar__1__P__95310,Vvar__2__Q__95312,Vvar__3__x__95314)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__95313 = Vvar__3__x__95314
& Vvar__2__Q__95311 = Vvar__2__Q__95312
& Vvar__1__P__95309 = Vvar__1__P__95310
& Vvar__0__A__95307 = Vvar__0__A__95308 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__95364,Vvar__0__A__95365,Vvar__1__P__95366,Vvar__1__P__95367,Vvar__2__x__95368,Vvar__2__x__95369,Vvar__3___24Anonymous__95370,Vvar__3___24Anonymous__95371] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__95364,Vvar__1__P__95366,Vvar__2__x__95368,Vvar__3___24Anonymous__95370) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__95365,Vvar__1__P__95367,Vvar__2__x__95369,Vvar__3___24Anonymous__95371)
=> ( Vvar__3___24Anonymous__95370 = Vvar__3___24Anonymous__95371
& Vvar__2__x__95368 = Vvar__2__x__95369
& Vvar__1__P__95366 = Vvar__1__P__95367
& Vvar__0__A__95364 = Vvar__0__A__95365 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__95416,Vvar__0__A__95417,Vvar__1__P__95418,Vvar__1__P__95419,Vvar__2__Q__95420,Vvar__2__Q__95421,Vvar__3__x__95422,Vvar__3__x__95423,Vvar__4___24Anonymous__95424,Vvar__4___24Anonymous__95425,Vvar__5___24Anonymous__95426,Vvar__5___24Anonymous__95427] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__95416,Vvar__1__P__95418,Vvar__2__Q__95420,Vvar__3__x__95422,Vvar__4___24Anonymous__95424,Vvar__5___24Anonymous__95426) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__95417,Vvar__1__P__95419,Vvar__2__Q__95421,Vvar__3__x__95423,Vvar__4___24Anonymous__95425,Vvar__5___24Anonymous__95427)
=> ( Vvar__5___24Anonymous__95426 = Vvar__5___24Anonymous__95427
& Vvar__4___24Anonymous__95424 = Vvar__4___24Anonymous__95425
& Vvar__3__x__95422 = Vvar__3__x__95423
& Vvar__2__Q__95420 = Vvar__2__Q__95421
& Vvar__1__P__95418 = Vvar__1__P__95419
& Vvar__0__A__95416 = Vvar__0__A__95417 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__78705,Vvar__0__A__78706,Vvar__1__B__78707,Vvar__1__B__78708,Vvar__2___24Anonymous__78709,Vvar__2___24Anonymous__78710] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__78705,Vvar__1__B__78707,Vvar__2___24Anonymous__78709) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__78706,Vvar__1__B__78708,Vvar__2___24Anonymous__78710)
=> ( Vvar__2___24Anonymous__78709 = Vvar__2___24Anonymous__78710
& Vvar__1__B__78707 = Vvar__1__B__78708
& Vvar__0__A__78705 = Vvar__0__A__78706 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__78711,Vvar__0__A__78712,Vvar__1__B__78713,Vvar__1__B__78714,Vvar__2___24Anonymous__78715,Vvar__2___24Anonymous__78716] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__78711,Vvar__1__B__78713) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__78712,Vvar__1__B__78714)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__78713 = Vvar__1__B__78714
& Vvar__0__A__78711 = Vvar__0__A__78712 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__78621,Vvar__0__A__78622,Vvar__1__B__78623,Vvar__1__B__78624,Vvar__2___24Anonymous__78625,Vvar__2___24Anonymous__78626] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__78621,Vvar__1__B__78623) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__78622,Vvar__1__B__78624)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__78623 = Vvar__1__B__78624
& Vvar__0__A__78621 = Vvar__0__A__78622 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__78627,Vvar__0__A__78628,Vvar__1__B__78629,Vvar__1__B__78630,Vvar__2___24Anonymous__78631,Vvar__2___24Anonymous__78632] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__78627,Vvar__1__B__78629) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__78628,Vvar__1__B__78630)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__78629 = Vvar__1__B__78630
& Vvar__0__A__78627 = Vvar__0__A__78628 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__778,Vvar__0___24Anonymous__779] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__778) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__779)
=> Vvar__0___24Anonymous__778 = Vvar__0___24Anonymous__779 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__791,Vvar__0___24Anonymous__792] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__791) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__792)
=> Vvar__0___24Anonymous__791 = Vvar__0___24Anonymous__792 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__789,Vvar__0___24Anonymous__790] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__789) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__790)
=> Vvar__0___24Anonymous__789 = Vvar__0___24Anonymous__790 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__180,Vvar__0___24Anonymous__181] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__180) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__181)
=> Vvar__0___24Anonymous__180 = Vvar__0___24Anonymous__181 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__182,Vvar__0___24Anonymous__183] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__182) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__183)
=> Vvar__0___24Anonymous__182 = Vvar__0___24Anonymous__183 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__191836,Vvar__0___24Anonymous__191837] :
( cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__191836) = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__191837)
=> Vvar__0___24Anonymous__191836 = Vvar__0___24Anonymous__191837 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__111824,Vvar__0__p__111825,Vvar__1___24Anonymous__111826,Vvar__1___24Anonymous__111827] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__111824,Vvar__1___24Anonymous__111826) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__111825,Vvar__1___24Anonymous__111827)
=> ( Vvar__1___24Anonymous__111826 = Vvar__1___24Anonymous__111827
& Vvar__0__p__111824 = Vvar__0__p__111825 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__83214,Vvar__0___24Anonymous__83215] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__83214) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__83215)
=> Vvar__0___24Anonymous__83214 = Vvar__0___24Anonymous__83215 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__91529,Vvar__0__Qnum__91530,Vvar__1__Qden__91531,Vvar__1__Qden__91532] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91529,Vvar__1__Qden__91531) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91530,Vvar__1__Qden__91532)
=> ( Vvar__1__Qden__91531 = Vvar__1__Qden__91532
& Vvar__0__Qnum__91529 = Vvar__0__Qnum__91530 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__104765,Vvar__0__neg__104766,Vvar__1__cond__neg__104767,Vvar__1__cond__neg__104768] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__104765) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__104766)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__104765 = Vvar__0__neg__104766 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__104744,Vvar__0__nonneg__104745,Vvar__1__cond__nonneg__104746,Vvar__1__cond__nonneg__104747] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__104744) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__104745)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__104744 = Vvar__0__nonneg__104745 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__104758,Vvar__0__nonpos__104759,Vvar__1__cond__nonpos__104760,Vvar__1__cond__nonpos__104761] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__104758) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__104759)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__104758 = Vvar__0__nonpos__104759 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__104772,Vvar__0__nonzero__104773,Vvar__1__cond__nonzero__104774,Vvar__1__cond__nonzero__104775] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__104772) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__104773)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__104772 = Vvar__0__nonzero__104773 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__104751,Vvar__0__pos__104752,Vvar__1__cond__pos__104753,Vvar__1__cond__pos__104754] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__104751) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__104752)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__104751 = Vvar__0__pos__104752 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__102470,Vvar__0__x__102471,Vvar__1__n__102472,Vvar__1__n__102473,Vvar__2___24Anonymous__102474,Vvar__2___24Anonymous__102475] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__102470,Vvar__1__n__102472) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__102471,Vvar__1__n__102473)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__102472 = Vvar__1__n__102473
& Vvar__0__x__102470 = Vvar__0__x__102471 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__102460,Vvar__0__x__102461,Vvar__1___24Anonymous__102462,Vvar__1___24Anonymous__102463] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__102460) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__102461)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__102460 = Vvar__0__x__102461 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__102464,Vvar__0__x__102465,Vvar__1__n__102466,Vvar__1__n__102467,Vvar__2___24Anonymous__102468,Vvar__2___24Anonymous__102469] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__102464,Vvar__1__n__102466) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__102465,Vvar__1__n__102467)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__102466 = Vvar__1__n__102467
& Vvar__0__x__102464 = Vvar__0__x__102465 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__66941,Vvar__0___24Anonymous__66942,Vvar__1___24Anonymous__66943,Vvar__1___24Anonymous__66944,Vvar__2___24Anonymous__66945,Vvar__2___24Anonymous__66946,Vvar__3___24Anonymous__66947,Vvar__3___24Anonymous__66948,Vvar__4___24Anonymous__66949,Vvar__4___24Anonymous__66950,Vvar__5___24Anonymous__66951,Vvar__5___24Anonymous__66952,Vvar__6___24Anonymous__66953,Vvar__6___24Anonymous__66954,Vvar__7___24Anonymous__66955,Vvar__7___24Anonymous__66956] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__66941,Vvar__1___24Anonymous__66943,Vvar__2___24Anonymous__66945,Vvar__3___24Anonymous__66947,Vvar__4___24Anonymous__66949,Vvar__5___24Anonymous__66951,Vvar__6___24Anonymous__66953,Vvar__7___24Anonymous__66955) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__66942,Vvar__1___24Anonymous__66944,Vvar__2___24Anonymous__66946,Vvar__3___24Anonymous__66948,Vvar__4___24Anonymous__66950,Vvar__5___24Anonymous__66952,Vvar__6___24Anonymous__66954,Vvar__7___24Anonymous__66956)
=> ( Vvar__7___24Anonymous__66955 = Vvar__7___24Anonymous__66956
& Vvar__6___24Anonymous__66953 = Vvar__6___24Anonymous__66954
& Vvar__5___24Anonymous__66951 = Vvar__5___24Anonymous__66952
& Vvar__4___24Anonymous__66949 = Vvar__4___24Anonymous__66950
& Vvar__3___24Anonymous__66947 = Vvar__3___24Anonymous__66948
& Vvar__2___24Anonymous__66945 = Vvar__2___24Anonymous__66946
& Vvar__1___24Anonymous__66943 = Vvar__1___24Anonymous__66944
& Vvar__0___24Anonymous__66941 = Vvar__0___24Anonymous__66942 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__82095,Vvar__0___24Anonymous__82096,Vvar__1___24Anonymous__82097,Vvar__1___24Anonymous__82098] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82095,Vvar__1___24Anonymous__82097) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82096,Vvar__1___24Anonymous__82098)
=> ( Vvar__1___24Anonymous__82097 = Vvar__1___24Anonymous__82098
& Vvar__0___24Anonymous__82095 = Vvar__0___24Anonymous__82096 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__102217,Vvar__0__X__102218,Vvar__1__lt__102219,Vvar__1__lt__102220,Vvar__2__eq__102221,Vvar__2__eq__102222,Vvar__3__x__102223,Vvar__3__x__102224,Vvar__4__y__102225,Vvar__4__y__102226,Vvar__5___24Anonymous__102227,Vvar__5___24Anonymous__102228] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__102217,Vvar__1__lt__102219,Vvar__2__eq__102221,Vvar__3__x__102223,Vvar__4__y__102225) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__102218,Vvar__1__lt__102220,Vvar__2__eq__102222,Vvar__3__x__102224,Vvar__4__y__102226)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__102225 = Vvar__4__y__102226
& Vvar__3__x__102223 = Vvar__3__x__102224
& Vvar__2__eq__102221 = Vvar__2__eq__102222
& Vvar__1__lt__102219 = Vvar__1__lt__102220
& Vvar__0__X__102217 = Vvar__0__X__102218 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__102229,Vvar__0__X__102230,Vvar__1__lt__102231,Vvar__1__lt__102232,Vvar__2__eq__102233,Vvar__2__eq__102234,Vvar__3__x__102235,Vvar__3__x__102236,Vvar__4__y__102237,Vvar__4__y__102238,Vvar__5___24Anonymous__102239,Vvar__5___24Anonymous__102240] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__102229,Vvar__1__lt__102231,Vvar__2__eq__102233,Vvar__3__x__102235,Vvar__4__y__102237) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__102230,Vvar__1__lt__102232,Vvar__2__eq__102234,Vvar__3__x__102236,Vvar__4__y__102238)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__102237 = Vvar__4__y__102238
& Vvar__3__x__102235 = Vvar__3__x__102236
& Vvar__2__eq__102233 = Vvar__2__eq__102234
& Vvar__1__lt__102231 = Vvar__1__lt__102232
& Vvar__0__X__102229 = Vvar__0__X__102230 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__102205,Vvar__0__X__102206,Vvar__1__lt__102207,Vvar__1__lt__102208,Vvar__2__eq__102209,Vvar__2__eq__102210,Vvar__3__x__102211,Vvar__3__x__102212,Vvar__4__y__102213,Vvar__4__y__102214,Vvar__5___24Anonymous__102215,Vvar__5___24Anonymous__102216] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__102205,Vvar__1__lt__102207,Vvar__2__eq__102209,Vvar__3__x__102211,Vvar__4__y__102213) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__102206,Vvar__1__lt__102208,Vvar__2__eq__102210,Vvar__3__x__102212,Vvar__4__y__102214)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__102213 = Vvar__4__y__102214
& Vvar__3__x__102211 = Vvar__3__x__102212
& Vvar__2__eq__102209 = Vvar__2__eq__102210
& Vvar__1__lt__102207 = Vvar__1__lt__102208
& Vvar__0__X__102205 = Vvar__0__X__102206 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__74910,Vvar__0__n__74911] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74910) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74911)
=> Vvar__0__n__74910 = Vvar__0__n__74911 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__74912,Vvar__0__n__74913,Vvar__1___24Anonymous__74914,Vvar__1___24Anonymous__74915] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74912,Vvar__1___24Anonymous__74914) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74913,Vvar__1___24Anonymous__74915)
=> ( Vvar__1___24Anonymous__74914 = Vvar__1___24Anonymous__74915
& Vvar__0__n__74912 = Vvar__0__n__74913 ) ) ).
fof('$_inj_Coq.Vectors.Vector.cons',axiom,
! [Vvar__0__A__191778,Vvar__0__A__191779,Vvar__1__h__191780,Vvar__1__h__191781,Vvar__2__n__191782,Vvar__2__n__191783,Vvar__3___24Anonymous__191784,Vvar__3___24Anonymous__191785] :
( cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__191778,Vvar__1__h__191780,Vvar__2__n__191782,Vvar__3___24Anonymous__191784) = cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__191779,Vvar__1__h__191781,Vvar__2__n__191783,Vvar__3___24Anonymous__191785)
=> ( Vvar__3___24Anonymous__191784 = Vvar__3___24Anonymous__191785
& Vvar__2__n__191782 = Vvar__2__n__191783
& Vvar__1__h__191780 = Vvar__1__h__191781
& Vvar__0__A__191778 = Vvar__0__A__191779 ) ) ).
fof('$_inj_Coq.Vectors.Vector.nil',axiom,
! [Vvar__0__A__191776,Vvar__0__A__191777] :
( cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__191776) = cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__191777)
=> Vvar__0__A__191776 = Vvar__0__A__191777 ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__78989,Vvar__0__A__78990,Vvar__1__h__78991,Vvar__1__h__78992,Vvar__2__n__78993,Vvar__2__n__78994,Vvar__3___24Anonymous__78995,Vvar__3___24Anonymous__78996] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__78989,Vvar__1__h__78991,Vvar__2__n__78993,Vvar__3___24Anonymous__78995) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__78990,Vvar__1__h__78992,Vvar__2__n__78994,Vvar__3___24Anonymous__78996)
=> ( Vvar__3___24Anonymous__78995 = Vvar__3___24Anonymous__78996
& Vvar__2__n__78993 = Vvar__2__n__78994
& Vvar__1__h__78991 = Vvar__1__h__78992
& Vvar__0__A__78989 = Vvar__0__A__78990 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__78987,Vvar__0__A__78988] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__78987) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__78988)
=> Vvar__0__A__78987 = Vvar__0__A__78988 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__103914,Vvar__0__a__103915,Vvar__1__b__103916,Vvar__1__b__103917,Vvar__2__u__103918,Vvar__2__u__103919,Vvar__3__v__103920,Vvar__3__v__103921,Vvar__4__d__103922,Vvar__4__d__103923,Vvar__5___24Anonymous__103924,Vvar__5___24Anonymous__103925,Vvar__6___24Anonymous__103926,Vvar__6___24Anonymous__103927] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__103914,Vvar__1__b__103916,Vvar__2__u__103918,Vvar__3__v__103920,Vvar__4__d__103922) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__103915,Vvar__1__b__103917,Vvar__2__u__103919,Vvar__3__v__103921,Vvar__4__d__103923)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__103922 = Vvar__4__d__103923
& Vvar__3__v__103920 = Vvar__3__v__103921
& Vvar__2__u__103918 = Vvar__2__u__103919
& Vvar__1__b__103916 = Vvar__1__b__103917
& Vvar__0__a__103914 = Vvar__0__a__103915 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__111526,Vvar__0__x__111527,Vvar__1__p__111528,Vvar__1__p__111529,Vvar__2__q__111530,Vvar__2__q__111531,Vvar__3__r__111532,Vvar__3__r__111533,Vvar__4___24Anonymous__111534,Vvar__4___24Anonymous__111535,Vvar__5___24Anonymous__111536,Vvar__5___24Anonymous__111537,Vvar__6___24Anonymous__111538,Vvar__6___24Anonymous__111539] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__111526,Vvar__1__p__111528,Vvar__2__q__111530,Vvar__3__r__111532) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__111527,Vvar__1__p__111529,Vvar__2__q__111531,Vvar__3__r__111533)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__111532 = Vvar__3__r__111533
& Vvar__2__q__111530 = Vvar__2__q__111531
& Vvar__1__p__111528 = Vvar__1__p__111529
& Vvar__0__x__111526 = Vvar__0__x__111527 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__99347,Vvar__0__C__99348,Vvar__1___24Anonymous__99349,Vvar__1___24Anonymous__99350] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__99347,Vvar__1___24Anonymous__99349) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__99348,Vvar__1___24Anonymous__99350)
=> ( Vvar__1___24Anonymous__99349 = Vvar__1___24Anonymous__99350
& Vvar__0__C__99347 = Vvar__0__C__99348 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__99351,Vvar__0__C__99352,Vvar__1___24Anonymous__99353,Vvar__1___24Anonymous__99354,Vvar__2___24Anonymous__99355,Vvar__2___24Anonymous__99356] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__99351,Vvar__1___24Anonymous__99353,Vvar__2___24Anonymous__99355) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__99352,Vvar__1___24Anonymous__99354,Vvar__2___24Anonymous__99356)
=> ( Vvar__2___24Anonymous__99355 = Vvar__2___24Anonymous__99356
& Vvar__1___24Anonymous__99353 = Vvar__1___24Anonymous__99354
& Vvar__0__C__99351 = Vvar__0__C__99352 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__99343,Vvar__0__C__99344,Vvar__1___24Anonymous__99345,Vvar__1___24Anonymous__99346] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__99343,Vvar__1___24Anonymous__99345) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__99344,Vvar__1___24Anonymous__99346)
=> ( Vvar__1___24Anonymous__99345 = Vvar__1___24Anonymous__99346
& Vvar__0__C__99343 = Vvar__0__C__99344 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__99363,Vvar__0__C__99364,Vvar__1___24Anonymous__99365,Vvar__1___24Anonymous__99366,Vvar__2___24Anonymous__99367,Vvar__2___24Anonymous__99368] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__99363,Vvar__1___24Anonymous__99365,Vvar__2___24Anonymous__99367) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__99364,Vvar__1___24Anonymous__99366,Vvar__2___24Anonymous__99368)
=> ( Vvar__2___24Anonymous__99367 = Vvar__2___24Anonymous__99368
& Vvar__1___24Anonymous__99365 = Vvar__1___24Anonymous__99366
& Vvar__0__C__99363 = Vvar__0__C__99364 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__99369,Vvar__0__C__99370,Vvar__1___24Anonymous__99371,Vvar__1___24Anonymous__99372] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__99369,Vvar__1___24Anonymous__99371) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__99370,Vvar__1___24Anonymous__99372)
=> ( Vvar__1___24Anonymous__99371 = Vvar__1___24Anonymous__99372
& Vvar__0__C__99369 = Vvar__0__C__99370 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__99373,Vvar__0__C__99374,Vvar__1___24Anonymous__99375,Vvar__1___24Anonymous__99376,Vvar__2___24Anonymous__99377,Vvar__2___24Anonymous__99378] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__99373,Vvar__1___24Anonymous__99375,Vvar__2___24Anonymous__99377) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__99374,Vvar__1___24Anonymous__99376,Vvar__2___24Anonymous__99378)
=> ( Vvar__2___24Anonymous__99377 = Vvar__2___24Anonymous__99378
& Vvar__1___24Anonymous__99375 = Vvar__1___24Anonymous__99376
& Vvar__0__C__99373 = Vvar__0__C__99374 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__99357,Vvar__0__C__99358,Vvar__1___24Anonymous__99359,Vvar__1___24Anonymous__99360,Vvar__2___24Anonymous__99361,Vvar__2___24Anonymous__99362] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__99357,Vvar__1___24Anonymous__99359,Vvar__2___24Anonymous__99361) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__99358,Vvar__1___24Anonymous__99360,Vvar__2___24Anonymous__99362)
=> ( Vvar__2___24Anonymous__99361 = Vvar__2___24Anonymous__99362
& Vvar__1___24Anonymous__99359 = Vvar__1___24Anonymous__99360
& Vvar__0__C__99357 = Vvar__0__C__99358 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__99418,Vvar__0__C__99419,Vvar__1___24Anonymous__99420,Vvar__1___24Anonymous__99421,Vvar__2___24Anonymous__99422,Vvar__2___24Anonymous__99423,Vvar__3___24Anonymous__99424,Vvar__3___24Anonymous__99425] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__99418,Vvar__1___24Anonymous__99420,Vvar__2___24Anonymous__99422,Vvar__3___24Anonymous__99424) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__99419,Vvar__1___24Anonymous__99421,Vvar__2___24Anonymous__99423,Vvar__3___24Anonymous__99425)
=> ( Vvar__3___24Anonymous__99424 = Vvar__3___24Anonymous__99425
& Vvar__2___24Anonymous__99422 = Vvar__2___24Anonymous__99423
& Vvar__1___24Anonymous__99420 = Vvar__1___24Anonymous__99421
& Vvar__0__C__99418 = Vvar__0__C__99419 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__99408,Vvar__0__C__99409,Vvar__1___24Anonymous__99410,Vvar__1___24Anonymous__99411] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__99408,Vvar__1___24Anonymous__99410) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__99409,Vvar__1___24Anonymous__99411)
=> ( Vvar__1___24Anonymous__99410 = Vvar__1___24Anonymous__99411
& Vvar__0__C__99408 = Vvar__0__C__99409 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__99412,Vvar__0__C__99413,Vvar__1___24Anonymous__99414,Vvar__1___24Anonymous__99415,Vvar__2___24Anonymous__99416,Vvar__2___24Anonymous__99417] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__99412,Vvar__1___24Anonymous__99414,Vvar__2___24Anonymous__99416) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__99413,Vvar__1___24Anonymous__99415,Vvar__2___24Anonymous__99417)
=> ( Vvar__2___24Anonymous__99416 = Vvar__2___24Anonymous__99417
& Vvar__1___24Anonymous__99414 = Vvar__1___24Anonymous__99415
& Vvar__0__C__99412 = Vvar__0__C__99413 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__99443,Vvar__0___24Anonymous__99444,Vvar__1___24Anonymous__99445,Vvar__1___24Anonymous__99446] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__99443,Vvar__1___24Anonymous__99445) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__99444,Vvar__1___24Anonymous__99446)
=> ( Vvar__1___24Anonymous__99445 = Vvar__1___24Anonymous__99446
& Vvar__0___24Anonymous__99443 = Vvar__0___24Anonymous__99444 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__99439,Vvar__0___24Anonymous__99440,Vvar__1___24Anonymous__99441,Vvar__1___24Anonymous__99442] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__99439,Vvar__1___24Anonymous__99441) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__99440,Vvar__1___24Anonymous__99442)
=> ( Vvar__1___24Anonymous__99441 = Vvar__1___24Anonymous__99442
& Vvar__0___24Anonymous__99439 = Vvar__0___24Anonymous__99440 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__102383,Vvar__0__r__102384] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__102383) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__102384)
=> Vvar__0__r__102383 = Vvar__0__r__102384 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__102371,Vvar__0__r1__102372,Vvar__1__r2__102373,Vvar__1__r2__102374] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__102371,Vvar__1__r2__102373) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__102372,Vvar__1__r2__102374)
=> ( Vvar__1__r2__102373 = Vvar__1__r2__102374
& Vvar__0__r1__102371 = Vvar__0__r1__102372 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__102375,Vvar__0__r1__102376,Vvar__1__r2__102377,Vvar__1__r2__102378] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__102375,Vvar__1__r2__102377) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__102376,Vvar__1__r2__102378)
=> ( Vvar__1__r2__102377 = Vvar__1__r2__102378
& Vvar__0__r1__102375 = Vvar__0__r1__102376 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__102385,Vvar__0__r__102386] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__102385) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__102386)
=> Vvar__0__r__102385 = Vvar__0__r__102386 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__102367,Vvar__0__r1__102368,Vvar__1__r2__102369,Vvar__1__r2__102370] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__102367,Vvar__1__r2__102369) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__102368,Vvar__1__r2__102370)
=> ( Vvar__1__r2__102369 = Vvar__1__r2__102370
& Vvar__0__r1__102367 = Vvar__0__r1__102368 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__102379,Vvar__0__r1__102380,Vvar__1__z__102381,Vvar__1__z__102382] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__102379,Vvar__1__z__102381) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__102380,Vvar__1__z__102382)
=> ( Vvar__1__z__102381 = Vvar__1__z__102382
& Vvar__0__r1__102379 = Vvar__0__r1__102380 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__102363,Vvar__0__r__102364] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__102363) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__102364)
=> Vvar__0__r__102363 = Vvar__0__r__102364 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__102365,Vvar__0__r__102366] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__102365) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__102366)
=> Vvar__0__r__102365 = Vvar__0__r__102366 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__102484,Vvar__0__T__102485,Vvar__1__Flhs__102486,Vvar__1__Flhs__102487,Vvar__2__Fop__102488,Vvar__2__Fop__102489,Vvar__3__Frhs__102490,Vvar__3__Frhs__102491] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__102484,Vvar__1__Flhs__102486,Vvar__2__Fop__102488,Vvar__3__Frhs__102490) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__102485,Vvar__1__Flhs__102487,Vvar__2__Fop__102489,Vvar__3__Frhs__102491)
=> ( Vvar__3__Frhs__102490 = Vvar__3__Frhs__102491
& Vvar__2__Fop__102488 = Vvar__2__Fop__102489
& Vvar__1__Flhs__102486 = Vvar__1__Flhs__102487
& Vvar__0__T__102484 = Vvar__0__T__102485 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__110278,Vvar__0__C__110279,Vvar__1___24Anonymous__110280,Vvar__1___24Anonymous__110281,Vvar__2___24Anonymous__110282,Vvar__2___24Anonymous__110283] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__110278,Vvar__1___24Anonymous__110280,Vvar__2___24Anonymous__110282) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__110279,Vvar__1___24Anonymous__110281,Vvar__2___24Anonymous__110283)
=> ( Vvar__2___24Anonymous__110282 = Vvar__2___24Anonymous__110283
& Vvar__1___24Anonymous__110280 = Vvar__1___24Anonymous__110281
& Vvar__0__C__110278 = Vvar__0__C__110279 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__110284,Vvar__0__C__110285,Vvar__1___24Anonymous__110286,Vvar__1___24Anonymous__110287] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__110284,Vvar__1___24Anonymous__110286) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__110285,Vvar__1___24Anonymous__110287)
=> ( Vvar__1___24Anonymous__110286 = Vvar__1___24Anonymous__110287
& Vvar__0__C__110284 = Vvar__0__C__110285 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__110258,Vvar__0__C__110259,Vvar__1___24Anonymous__110260,Vvar__1___24Anonymous__110261] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__110258,Vvar__1___24Anonymous__110260) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__110259,Vvar__1___24Anonymous__110261)
=> ( Vvar__1___24Anonymous__110260 = Vvar__1___24Anonymous__110261
& Vvar__0__C__110258 = Vvar__0__C__110259 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__110266,Vvar__0__C__110267,Vvar__1___24Anonymous__110268,Vvar__1___24Anonymous__110269,Vvar__2___24Anonymous__110270,Vvar__2___24Anonymous__110271] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__110266,Vvar__1___24Anonymous__110268,Vvar__2___24Anonymous__110270) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__110267,Vvar__1___24Anonymous__110269,Vvar__2___24Anonymous__110271)
=> ( Vvar__2___24Anonymous__110270 = Vvar__2___24Anonymous__110271
& Vvar__1___24Anonymous__110268 = Vvar__1___24Anonymous__110269
& Vvar__0__C__110266 = Vvar__0__C__110267 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__110272,Vvar__0__C__110273,Vvar__1___24Anonymous__110274,Vvar__1___24Anonymous__110275,Vvar__2___24Anonymous__110276,Vvar__2___24Anonymous__110277] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__110272,Vvar__1___24Anonymous__110274,Vvar__2___24Anonymous__110276) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__110273,Vvar__1___24Anonymous__110275,Vvar__2___24Anonymous__110277)
=> ( Vvar__2___24Anonymous__110276 = Vvar__2___24Anonymous__110277
& Vvar__1___24Anonymous__110274 = Vvar__1___24Anonymous__110275
& Vvar__0__C__110272 = Vvar__0__C__110273 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__110262,Vvar__0__C__110263,Vvar__1___24Anonymous__110264,Vvar__1___24Anonymous__110265] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__110262,Vvar__1___24Anonymous__110264) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__110263,Vvar__1___24Anonymous__110265)
=> ( Vvar__1___24Anonymous__110264 = Vvar__1___24Anonymous__110265
& Vvar__0__C__110262 = Vvar__0__C__110263 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__110288,Vvar__0__C__110289] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__110288) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__110289)
=> Vvar__0__C__110288 = Vvar__0__C__110289 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__103815,Vvar__0__TA__103816,Vvar__1__TX__103817,Vvar__1__TX__103818,Vvar__2__AA__103819,Vvar__2__AA__103820,Vvar__3__AF__103821,Vvar__3__AF__103822,Vvar__4___24Anonymous__103823,Vvar__4___24Anonymous__103824,Vvar__5___24Anonymous__103825,Vvar__5___24Anonymous__103826] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__103815,Vvar__1__TX__103817,Vvar__2__AA__103819,Vvar__3__AF__103821,Vvar__4___24Anonymous__103823,Vvar__5___24Anonymous__103825) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__103816,Vvar__1__TX__103818,Vvar__2__AA__103820,Vvar__3__AF__103822,Vvar__4___24Anonymous__103824,Vvar__5___24Anonymous__103826)
=> ( Vvar__5___24Anonymous__103825 = Vvar__5___24Anonymous__103826
& Vvar__4___24Anonymous__103823 = Vvar__4___24Anonymous__103824
& Vvar__3__AF__103821 = Vvar__3__AF__103822
& Vvar__2__AA__103819 = Vvar__2__AA__103820
& Vvar__1__TX__103817 = Vvar__1__TX__103818
& Vvar__0__TA__103815 = Vvar__0__TA__103816 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__103827,Vvar__0__TA__103828,Vvar__1__TX__103829,Vvar__1__TX__103830,Vvar__2__AA__103831,Vvar__2__AA__103832,Vvar__3__AF__103833,Vvar__3__AF__103834,Vvar__4___24Anonymous__103835,Vvar__4___24Anonymous__103836,Vvar__5___24Anonymous__103837,Vvar__5___24Anonymous__103838] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__103827,Vvar__1__TX__103829,Vvar__2__AA__103831,Vvar__3__AF__103833,Vvar__4___24Anonymous__103835,Vvar__5___24Anonymous__103837) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__103828,Vvar__1__TX__103830,Vvar__2__AA__103832,Vvar__3__AF__103834,Vvar__4___24Anonymous__103836,Vvar__5___24Anonymous__103838)
=> ( Vvar__5___24Anonymous__103837 = Vvar__5___24Anonymous__103838
& Vvar__4___24Anonymous__103835 = Vvar__4___24Anonymous__103836
& Vvar__3__AF__103833 = Vvar__3__AF__103834
& Vvar__2__AA__103831 = Vvar__2__AA__103832
& Vvar__1__TX__103829 = Vvar__1__TX__103830
& Vvar__0__TA__103827 = Vvar__0__TA__103828 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__103839,Vvar__0__TA__103840,Vvar__1__TX__103841,Vvar__1__TX__103842,Vvar__2__AA__103843,Vvar__2__AA__103844,Vvar__3__AF__103845,Vvar__3__AF__103846,Vvar__4___24Anonymous__103847,Vvar__4___24Anonymous__103848,Vvar__5___24Anonymous__103849,Vvar__5___24Anonymous__103850] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__103839,Vvar__1__TX__103841,Vvar__2__AA__103843,Vvar__3__AF__103845,Vvar__4___24Anonymous__103847,Vvar__5___24Anonymous__103849) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__103840,Vvar__1__TX__103842,Vvar__2__AA__103844,Vvar__3__AF__103846,Vvar__4___24Anonymous__103848,Vvar__5___24Anonymous__103850)
=> ( Vvar__5___24Anonymous__103849 = Vvar__5___24Anonymous__103850
& Vvar__4___24Anonymous__103847 = Vvar__4___24Anonymous__103848
& Vvar__3__AF__103845 = Vvar__3__AF__103846
& Vvar__2__AA__103843 = Vvar__2__AA__103844
& Vvar__1__TX__103841 = Vvar__1__TX__103842
& Vvar__0__TA__103839 = Vvar__0__TA__103840 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__103797,Vvar__0__TA__103798,Vvar__1__TX__103799,Vvar__1__TX__103800,Vvar__2__AA__103801,Vvar__2__AA__103802,Vvar__3__AF__103803,Vvar__3__AF__103804] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__103797,Vvar__1__TX__103799,Vvar__2__AA__103801,Vvar__3__AF__103803) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__103798,Vvar__1__TX__103800,Vvar__2__AA__103802,Vvar__3__AF__103804)
=> ( Vvar__3__AF__103803 = Vvar__3__AF__103804
& Vvar__2__AA__103801 = Vvar__2__AA__103802
& Vvar__1__TX__103799 = Vvar__1__TX__103800
& Vvar__0__TA__103797 = Vvar__0__TA__103798 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__103861,Vvar__0__TA__103862,Vvar__1__TX__103863,Vvar__1__TX__103864,Vvar__2__AA__103865,Vvar__2__AA__103866,Vvar__3__AF__103867,Vvar__3__AF__103868,Vvar__4___24Anonymous__103869,Vvar__4___24Anonymous__103870,Vvar__5___24Anonymous__103871,Vvar__5___24Anonymous__103872,Vvar__6___24Anonymous__103873,Vvar__6___24Anonymous__103874] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__103861,Vvar__1__TX__103863,Vvar__2__AA__103865,Vvar__3__AF__103867,Vvar__4___24Anonymous__103869,Vvar__5___24Anonymous__103871,Vvar__6___24Anonymous__103873) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__103862,Vvar__1__TX__103864,Vvar__2__AA__103866,Vvar__3__AF__103868,Vvar__4___24Anonymous__103870,Vvar__5___24Anonymous__103872,Vvar__6___24Anonymous__103874)
=> ( Vvar__6___24Anonymous__103873 = Vvar__6___24Anonymous__103874
& Vvar__5___24Anonymous__103871 = Vvar__5___24Anonymous__103872
& Vvar__4___24Anonymous__103869 = Vvar__4___24Anonymous__103870
& Vvar__3__AF__103867 = Vvar__3__AF__103868
& Vvar__2__AA__103865 = Vvar__2__AA__103866
& Vvar__1__TX__103863 = Vvar__1__TX__103864
& Vvar__0__TA__103861 = Vvar__0__TA__103862 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__103851,Vvar__0__TA__103852,Vvar__1__TX__103853,Vvar__1__TX__103854,Vvar__2__AA__103855,Vvar__2__AA__103856,Vvar__3__AF__103857,Vvar__3__AF__103858,Vvar__4___24Anonymous__103859,Vvar__4___24Anonymous__103860] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__103851,Vvar__1__TX__103853,Vvar__2__AA__103855,Vvar__3__AF__103857,Vvar__4___24Anonymous__103859) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__103852,Vvar__1__TX__103854,Vvar__2__AA__103856,Vvar__3__AF__103858,Vvar__4___24Anonymous__103860)
=> ( Vvar__4___24Anonymous__103859 = Vvar__4___24Anonymous__103860
& Vvar__3__AF__103857 = Vvar__3__AF__103858
& Vvar__2__AA__103855 = Vvar__2__AA__103856
& Vvar__1__TX__103853 = Vvar__1__TX__103854
& Vvar__0__TA__103851 = Vvar__0__TA__103852 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__103789,Vvar__0__TA__103790,Vvar__1__TX__103791,Vvar__1__TX__103792,Vvar__2__AA__103793,Vvar__2__AA__103794,Vvar__3__AF__103795,Vvar__3__AF__103796] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__103789,Vvar__1__TX__103791,Vvar__2__AA__103793,Vvar__3__AF__103795) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__103790,Vvar__1__TX__103792,Vvar__2__AA__103794,Vvar__3__AF__103796)
=> ( Vvar__3__AF__103795 = Vvar__3__AF__103796
& Vvar__2__AA__103793 = Vvar__2__AA__103794
& Vvar__1__TX__103791 = Vvar__1__TX__103792
& Vvar__0__TA__103789 = Vvar__0__TA__103790 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__103805,Vvar__0__TA__103806,Vvar__1__TX__103807,Vvar__1__TX__103808,Vvar__2__AA__103809,Vvar__2__AA__103810,Vvar__3__AF__103811,Vvar__3__AF__103812,Vvar__4___24Anonymous__103813,Vvar__4___24Anonymous__103814] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__103805,Vvar__1__TX__103807,Vvar__2__AA__103809,Vvar__3__AF__103811,Vvar__4___24Anonymous__103813) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__103806,Vvar__1__TX__103808,Vvar__2__AA__103810,Vvar__3__AF__103812,Vvar__4___24Anonymous__103814)
=> ( Vvar__4___24Anonymous__103813 = Vvar__4___24Anonymous__103814
& Vvar__3__AF__103811 = Vvar__3__AF__103812
& Vvar__2__AA__103809 = Vvar__2__AA__103810
& Vvar__1__TX__103807 = Vvar__1__TX__103808
& Vvar__0__TA__103805 = Vvar__0__TA__103806 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__111417,Vvar__0__A__111418,Vvar__1___24Anonymous__111419,Vvar__1___24Anonymous__111420,Vvar__2___24Anonymous__111421,Vvar__2___24Anonymous__111422,Vvar__3___24Anonymous__111423,Vvar__3___24Anonymous__111424] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__111417,Vvar__1___24Anonymous__111419,Vvar__2___24Anonymous__111421,Vvar__3___24Anonymous__111423) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__111418,Vvar__1___24Anonymous__111420,Vvar__2___24Anonymous__111422,Vvar__3___24Anonymous__111424)
=> ( Vvar__3___24Anonymous__111423 = Vvar__3___24Anonymous__111424
& Vvar__2___24Anonymous__111421 = Vvar__2___24Anonymous__111422
& Vvar__1___24Anonymous__111419 = Vvar__1___24Anonymous__111420
& Vvar__0__A__111417 = Vvar__0__A__111418 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__111413,Vvar__0__A__111414,Vvar__1___24Anonymous__111415,Vvar__1___24Anonymous__111416] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__111413,Vvar__1___24Anonymous__111415) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__111414,Vvar__1___24Anonymous__111416)
=> ( Vvar__1___24Anonymous__111415 = Vvar__1___24Anonymous__111416
& Vvar__0__A__111413 = Vvar__0__A__111414 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__111411,Vvar__0__A__111412] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__111411) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__111412)
=> Vvar__0__A__111411 = Vvar__0__A__111412 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__81133,Vvar__0___24Anonymous__81134,Vvar__1___24Anonymous__81135,Vvar__1___24Anonymous__81136] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__81133,Vvar__1___24Anonymous__81135) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__81134,Vvar__1___24Anonymous__81136)
=> ( Vvar__1___24Anonymous__81135 = Vvar__1___24Anonymous__81136
& Vvar__0___24Anonymous__81133 = Vvar__0___24Anonymous__81134 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__81137,Vvar__0___24Anonymous__81138,Vvar__1___24Anonymous__81139,Vvar__1___24Anonymous__81140,Vvar__2___24Anonymous__81141,Vvar__2___24Anonymous__81142] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__81137,Vvar__1___24Anonymous__81139,Vvar__2___24Anonymous__81141) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__81138,Vvar__1___24Anonymous__81140,Vvar__2___24Anonymous__81142)
=> ( Vvar__2___24Anonymous__81141 = Vvar__2___24Anonymous__81142
& Vvar__1___24Anonymous__81139 = Vvar__1___24Anonymous__81140
& Vvar__0___24Anonymous__81137 = Vvar__0___24Anonymous__81138 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__81129,Vvar__0___24Anonymous__81130,Vvar__1___24Anonymous__81131,Vvar__1___24Anonymous__81132] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__81129,Vvar__1___24Anonymous__81131) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__81130,Vvar__1___24Anonymous__81132)
=> ( Vvar__1___24Anonymous__81131 = Vvar__1___24Anonymous__81132
& Vvar__0___24Anonymous__81129 = Vvar__0___24Anonymous__81130 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.Vars.Node',axiom,
! [Vvar__0___24Anonymous__191871,Vvar__0___24Anonymous__191872,Vvar__1___24Anonymous__191873,Vvar__1___24Anonymous__191874,Vvar__2___24Anonymous__191875,Vvar__2___24Anonymous__191876] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__191871,Vvar__1___24Anonymous__191873,Vvar__2___24Anonymous__191875) = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__191872,Vvar__1___24Anonymous__191874,Vvar__2___24Anonymous__191876)
=> ( Vvar__2___24Anonymous__191875 = Vvar__2___24Anonymous__191876
& Vvar__1___24Anonymous__191873 = Vvar__1___24Anonymous__191874
& Vvar__0___24Anonymous__191871 = Vvar__0___24Anonymous__191872 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__90246,Vvar__0__C__90247] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__90246) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__90247)
=> Vvar__0__C__90246 = Vvar__0__C__90247 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__90244,Vvar__0__C__90245] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__90244) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__90245)
=> Vvar__0__C__90244 = Vvar__0__C__90245 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__90252,Vvar__0__C__90253,Vvar__1___24Anonymous__90254,Vvar__1___24Anonymous__90255] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__90252,Vvar__1___24Anonymous__90254) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__90253,Vvar__1___24Anonymous__90255)
=> ( Vvar__1___24Anonymous__90254 = Vvar__1___24Anonymous__90255
& Vvar__0__C__90252 = Vvar__0__C__90253 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__90256,Vvar__0__C__90257,Vvar__1___24Anonymous__90258,Vvar__1___24Anonymous__90259,Vvar__2___24Anonymous__90260,Vvar__2___24Anonymous__90261] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__90256,Vvar__1___24Anonymous__90258,Vvar__2___24Anonymous__90260) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__90257,Vvar__1___24Anonymous__90259,Vvar__2___24Anonymous__90261)
=> ( Vvar__2___24Anonymous__90260 = Vvar__2___24Anonymous__90261
& Vvar__1___24Anonymous__90258 = Vvar__1___24Anonymous__90259
& Vvar__0__C__90256 = Vvar__0__C__90257 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__90248,Vvar__0__C__90249,Vvar__1___24Anonymous__90250,Vvar__1___24Anonymous__90251] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__90248,Vvar__1___24Anonymous__90250) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__90249,Vvar__1___24Anonymous__90251)
=> ( Vvar__1___24Anonymous__90250 = Vvar__1___24Anonymous__90251
& Vvar__0__C__90248 = Vvar__0__C__90249 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__90282,Vvar__0__C__90283,Vvar__1___24Anonymous__90284,Vvar__1___24Anonymous__90285,Vvar__2___24Anonymous__90286,Vvar__2___24Anonymous__90287] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__90282,Vvar__1___24Anonymous__90284,Vvar__2___24Anonymous__90286) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__90283,Vvar__1___24Anonymous__90285,Vvar__2___24Anonymous__90287)
=> ( Vvar__2___24Anonymous__90286 = Vvar__2___24Anonymous__90287
& Vvar__1___24Anonymous__90284 = Vvar__1___24Anonymous__90285
& Vvar__0__C__90282 = Vvar__0__C__90283 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__90278,Vvar__0__C__90279,Vvar__1___24Anonymous__90280,Vvar__1___24Anonymous__90281] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__90278,Vvar__1___24Anonymous__90280) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__90279,Vvar__1___24Anonymous__90281)
=> ( Vvar__1___24Anonymous__90280 = Vvar__1___24Anonymous__90281
& Vvar__0__C__90278 = Vvar__0__C__90279 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__90268,Vvar__0__C__90269,Vvar__1___24Anonymous__90270,Vvar__1___24Anonymous__90271,Vvar__2___24Anonymous__90272,Vvar__2___24Anonymous__90273] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__90268,Vvar__1___24Anonymous__90270,Vvar__2___24Anonymous__90272) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__90269,Vvar__1___24Anonymous__90271,Vvar__2___24Anonymous__90273)
=> ( Vvar__2___24Anonymous__90272 = Vvar__2___24Anonymous__90273
& Vvar__1___24Anonymous__90270 = Vvar__1___24Anonymous__90271
& Vvar__0__C__90268 = Vvar__0__C__90269 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__90274,Vvar__0__C__90275,Vvar__1___24Anonymous__90276,Vvar__1___24Anonymous__90277] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__90274,Vvar__1___24Anonymous__90276) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__90275,Vvar__1___24Anonymous__90277)
=> ( Vvar__1___24Anonymous__90276 = Vvar__1___24Anonymous__90277
& Vvar__0__C__90274 = Vvar__0__C__90275 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__90288,Vvar__0__C__90289,Vvar__1___24Anonymous__90290,Vvar__1___24Anonymous__90291,Vvar__2___24Anonymous__90292,Vvar__2___24Anonymous__90293] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__90288,Vvar__1___24Anonymous__90290,Vvar__2___24Anonymous__90292) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__90289,Vvar__1___24Anonymous__90291,Vvar__2___24Anonymous__90293)
=> ( Vvar__2___24Anonymous__90292 = Vvar__2___24Anonymous__90293
& Vvar__1___24Anonymous__90290 = Vvar__1___24Anonymous__90291
& Vvar__0__C__90288 = Vvar__0__C__90289 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__90262,Vvar__0__C__90263,Vvar__1___24Anonymous__90264,Vvar__1___24Anonymous__90265,Vvar__2___24Anonymous__90266,Vvar__2___24Anonymous__90267] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__90262,Vvar__1___24Anonymous__90264,Vvar__2___24Anonymous__90266) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__90263,Vvar__1___24Anonymous__90265,Vvar__2___24Anonymous__90267)
=> ( Vvar__2___24Anonymous__90266 = Vvar__2___24Anonymous__90267
& Vvar__1___24Anonymous__90264 = Vvar__1___24Anonymous__90265
& Vvar__0__C__90262 = Vvar__0__C__90263 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__90591,Vvar__0__C__90592,Vvar__1__num__90593,Vvar__1__num__90594,Vvar__2__denum__90595,Vvar__2__denum__90596,Vvar__3__condition__90597,Vvar__3__condition__90598] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__90591,Vvar__1__num__90593,Vvar__2__denum__90595,Vvar__3__condition__90597) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__90592,Vvar__1__num__90594,Vvar__2__denum__90596,Vvar__3__condition__90598)
=> ( Vvar__3__condition__90597 = Vvar__3__condition__90598
& Vvar__2__denum__90595 = Vvar__2__denum__90596
& Vvar__1__num__90593 = Vvar__1__num__90594
& Vvar__0__C__90591 = Vvar__0__C__90592 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__104166,Vvar__0__C__104167,Vvar__1__rsplit__left__104168,Vvar__1__rsplit__left__104169,Vvar__2__rsplit__common__104170,Vvar__2__rsplit__common__104171,Vvar__3__rsplit__right__104172,Vvar__3__rsplit__right__104173] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__104166,Vvar__1__rsplit__left__104168,Vvar__2__rsplit__common__104170,Vvar__3__rsplit__right__104172) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__104167,Vvar__1__rsplit__left__104169,Vvar__2__rsplit__common__104171,Vvar__3__rsplit__right__104173)
=> ( Vvar__3__rsplit__right__104172 = Vvar__3__rsplit__right__104173
& Vvar__2__rsplit__common__104170 = Vvar__2__rsplit__common__104171
& Vvar__1__rsplit__left__104168 = Vvar__1__rsplit__left__104169
& Vvar__0__C__104166 = Vvar__0__C__104167 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__104577,Vvar__0__hypo__type__104578,Vvar__1__hypo__proof__104579,Vvar__1__hypo__proof__104580] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__104577,Vvar__1__hypo__proof__104579) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__104578,Vvar__1__hypo__proof__104580)
=> ( Vvar__1__hypo__proof__104579 = Vvar__1__hypo__proof__104580
& Vvar__0__hypo__type__104577 = Vvar__0__hypo__type__104578 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__439,Vvar__0__C__440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__439) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__440)
=> Vvar__0__C__439 = Vvar__0__C__440 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__437,Vvar__0__C__438] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__437) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__438)
=> Vvar__0__C__437 = Vvar__0__C__438 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__445,Vvar__0__C__446,Vvar__1___24Anonymous__447,Vvar__1___24Anonymous__448] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__445,Vvar__1___24Anonymous__447) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__446,Vvar__1___24Anonymous__448)
=> ( Vvar__1___24Anonymous__447 = Vvar__1___24Anonymous__448
& Vvar__0__C__445 = Vvar__0__C__446 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__449,Vvar__0__C__450,Vvar__1___24Anonymous__451,Vvar__1___24Anonymous__452,Vvar__2___24Anonymous__453,Vvar__2___24Anonymous__454] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__449,Vvar__1___24Anonymous__451,Vvar__2___24Anonymous__453) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__450,Vvar__1___24Anonymous__452,Vvar__2___24Anonymous__454)
=> ( Vvar__2___24Anonymous__453 = Vvar__2___24Anonymous__454
& Vvar__1___24Anonymous__451 = Vvar__1___24Anonymous__452
& Vvar__0__C__449 = Vvar__0__C__450 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__441,Vvar__0__C__442,Vvar__1___24Anonymous__443,Vvar__1___24Anonymous__444] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__441,Vvar__1___24Anonymous__443) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__442,Vvar__1___24Anonymous__444)
=> ( Vvar__1___24Anonymous__443 = Vvar__1___24Anonymous__444
& Vvar__0__C__441 = Vvar__0__C__442 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__461,Vvar__0__C__462,Vvar__1___24Anonymous__463,Vvar__1___24Anonymous__464,Vvar__2___24Anonymous__465,Vvar__2___24Anonymous__466] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__461,Vvar__1___24Anonymous__463,Vvar__2___24Anonymous__465) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__462,Vvar__1___24Anonymous__464,Vvar__2___24Anonymous__466)
=> ( Vvar__2___24Anonymous__465 = Vvar__2___24Anonymous__466
& Vvar__1___24Anonymous__463 = Vvar__1___24Anonymous__464
& Vvar__0__C__461 = Vvar__0__C__462 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__467,Vvar__0__C__468,Vvar__1___24Anonymous__469,Vvar__1___24Anonymous__470] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__467,Vvar__1___24Anonymous__469) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__468,Vvar__1___24Anonymous__470)
=> ( Vvar__1___24Anonymous__469 = Vvar__1___24Anonymous__470
& Vvar__0__C__467 = Vvar__0__C__468 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__471,Vvar__0__C__472,Vvar__1___24Anonymous__473,Vvar__1___24Anonymous__474,Vvar__2___24Anonymous__475,Vvar__2___24Anonymous__476] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__471,Vvar__1___24Anonymous__473,Vvar__2___24Anonymous__475) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__472,Vvar__1___24Anonymous__474,Vvar__2___24Anonymous__476)
=> ( Vvar__2___24Anonymous__475 = Vvar__2___24Anonymous__476
& Vvar__1___24Anonymous__473 = Vvar__1___24Anonymous__474
& Vvar__0__C__471 = Vvar__0__C__472 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__455,Vvar__0__C__456,Vvar__1___24Anonymous__457,Vvar__1___24Anonymous__458,Vvar__2___24Anonymous__459,Vvar__2___24Anonymous__460] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__455,Vvar__1___24Anonymous__457,Vvar__2___24Anonymous__459) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__456,Vvar__1___24Anonymous__458,Vvar__2___24Anonymous__460)
=> ( Vvar__2___24Anonymous__459 = Vvar__2___24Anonymous__460
& Vvar__1___24Anonymous__457 = Vvar__1___24Anonymous__458
& Vvar__0__C__455 = Vvar__0__C__456 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__226,Vvar__0__C__227,Vvar__1___24Anonymous__228,Vvar__1___24Anonymous__229,Vvar__2___24Anonymous__230,Vvar__2___24Anonymous__231,Vvar__3___24Anonymous__232,Vvar__3___24Anonymous__233] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__226,Vvar__1___24Anonymous__228,Vvar__2___24Anonymous__230,Vvar__3___24Anonymous__232) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__227,Vvar__1___24Anonymous__229,Vvar__2___24Anonymous__231,Vvar__3___24Anonymous__233)
=> ( Vvar__3___24Anonymous__232 = Vvar__3___24Anonymous__233
& Vvar__2___24Anonymous__230 = Vvar__2___24Anonymous__231
& Vvar__1___24Anonymous__228 = Vvar__1___24Anonymous__229
& Vvar__0__C__226 = Vvar__0__C__227 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__216,Vvar__0__C__217,Vvar__1___24Anonymous__218,Vvar__1___24Anonymous__219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__216,Vvar__1___24Anonymous__218) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__217,Vvar__1___24Anonymous__219)
=> ( Vvar__1___24Anonymous__218 = Vvar__1___24Anonymous__219
& Vvar__0__C__216 = Vvar__0__C__217 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__220,Vvar__0__C__221,Vvar__1___24Anonymous__222,Vvar__1___24Anonymous__223,Vvar__2___24Anonymous__224,Vvar__2___24Anonymous__225] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__220,Vvar__1___24Anonymous__222,Vvar__2___24Anonymous__224) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__221,Vvar__1___24Anonymous__223,Vvar__2___24Anonymous__225)
=> ( Vvar__2___24Anonymous__224 = Vvar__2___24Anonymous__225
& Vvar__1___24Anonymous__222 = Vvar__1___24Anonymous__223
& Vvar__0__C__220 = Vvar__0__C__221 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__251,Vvar__0___24Anonymous__252,Vvar__1___24Anonymous__253,Vvar__1___24Anonymous__254] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__251,Vvar__1___24Anonymous__253) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__252,Vvar__1___24Anonymous__254)
=> ( Vvar__1___24Anonymous__253 = Vvar__1___24Anonymous__254
& Vvar__0___24Anonymous__251 = Vvar__0___24Anonymous__252 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__247,Vvar__0___24Anonymous__248,Vvar__1___24Anonymous__249,Vvar__1___24Anonymous__250] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__247,Vvar__1___24Anonymous__249) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__248,Vvar__1___24Anonymous__250)
=> ( Vvar__1___24Anonymous__249 = Vvar__1___24Anonymous__250
& Vvar__0___24Anonymous__247 = Vvar__0___24Anonymous__248 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__83057,Vvar__0__R__83058,Vvar__1__req__83059,Vvar__1__req__83060,Vvar__2__reqb__83061,Vvar__2__reqb__83062,Vvar__3___24Anonymous__83063,Vvar__3___24Anonymous__83064] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__83057,Vvar__1__req__83059,Vvar__2__reqb__83061) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__83058,Vvar__1__req__83060,Vvar__2__reqb__83062)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__83061 = Vvar__2__reqb__83062
& Vvar__1__req__83059 = Vvar__1__req__83060
& Vvar__0__R__83057 = Vvar__0__R__83058 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__83065,Vvar__0__R__83066,Vvar__1__rO__83067,Vvar__1__rO__83068,Vvar__2__rI__83069,Vvar__2__rI__83070,Vvar__3__radd__83071,Vvar__3__radd__83072,Vvar__4__rmul__83073,Vvar__4__rmul__83074,Vvar__5__rsub__83075,Vvar__5__rsub__83076,Vvar__6__ropp__83077,Vvar__6__ropp__83078,Vvar__7__req__83079,Vvar__7__req__83080,Vvar__8__C__83081,Vvar__8__C__83082,Vvar__9__cO__83083,Vvar__9__cO__83084,Vvar__10__cI__83085,Vvar__10__cI__83086,Vvar__11__cadd__83087,Vvar__11__cadd__83088,Vvar__12__cmul__83089,Vvar__12__cmul__83090,Vvar__13__csub__83091,Vvar__13__csub__83092,Vvar__14__copp__83093,Vvar__14__copp__83094,Vvar__15__ceqb__83095,Vvar__15__ceqb__83096,Vvar__16__phi__83097,Vvar__16__phi__83098,Vvar__17___24Anonymous__83099,Vvar__17___24Anonymous__83100] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__83065,Vvar__1__rO__83067,Vvar__2__rI__83069,Vvar__3__radd__83071,Vvar__4__rmul__83073,Vvar__5__rsub__83075,Vvar__6__ropp__83077,Vvar__7__req__83079,Vvar__8__C__83081,Vvar__9__cO__83083,Vvar__10__cI__83085,Vvar__11__cadd__83087,Vvar__12__cmul__83089,Vvar__13__csub__83091,Vvar__14__copp__83093,Vvar__15__ceqb__83095,Vvar__16__phi__83097) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__83066,Vvar__1__rO__83068,Vvar__2__rI__83070,Vvar__3__radd__83072,Vvar__4__rmul__83074,Vvar__5__rsub__83076,Vvar__6__ropp__83078,Vvar__7__req__83080,Vvar__8__C__83082,Vvar__9__cO__83084,Vvar__10__cI__83086,Vvar__11__cadd__83088,Vvar__12__cmul__83090,Vvar__13__csub__83092,Vvar__14__copp__83094,Vvar__15__ceqb__83096,Vvar__16__phi__83098)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__83097 = Vvar__16__phi__83098
& Vvar__15__ceqb__83095 = Vvar__15__ceqb__83096
& Vvar__14__copp__83093 = Vvar__14__copp__83094
& Vvar__13__csub__83091 = Vvar__13__csub__83092
& Vvar__12__cmul__83089 = Vvar__12__cmul__83090
& Vvar__11__cadd__83087 = Vvar__11__cadd__83088
& Vvar__10__cI__83085 = Vvar__10__cI__83086
& Vvar__9__cO__83083 = Vvar__9__cO__83084
& Vvar__8__C__83081 = Vvar__8__C__83082
& Vvar__7__req__83079 = Vvar__7__req__83080
& Vvar__6__ropp__83077 = Vvar__6__ropp__83078
& Vvar__5__rsub__83075 = Vvar__5__rsub__83076
& Vvar__4__rmul__83073 = Vvar__4__rmul__83074
& Vvar__3__radd__83071 = Vvar__3__radd__83072
& Vvar__2__rI__83069 = Vvar__2__rI__83070
& Vvar__1__rO__83067 = Vvar__1__rO__83068
& Vvar__0__R__83065 = Vvar__0__R__83066 ) ) ).
fof('$_inj_LF.Basics.A',axiom,
! [Vvar__0__n__104007,Vvar__0__n__104008] :
( cLF_2eBasics_2eA___24a1(Vvar__0__n__104007) = cLF_2eBasics_2eA___24a1(Vvar__0__n__104008)
=> Vvar__0__n__104007 = Vvar__0__n__104008 ) ).
fof('$_inj_LF.Basics.B',axiom,
! [Vvar__0__n__104009,Vvar__0__n__104010] :
( cLF_2eBasics_2eB___24a1(Vvar__0__n__104009) = cLF_2eBasics_2eB___24a1(Vvar__0__n__104010)
=> Vvar__0__n__104009 = Vvar__0__n__104010 ) ).
fof('$_inj_LF.Basics.NatPlayground.S',axiom,
! [Vvar__0__n__111685,Vvar__0__n__111686] :
( cLF_2eBasics_2eNatPlayground_2eS___24a1(Vvar__0__n__111685) = cLF_2eBasics_2eNatPlayground_2eS___24a1(Vvar__0__n__111686)
=> Vvar__0__n__111685 = Vvar__0__n__111686 ) ).
fof('$_inj_LF.Basics.NatPlayground.tick',axiom,
! [Vvar__0__foo__111690,Vvar__0__foo__111691] :
( cLF_2eBasics_2eNatPlayground_2etick___24a1(Vvar__0__foo__111690) = cLF_2eBasics_2eNatPlayground_2etick___24a1(Vvar__0__foo__111691)
=> Vvar__0__foo__111690 = Vvar__0__foo__111691 ) ).
fof('$_inj_LF.Basics.bits',axiom,
! [Vvar__0__b0__82296,Vvar__0__b0__82297,Vvar__1__b1__82298,Vvar__1__b1__82299,Vvar__2__b2__82300,Vvar__2__b2__82301,Vvar__3__b3__82302,Vvar__3__b3__82303] :
( cLF_2eBasics_2ebits___24a4(Vvar__0__b0__82296,Vvar__1__b1__82298,Vvar__2__b2__82300,Vvar__3__b3__82302) = cLF_2eBasics_2ebits___24a4(Vvar__0__b0__82297,Vvar__1__b1__82299,Vvar__2__b2__82301,Vvar__3__b3__82303)
=> ( Vvar__3__b3__82302 = Vvar__3__b3__82303
& Vvar__2__b2__82300 = Vvar__2__b2__82301
& Vvar__1__b1__82298 = Vvar__1__b1__82299
& Vvar__0__b0__82296 = Vvar__0__b0__82297 ) ) ).
fof('$_inj_LF.Basics.primary',axiom,
! [Vvar__0__p__82283,Vvar__0__p__82284] :
( cLF_2eBasics_2eprimary___24a1(Vvar__0__p__82283) = cLF_2eBasics_2eprimary___24a1(Vvar__0__p__82284)
=> Vvar__0__p__82283 = Vvar__0__p__82284 ) ).
fof('$_inj_LF.Lists.Baz1',axiom,
! [Vvar__0__x__82364,Vvar__0__x__82365] :
( cLF_2eLists_2eBaz1___24a1(Vvar__0__x__82364) = cLF_2eLists_2eBaz1___24a1(Vvar__0__x__82365)
=> Vvar__0__x__82364 = Vvar__0__x__82365 ) ).
fof('$_inj_LF.Lists.Baz2',axiom,
! [Vvar__0__y__82366,Vvar__0__y__82367,Vvar__1__b__82368,Vvar__1__b__82369] :
( cLF_2eLists_2eBaz2___24a2(Vvar__0__y__82366,Vvar__1__b__82368) = cLF_2eLists_2eBaz2___24a2(Vvar__0__y__82367,Vvar__1__b__82369)
=> ( Vvar__1__b__82368 = Vvar__1__b__82369
& Vvar__0__y__82366 = Vvar__0__y__82367 ) ) ).
fof('$_inj_LF.Lists.Id',axiom,
! [Vvar__0__n__82348,Vvar__0__n__82349] :
( cLF_2eLists_2eId___24a1(Vvar__0__n__82348) = cLF_2eLists_2eId___24a1(Vvar__0__n__82349)
=> Vvar__0__n__82348 = Vvar__0__n__82349 ) ).
fof('$_inj_LF.Lists.NatList.Some',axiom,
! [Vvar__0__n__66750,Vvar__0__n__66751] :
( cLF_2eLists_2eNatList_2eSome___24a1(Vvar__0__n__66750) = cLF_2eLists_2eNatList_2eSome___24a1(Vvar__0__n__66751)
=> Vvar__0__n__66750 = Vvar__0__n__66751 ) ).
fof('$_inj_LF.Lists.NatList.cons',axiom,
! [Vvar__0__n__45,Vvar__0__n__46,Vvar__1__l__47,Vvar__1__l__48] :
( cLF_2eLists_2eNatList_2econs___24a2(Vvar__0__n__45,Vvar__1__l__47) = cLF_2eLists_2eNatList_2econs___24a2(Vvar__0__n__46,Vvar__1__l__48)
=> ( Vvar__1__l__47 = Vvar__1__l__48
& Vvar__0__n__45 = Vvar__0__n__46 ) ) ).
fof('$_inj_LF.Lists.NatList.pair',axiom,
! [Vvar__0__n1__103989,Vvar__0__n1__103990,Vvar__1__n2__103991,Vvar__1__n2__103992] :
( cLF_2eLists_2eNatList_2epair___24a2(Vvar__0__n1__103989,Vvar__1__n2__103991) = cLF_2eLists_2eNatList_2epair___24a2(Vvar__0__n1__103990,Vvar__1__n2__103992)
=> ( Vvar__1__n2__103991 = Vvar__1__n2__103992
& Vvar__0__n1__103989 = Vvar__0__n1__103990 ) ) ).
fof('$_inj_LF.Lists.PartialMap.record',axiom,
! [Vvar__0__i__82457,Vvar__0__i__82458,Vvar__1__v__82459,Vvar__1__v__82460,Vvar__2__m__82461,Vvar__2__m__82462] :
( cLF_2eLists_2ePartialMap_2erecord___24a3(Vvar__0__i__82457,Vvar__1__v__82459,Vvar__2__m__82461) = cLF_2eLists_2ePartialMap_2erecord___24a3(Vvar__0__i__82458,Vvar__1__v__82460,Vvar__2__m__82462)
=> ( Vvar__2__m__82461 = Vvar__2__m__82462
& Vvar__1__v__82459 = Vvar__1__v__82460
& Vvar__0__i__82457 = Vvar__0__i__82458 ) ) ).
fof('$_inj_Poly.MumbleGrumble.b',axiom,
! [Vvar__0__x__111580,Vvar__0__x__111581,Vvar__1__y__111582,Vvar__1__y__111583] :
( cPoly_2eMumbleGrumble_2eb___24a2(Vvar__0__x__111580,Vvar__1__y__111582) = cPoly_2eMumbleGrumble_2eb___24a2(Vvar__0__x__111581,Vvar__1__y__111583)
=> ( Vvar__1__y__111582 = Vvar__1__y__111583
& Vvar__0__x__111580 = Vvar__0__x__111581 ) ) ).
fof('$_inj_Poly.MumbleGrumble.d',axiom,
! [Vvar__0__X__111594,Vvar__0__X__111595,Vvar__1__m__111596,Vvar__1__m__111597] :
( cPoly_2eMumbleGrumble_2ed___24a2(Vvar__0__X__111594,Vvar__1__m__111596) = cPoly_2eMumbleGrumble_2ed___24a2(Vvar__0__X__111595,Vvar__1__m__111597)
=> ( Vvar__1__m__111596 = Vvar__1__m__111597
& Vvar__0__X__111594 = Vvar__0__X__111595 ) ) ).
fof('$_inj_Poly.MumbleGrumble.e',axiom,
! [Vvar__0__X__111598,Vvar__0__X__111599,Vvar__1__x__111600,Vvar__1__x__111601] :
( cPoly_2eMumbleGrumble_2ee___24a2(Vvar__0__X__111598,Vvar__1__x__111600) = cPoly_2eMumbleGrumble_2ee___24a2(Vvar__0__X__111599,Vvar__1__x__111601)
=> ( Vvar__1__x__111600 = Vvar__1__x__111601
& Vvar__0__X__111598 = Vvar__0__X__111599 ) ) ).
fof('$_inj_Poly.OptionPlayground.None',axiom,
! [Vvar__0__X__153816,Vvar__0__X__153817] :
( cPoly_2eOptionPlayground_2eNone___24a1(Vvar__0__X__153816) = cPoly_2eOptionPlayground_2eNone___24a1(Vvar__0__X__153817)
=> Vvar__0__X__153816 = Vvar__0__X__153817 ) ).
fof('$_inj_Poly.OptionPlayground.Some',axiom,
! [Vvar__0__X__153812,Vvar__0__X__153813,Vvar__1__x__153814,Vvar__1__x__153815] :
( cPoly_2eOptionPlayground_2eSome___24a2(Vvar__0__X__153812,Vvar__1__x__153814) = cPoly_2eOptionPlayground_2eSome___24a2(Vvar__0__X__153813,Vvar__1__x__153815)
=> ( Vvar__1__x__153814 = Vvar__1__x__153815
& Vvar__0__X__153812 = Vvar__0__X__153813 ) ) ).
fof('$_inj_Poly.bool_cons',axiom,
! [Vvar__0__b__82540,Vvar__0__b__82541,Vvar__1__l__82542,Vvar__1__l__82543] :
( cPoly_2ebool__cons___24a2(Vvar__0__b__82540,Vvar__1__l__82542) = cPoly_2ebool__cons___24a2(Vvar__0__b__82541,Vvar__1__l__82543)
=> ( Vvar__1__l__82542 = Vvar__1__l__82543
& Vvar__0__b__82540 = Vvar__0__b__82541 ) ) ).
fof('$_inj_Poly.cons',axiom,
! [Vvar__0__X__160,Vvar__0__X__161,Vvar__1__x__162,Vvar__1__x__163,Vvar__2__l__164,Vvar__2__l__165] :
( cPoly_2econs___24a3(Vvar__0__X__160,Vvar__1__x__162,Vvar__2__l__164) = cPoly_2econs___24a3(Vvar__0__X__161,Vvar__1__x__163,Vvar__2__l__165)
=> ( Vvar__2__l__164 = Vvar__2__l__165
& Vvar__1__x__162 = Vvar__1__x__163
& Vvar__0__X__160 = Vvar__0__X__161 ) ) ).
fof('$_inj_Poly.cons\'',axiom,
! [Vvar__0__X__111925,Vvar__0__X__111926,Vvar__1__x__111927,Vvar__1__x__111928,Vvar__2__l__111929,Vvar__2__l__111930] :
( cPoly_2econs_27___24a3(Vvar__0__X__111925,Vvar__1__x__111927,Vvar__2__l__111929) = cPoly_2econs_27___24a3(Vvar__0__X__111926,Vvar__1__x__111928,Vvar__2__l__111930)
=> ( Vvar__2__l__111929 = Vvar__2__l__111930
& Vvar__1__x__111927 = Vvar__1__x__111928
& Vvar__0__X__111925 = Vvar__0__X__111926 ) ) ).
fof('$_inj_Poly.nil',axiom,
! [Vvar__0__X__158,Vvar__0__X__159] :
( cPoly_2enil___24a1(Vvar__0__X__158) = cPoly_2enil___24a1(Vvar__0__X__159)
=> Vvar__0__X__158 = Vvar__0__X__159 ) ).
fof('$_inj_Poly.nil\'',axiom,
! [Vvar__0__X__111923,Vvar__0__X__111924] :
( cPoly_2enil_27___24a1(Vvar__0__X__111923) = cPoly_2enil_27___24a1(Vvar__0__X__111924)
=> Vvar__0__X__111923 = Vvar__0__X__111924 ) ).
fof('$_inj_Poly.pair',axiom,
! [Vvar__0__X__142556,Vvar__0__X__142557,Vvar__1__Y__142558,Vvar__1__Y__142559,Vvar__2__x__142560,Vvar__2__x__142561,Vvar__3__y__142562,Vvar__3__y__142563] :
( cPoly_2epair___24a4(Vvar__0__X__142556,Vvar__1__Y__142558,Vvar__2__x__142560,Vvar__3__y__142562) = cPoly_2epair___24a4(Vvar__0__X__142557,Vvar__1__Y__142559,Vvar__2__x__142561,Vvar__3__y__142563)
=> ( Vvar__3__y__142562 = Vvar__3__y__142563
& Vvar__2__x__142560 = Vvar__2__x__142561
& Vvar__1__Y__142558 = Vvar__1__Y__142559
& Vvar__0__X__142556 = Vvar__0__X__142557 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__67113,Vvar__1__Q__67115,Vvar__2__init__67118,Vvar__3___24Anonymous__67119,Vvar__4___24Anonymous__67120] :
( c_24__type__67146___24t(Vvar__0__P__67113,Vvar__1__Q__67115,Vvar__2__init__67118,Vvar__3___24Anonymous__67119,Vvar__4___24Anonymous__67120,Vvar__0__P__67113)
=> ( c_24__type__67154___24t(Vvar__0__P__67113,Vvar__1__Q__67115,Vvar__2__init__67118,Vvar__3___24Anonymous__67119,Vvar__4___24Anonymous__67120,Vvar__1__Q__67115)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__67118)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__67119)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__67120)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__67113,Vvar__1__Q__67115,Vvar__2__init__67118,Vvar__3___24Anonymous__67119,Vvar__4___24Anonymous__67120)
=> ( ( Vvar__4___24Anonymous__67120 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__67119 = Vvar__2__init__67118 )
| ? [Vvar__3__k__67134] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__67134)
& ? [Vvar__4__l__67135] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__67135)
& ? [Vvar__5__n__67136] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__67136)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__67113,Vvar__1__Q__67115,Vvar__2__init__67118,Vvar__3__k__67134,Vvar__5__n__67136)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__67113,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__67134),Vvar__4__l__67135)
& p(happ(Vvar__1__Q__67115,Vvar__4__l__67135))
& Vvar__4___24Anonymous__67120 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__67136)
& Vvar__3___24Anonymous__67119 = Vvar__4__l__67135 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__67094,Vvar__1__k__67096,Vvar__2___24Anonymous__67097] :
( c_24__type__67111___24t(Vvar__0__P__67094,Vvar__1__k__67096,Vvar__2___24Anonymous__67097,Vvar__0__P__67094)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__67096)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__67097)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__67094,Vvar__1__k__67096,Vvar__2___24Anonymous__67097)
=> ( Vvar__2___24Anonymous__67097 = Vvar__1__k__67096
| ? [Vvar__2__l__67105] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__67105)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__67094,Vvar__1__k__67096,Vvar__2__l__67105)
& p(happ(Vvar__0__P__67094,Vvar__2__l__67105))
& Vvar__2___24Anonymous__67097 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__67105) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__81930,Vvar__1__k__81932,Vvar__2___24Anonymous__81933] :
( c_24__type__81949___24t(Vvar__0__Q__81930,Vvar__1__k__81932,Vvar__2___24Anonymous__81933,Vvar__0__Q__81930)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__81932)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__81933)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__81930,Vvar__1__k__81932,Vvar__2___24Anonymous__81933)
=> ( ? [Vvar__2__l__81938] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__81938)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__81930,Vvar__1__k__81932,Vvar__2__l__81938)
& Vvar__2___24Anonymous__81933 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__81938) )
| ? [Vvar__2__l__81943] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__81943)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__81932,Vvar__2__l__81943)
& p(happ(Vvar__0__Q__81930,Vvar__2__l__81943))
& Vvar__2___24Anonymous__81933 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__81943) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__74871] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74871)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__74871)
=> ( Vvar__0___24Anonymous__74871 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__74873] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74873)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__74873)
& Vvar__0___24Anonymous__74871 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__74873) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__74875] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74875)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__74875)
=> ? [Vvar__0__n__74877] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74877)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__74877)
& Vvar__0___24Anonymous__74875 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__74877) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__99162,Vvar__1___24Anonymous__99163,VX99164] :
( cProp___24t(Vvar__0__P__99162)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__99163)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__99162,Vvar__1___24Anonymous__99163,VX99164)
=> ( ( p(Vvar__0__P__99162)
& Vvar__1___24Anonymous__99163 = cCoq_2eInit_2eDatatypes_2etrue
& VX99164 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__99162) )
| ( ~ p(Vvar__0__P__99162)
& Vvar__1___24Anonymous__99163 = cCoq_2eInit_2eDatatypes_2efalse
& VX99164 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__99162) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__111853,Vvar__1___24Anonymous__111854,Vvar__2___24Anonymous__111855] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__111853)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__111854)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__111855)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__111853,Vvar__1___24Anonymous__111854,Vvar__2___24Anonymous__111855)
=> ( ? [Vvar__0__x__111857] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__111857)
& Vvar__2___24Anonymous__111855 = Vvar__0__x__111857
& Vvar__1___24Anonymous__111854 = Vvar__0__x__111857
& Vvar__0___24Anonymous__111853 = Vvar__0__x__111857 )
| ? [Vvar__0__x__111858] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__111858)
& Vvar__2___24Anonymous__111855 = Vvar__0__x__111858
& Vvar__1___24Anonymous__111854 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__111853 = Vvar__0__x__111858 )
| ? [Vvar__0__x__111859] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__111859)
& Vvar__2___24Anonymous__111855 = Vvar__0__x__111859
& Vvar__1___24Anonymous__111854 = Vvar__0__x__111859
& Vvar__0___24Anonymous__111853 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__111860] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__111860)
& Vvar__2___24Anonymous__111855 = Vvar__0__x__111860
& Vvar__1___24Anonymous__111854 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__111853 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__111861] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__111861)
& Vvar__2___24Anonymous__111855 = Vvar__0__x__111861
& Vvar__1___24Anonymous__111854 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__111853 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX81762] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX81762)
=> ( VX81762 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__81763] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__81763)
& ? [Vvar__1___24Anonymous__81764] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__81764)
& ? [Vvar__2___24Anonymous__81765] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__81765)
& VX81762 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__81763,Vvar__1___24Anonymous__81764,Vvar__2___24Anonymous__81765) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX795] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX795)
=> ( VX795 = cCoq_2eInit_2eByte_2ex00
| VX795 = cCoq_2eInit_2eByte_2ex01
| VX795 = cCoq_2eInit_2eByte_2ex02
| VX795 = cCoq_2eInit_2eByte_2ex03
| VX795 = cCoq_2eInit_2eByte_2ex04
| VX795 = cCoq_2eInit_2eByte_2ex05
| VX795 = cCoq_2eInit_2eByte_2ex06
| VX795 = cCoq_2eInit_2eByte_2ex07
| VX795 = cCoq_2eInit_2eByte_2ex08
| VX795 = cCoq_2eInit_2eByte_2ex09
| VX795 = cCoq_2eInit_2eByte_2ex0a
| VX795 = cCoq_2eInit_2eByte_2ex0b
| VX795 = cCoq_2eInit_2eByte_2ex0c
| VX795 = cCoq_2eInit_2eByte_2ex0d
| VX795 = cCoq_2eInit_2eByte_2ex0e
| VX795 = cCoq_2eInit_2eByte_2ex0f
| VX795 = cCoq_2eInit_2eByte_2ex10
| VX795 = cCoq_2eInit_2eByte_2ex11
| VX795 = cCoq_2eInit_2eByte_2ex12
| VX795 = cCoq_2eInit_2eByte_2ex13
| VX795 = cCoq_2eInit_2eByte_2ex14
| VX795 = cCoq_2eInit_2eByte_2ex15
| VX795 = cCoq_2eInit_2eByte_2ex16
| VX795 = cCoq_2eInit_2eByte_2ex17
| VX795 = cCoq_2eInit_2eByte_2ex18
| VX795 = cCoq_2eInit_2eByte_2ex19
| VX795 = cCoq_2eInit_2eByte_2ex1a
| VX795 = cCoq_2eInit_2eByte_2ex1b
| VX795 = cCoq_2eInit_2eByte_2ex1c
| VX795 = cCoq_2eInit_2eByte_2ex1d
| VX795 = cCoq_2eInit_2eByte_2ex1e
| VX795 = cCoq_2eInit_2eByte_2ex1f
| VX795 = cCoq_2eInit_2eByte_2ex20
| VX795 = cCoq_2eInit_2eByte_2ex21
| VX795 = cCoq_2eInit_2eByte_2ex22
| VX795 = cCoq_2eInit_2eByte_2ex23
| VX795 = cCoq_2eInit_2eByte_2ex24
| VX795 = cCoq_2eInit_2eByte_2ex25
| VX795 = cCoq_2eInit_2eByte_2ex26
| VX795 = cCoq_2eInit_2eByte_2ex27
| VX795 = cCoq_2eInit_2eByte_2ex28
| VX795 = cCoq_2eInit_2eByte_2ex29
| VX795 = cCoq_2eInit_2eByte_2ex2a
| VX795 = cCoq_2eInit_2eByte_2ex2b
| VX795 = cCoq_2eInit_2eByte_2ex2c
| VX795 = cCoq_2eInit_2eByte_2ex2d
| VX795 = cCoq_2eInit_2eByte_2ex2e
| VX795 = cCoq_2eInit_2eByte_2ex2f
| VX795 = cCoq_2eInit_2eByte_2ex30
| VX795 = cCoq_2eInit_2eByte_2ex31
| VX795 = cCoq_2eInit_2eByte_2ex32
| VX795 = cCoq_2eInit_2eByte_2ex33
| VX795 = cCoq_2eInit_2eByte_2ex34
| VX795 = cCoq_2eInit_2eByte_2ex35
| VX795 = cCoq_2eInit_2eByte_2ex36
| VX795 = cCoq_2eInit_2eByte_2ex37
| VX795 = cCoq_2eInit_2eByte_2ex38
| VX795 = cCoq_2eInit_2eByte_2ex39
| VX795 = cCoq_2eInit_2eByte_2ex3a
| VX795 = cCoq_2eInit_2eByte_2ex3b
| VX795 = cCoq_2eInit_2eByte_2ex3c
| VX795 = cCoq_2eInit_2eByte_2ex3d
| VX795 = cCoq_2eInit_2eByte_2ex3e
| VX795 = cCoq_2eInit_2eByte_2ex3f
| VX795 = cCoq_2eInit_2eByte_2ex40
| VX795 = cCoq_2eInit_2eByte_2ex41
| VX795 = cCoq_2eInit_2eByte_2ex42
| VX795 = cCoq_2eInit_2eByte_2ex43
| VX795 = cCoq_2eInit_2eByte_2ex44
| VX795 = cCoq_2eInit_2eByte_2ex45
| VX795 = cCoq_2eInit_2eByte_2ex46
| VX795 = cCoq_2eInit_2eByte_2ex47
| VX795 = cCoq_2eInit_2eByte_2ex48
| VX795 = cCoq_2eInit_2eByte_2ex49
| VX795 = cCoq_2eInit_2eByte_2ex4a
| VX795 = cCoq_2eInit_2eByte_2ex4b
| VX795 = cCoq_2eInit_2eByte_2ex4c
| VX795 = cCoq_2eInit_2eByte_2ex4d
| VX795 = cCoq_2eInit_2eByte_2ex4e
| VX795 = cCoq_2eInit_2eByte_2ex4f
| VX795 = cCoq_2eInit_2eByte_2ex50
| VX795 = cCoq_2eInit_2eByte_2ex51
| VX795 = cCoq_2eInit_2eByte_2ex52
| VX795 = cCoq_2eInit_2eByte_2ex53
| VX795 = cCoq_2eInit_2eByte_2ex54
| VX795 = cCoq_2eInit_2eByte_2ex55
| VX795 = cCoq_2eInit_2eByte_2ex56
| VX795 = cCoq_2eInit_2eByte_2ex57
| VX795 = cCoq_2eInit_2eByte_2ex58
| VX795 = cCoq_2eInit_2eByte_2ex59
| VX795 = cCoq_2eInit_2eByte_2ex5a
| VX795 = cCoq_2eInit_2eByte_2ex5b
| VX795 = cCoq_2eInit_2eByte_2ex5c
| VX795 = cCoq_2eInit_2eByte_2ex5d
| VX795 = cCoq_2eInit_2eByte_2ex5e
| VX795 = cCoq_2eInit_2eByte_2ex5f
| VX795 = cCoq_2eInit_2eByte_2ex60
| VX795 = cCoq_2eInit_2eByte_2ex61
| VX795 = cCoq_2eInit_2eByte_2ex62
| VX795 = cCoq_2eInit_2eByte_2ex63
| VX795 = cCoq_2eInit_2eByte_2ex64
| VX795 = cCoq_2eInit_2eByte_2ex65
| VX795 = cCoq_2eInit_2eByte_2ex66
| VX795 = cCoq_2eInit_2eByte_2ex67
| VX795 = cCoq_2eInit_2eByte_2ex68
| VX795 = cCoq_2eInit_2eByte_2ex69
| VX795 = cCoq_2eInit_2eByte_2ex6a
| VX795 = cCoq_2eInit_2eByte_2ex6b
| VX795 = cCoq_2eInit_2eByte_2ex6c
| VX795 = cCoq_2eInit_2eByte_2ex6d
| VX795 = cCoq_2eInit_2eByte_2ex6e
| VX795 = cCoq_2eInit_2eByte_2ex6f
| VX795 = cCoq_2eInit_2eByte_2ex70
| VX795 = cCoq_2eInit_2eByte_2ex71
| VX795 = cCoq_2eInit_2eByte_2ex72
| VX795 = cCoq_2eInit_2eByte_2ex73
| VX795 = cCoq_2eInit_2eByte_2ex74
| VX795 = cCoq_2eInit_2eByte_2ex75
| VX795 = cCoq_2eInit_2eByte_2ex76
| VX795 = cCoq_2eInit_2eByte_2ex77
| VX795 = cCoq_2eInit_2eByte_2ex78
| VX795 = cCoq_2eInit_2eByte_2ex79
| VX795 = cCoq_2eInit_2eByte_2ex7a
| VX795 = cCoq_2eInit_2eByte_2ex7b
| VX795 = cCoq_2eInit_2eByte_2ex7c
| VX795 = cCoq_2eInit_2eByte_2ex7d
| VX795 = cCoq_2eInit_2eByte_2ex7e
| VX795 = cCoq_2eInit_2eByte_2ex7f
| VX795 = cCoq_2eInit_2eByte_2ex80
| VX795 = cCoq_2eInit_2eByte_2ex81
| VX795 = cCoq_2eInit_2eByte_2ex82
| VX795 = cCoq_2eInit_2eByte_2ex83
| VX795 = cCoq_2eInit_2eByte_2ex84
| VX795 = cCoq_2eInit_2eByte_2ex85
| VX795 = cCoq_2eInit_2eByte_2ex86
| VX795 = cCoq_2eInit_2eByte_2ex87
| VX795 = cCoq_2eInit_2eByte_2ex88
| VX795 = cCoq_2eInit_2eByte_2ex89
| VX795 = cCoq_2eInit_2eByte_2ex8a
| VX795 = cCoq_2eInit_2eByte_2ex8b
| VX795 = cCoq_2eInit_2eByte_2ex8c
| VX795 = cCoq_2eInit_2eByte_2ex8d
| VX795 = cCoq_2eInit_2eByte_2ex8e
| VX795 = cCoq_2eInit_2eByte_2ex8f
| VX795 = cCoq_2eInit_2eByte_2ex90
| VX795 = cCoq_2eInit_2eByte_2ex91
| VX795 = cCoq_2eInit_2eByte_2ex92
| VX795 = cCoq_2eInit_2eByte_2ex93
| VX795 = cCoq_2eInit_2eByte_2ex94
| VX795 = cCoq_2eInit_2eByte_2ex95
| VX795 = cCoq_2eInit_2eByte_2ex96
| VX795 = cCoq_2eInit_2eByte_2ex97
| VX795 = cCoq_2eInit_2eByte_2ex98
| VX795 = cCoq_2eInit_2eByte_2ex99
| VX795 = cCoq_2eInit_2eByte_2ex9a
| VX795 = cCoq_2eInit_2eByte_2ex9b
| VX795 = cCoq_2eInit_2eByte_2ex9c
| VX795 = cCoq_2eInit_2eByte_2ex9d
| VX795 = cCoq_2eInit_2eByte_2ex9e
| VX795 = cCoq_2eInit_2eByte_2ex9f
| VX795 = cCoq_2eInit_2eByte_2exa0
| VX795 = cCoq_2eInit_2eByte_2exa1
| VX795 = cCoq_2eInit_2eByte_2exa2
| VX795 = cCoq_2eInit_2eByte_2exa3
| VX795 = cCoq_2eInit_2eByte_2exa4
| VX795 = cCoq_2eInit_2eByte_2exa5
| VX795 = cCoq_2eInit_2eByte_2exa6
| VX795 = cCoq_2eInit_2eByte_2exa7
| VX795 = cCoq_2eInit_2eByte_2exa8
| VX795 = cCoq_2eInit_2eByte_2exa9
| VX795 = cCoq_2eInit_2eByte_2exaa
| VX795 = cCoq_2eInit_2eByte_2exab
| VX795 = cCoq_2eInit_2eByte_2exac
| VX795 = cCoq_2eInit_2eByte_2exad
| VX795 = cCoq_2eInit_2eByte_2exae
| VX795 = cCoq_2eInit_2eByte_2exaf
| VX795 = cCoq_2eInit_2eByte_2exb0
| VX795 = cCoq_2eInit_2eByte_2exb1
| VX795 = cCoq_2eInit_2eByte_2exb2
| VX795 = cCoq_2eInit_2eByte_2exb3
| VX795 = cCoq_2eInit_2eByte_2exb4
| VX795 = cCoq_2eInit_2eByte_2exb5
| VX795 = cCoq_2eInit_2eByte_2exb6
| VX795 = cCoq_2eInit_2eByte_2exb7
| VX795 = cCoq_2eInit_2eByte_2exb8
| VX795 = cCoq_2eInit_2eByte_2exb9
| VX795 = cCoq_2eInit_2eByte_2exba
| VX795 = cCoq_2eInit_2eByte_2exbb
| VX795 = cCoq_2eInit_2eByte_2exbc
| VX795 = cCoq_2eInit_2eByte_2exbd
| VX795 = cCoq_2eInit_2eByte_2exbe
| VX795 = cCoq_2eInit_2eByte_2exbf
| VX795 = cCoq_2eInit_2eByte_2exc0
| VX795 = cCoq_2eInit_2eByte_2exc1
| VX795 = cCoq_2eInit_2eByte_2exc2
| VX795 = cCoq_2eInit_2eByte_2exc3
| VX795 = cCoq_2eInit_2eByte_2exc4
| VX795 = cCoq_2eInit_2eByte_2exc5
| VX795 = cCoq_2eInit_2eByte_2exc6
| VX795 = cCoq_2eInit_2eByte_2exc7
| VX795 = cCoq_2eInit_2eByte_2exc8
| VX795 = cCoq_2eInit_2eByte_2exc9
| VX795 = cCoq_2eInit_2eByte_2exca
| VX795 = cCoq_2eInit_2eByte_2excb
| VX795 = cCoq_2eInit_2eByte_2excc
| VX795 = cCoq_2eInit_2eByte_2excd
| VX795 = cCoq_2eInit_2eByte_2exce
| VX795 = cCoq_2eInit_2eByte_2excf
| VX795 = cCoq_2eInit_2eByte_2exd0
| VX795 = cCoq_2eInit_2eByte_2exd1
| VX795 = cCoq_2eInit_2eByte_2exd2
| VX795 = cCoq_2eInit_2eByte_2exd3
| VX795 = cCoq_2eInit_2eByte_2exd4
| VX795 = cCoq_2eInit_2eByte_2exd5
| VX795 = cCoq_2eInit_2eByte_2exd6
| VX795 = cCoq_2eInit_2eByte_2exd7
| VX795 = cCoq_2eInit_2eByte_2exd8
| VX795 = cCoq_2eInit_2eByte_2exd9
| VX795 = cCoq_2eInit_2eByte_2exda
| VX795 = cCoq_2eInit_2eByte_2exdb
| VX795 = cCoq_2eInit_2eByte_2exdc
| VX795 = cCoq_2eInit_2eByte_2exdd
| VX795 = cCoq_2eInit_2eByte_2exde
| VX795 = cCoq_2eInit_2eByte_2exdf
| VX795 = cCoq_2eInit_2eByte_2exe0
| VX795 = cCoq_2eInit_2eByte_2exe1
| VX795 = cCoq_2eInit_2eByte_2exe2
| VX795 = cCoq_2eInit_2eByte_2exe3
| VX795 = cCoq_2eInit_2eByte_2exe4
| VX795 = cCoq_2eInit_2eByte_2exe5
| VX795 = cCoq_2eInit_2eByte_2exe6
| VX795 = cCoq_2eInit_2eByte_2exe7
| VX795 = cCoq_2eInit_2eByte_2exe8
| VX795 = cCoq_2eInit_2eByte_2exe9
| VX795 = cCoq_2eInit_2eByte_2exea
| VX795 = cCoq_2eInit_2eByte_2exeb
| VX795 = cCoq_2eInit_2eByte_2exec
| VX795 = cCoq_2eInit_2eByte_2exed
| VX795 = cCoq_2eInit_2eByte_2exee
| VX795 = cCoq_2eInit_2eByte_2exef
| VX795 = cCoq_2eInit_2eByte_2exf0
| VX795 = cCoq_2eInit_2eByte_2exf1
| VX795 = cCoq_2eInit_2eByte_2exf2
| VX795 = cCoq_2eInit_2eByte_2exf3
| VX795 = cCoq_2eInit_2eByte_2exf4
| VX795 = cCoq_2eInit_2eByte_2exf5
| VX795 = cCoq_2eInit_2eByte_2exf6
| VX795 = cCoq_2eInit_2eByte_2exf7
| VX795 = cCoq_2eInit_2eByte_2exf8
| VX795 = cCoq_2eInit_2eByte_2exf9
| VX795 = cCoq_2eInit_2eByte_2exfa
| VX795 = cCoq_2eInit_2eByte_2exfb
| VX795 = cCoq_2eInit_2eByte_2exfc
| VX795 = cCoq_2eInit_2eByte_2exfd
| VX795 = cCoq_2eInit_2eByte_2exfe
| VX795 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__74594,Vvar__1__Q__74595,Vvar__2___24Anonymous__74596] :
( cProp___24t(Vvar__0__P__74594)
=> ( cProp___24t(Vvar__1__Q__74595)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__74596)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__74594,Vvar__1__Q__74595,Vvar__2___24Anonymous__74596)
=> ( ( p(Vvar__0__P__74594)
& Vvar__2___24Anonymous__74596 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__74595)
& Vvar__2___24Anonymous__74596 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__74659,Vvar__1__Plt__74660,Vvar__2__Pgt__74661,Vvar__3___24Anonymous__74662] :
( cProp___24t(Vvar__0__Peq__74659)
=> ( cProp___24t(Vvar__1__Plt__74660)
=> ( cProp___24t(Vvar__2__Pgt__74661)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__74662)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__74659,Vvar__1__Plt__74660,Vvar__2__Pgt__74661,Vvar__3___24Anonymous__74662)
=> ( ( p(Vvar__0__Peq__74659)
& Vvar__3___24Anonymous__74662 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__74660)
& Vvar__3___24Anonymous__74662 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__74661)
& Vvar__3___24Anonymous__74662 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__82722,Vvar__1__Plt__82723,Vvar__2__Pgt__82724,Vvar__3___24Anonymous__82725,VX82726] :
( cProp___24t(Vvar__0__Peq__82722)
=> ( cProp___24t(Vvar__1__Plt__82723)
=> ( cProp___24t(Vvar__2__Pgt__82724)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__82725)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__82722,Vvar__1__Plt__82723,Vvar__2__Pgt__82724,Vvar__3___24Anonymous__82725,VX82726)
=> ( ( p(Vvar__0__Peq__82722)
& Vvar__3___24Anonymous__82725 = cCoq_2eInit_2eDatatypes_2eEq
& VX82726 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__82722,Vvar__1__Plt__82723,Vvar__2__Pgt__82724) )
| ( p(Vvar__1__Plt__82723)
& Vvar__3___24Anonymous__82725 = cCoq_2eInit_2eDatatypes_2eLt
& VX82726 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__82722,Vvar__1__Plt__82723,Vvar__2__Pgt__82724) )
| ( p(Vvar__2__Pgt__82724)
& Vvar__3___24Anonymous__82725 = cCoq_2eInit_2eDatatypes_2eGt
& VX82726 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__82722,Vvar__1__Plt__82723,Vvar__2__Pgt__82724) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX186] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX186)
=> ( VX186 = cCoq_2eInit_2eDatatypes_2etrue
| VX186 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX74658] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX74658)
=> ( VX74658 = cCoq_2eInit_2eDatatypes_2eEq
| VX74658 = cCoq_2eInit_2eDatatypes_2eLt
| VX74658 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__104023] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__104023)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__104023)
=> Vvar__0___24Anonymous__104023 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__104037,Vvar__1__a__104038,Vvar__2___24Anonymous__104039] :
( cType___24t(Vvar__0__A__104037)
=> ( t(Vvar__1__a__104038,Vvar__0__A__104037)
=> ( t(Vvar__2___24Anonymous__104039,Vvar__0__A__104037)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__104037,Vvar__1__a__104038,Vvar__2___24Anonymous__104039)
=> Vvar__2___24Anonymous__104039 = Vvar__1__a__104038 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__66393,VX66394] :
( cType___24t(Vvar__0__A__66393)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__66393,VX66394)
=> ( VX66394 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__66393)
| ? [Vvar__1___24Anonymous__66397] :
( t(Vvar__1___24Anonymous__66397,Vvar__0__A__66393)
& ? [Vvar__2___24Anonymous__66398] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__66393,Vvar__2___24Anonymous__66398)
& VX66394 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__66393,Vvar__1___24Anonymous__66397,Vvar__2___24Anonymous__66398) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__66338,VX66339] :
( cType___24t(Vvar__0__A__66338)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__66338,VX66339)
=> ( ? [Vvar__1___24Anonymous__66341] :
( t(Vvar__1___24Anonymous__66341,Vvar__0__A__66338)
& VX66339 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__66338,Vvar__1___24Anonymous__66341) )
| VX66339 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__66338) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__66375,Vvar__1__B__66376,VX66377] :
( cType___24t(Vvar__0__A__66375)
=> ( cType___24t(Vvar__1__B__66376)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__66375,Vvar__1__B__66376,VX66377)
=> ? [Vvar__2___24Anonymous__66380] :
( t(Vvar__2___24Anonymous__66380,Vvar__0__A__66375)
& ? [Vvar__3___24Anonymous__66381] :
( t(Vvar__3___24Anonymous__66381,Vvar__1__B__66376)
& VX66377 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__66375,Vvar__1__B__66376,Vvar__2___24Anonymous__66380,Vvar__3___24Anonymous__66381) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__99184,Vvar__1__B__99185,VX99186] :
( cType___24t(Vvar__0__A__99184)
=> ( cType___24t(Vvar__1__B__99185)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__99184,Vvar__1__B__99185,VX99186)
=> ( ? [Vvar__2___24Anonymous__99189] :
( t(Vvar__2___24Anonymous__99189,Vvar__0__A__99184)
& VX99186 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__99184,Vvar__1__B__99185,Vvar__2___24Anonymous__99189) )
| ? [Vvar__2___24Anonymous__99192] :
( t(Vvar__2___24Anonymous__99192,Vvar__1__B__99185)
& VX99186 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__99184,Vvar__1__B__99185,Vvar__2___24Anonymous__99192) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX66865] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX66865)
=> VX66865 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX104053] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX104053)
=> ( ? [Vvar__0__i__104054] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__104054)
& ? [Vvar__1__f__104055] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__104055)
& VX104053 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__104054,Vvar__1__f__104055) ) )
| ? [Vvar__0__i__104056] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__104056)
& ? [Vvar__1__f__104057] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__104057)
& ? [Vvar__2__e__104058] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__104058)
& VX104053 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__104056,Vvar__1__f__104057,Vvar__2__e__104058) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX104044] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX104044)
=> ( ? [Vvar__0__d__104045] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__104045)
& VX104044 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__104045) )
| ? [Vvar__0__d__104046] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__104046)
& VX104044 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__104046) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX74677] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX74677)
=> ( VX74677 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__74678] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74678)
& VX74677 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__74678) )
| ? [Vvar__0___24Anonymous__74679] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74679)
& VX74677 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__74679) )
| ? [Vvar__0___24Anonymous__74680] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74680)
& VX74677 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__74680) )
| ? [Vvar__0___24Anonymous__74681] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74681)
& VX74677 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__74681) )
| ? [Vvar__0___24Anonymous__74682] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74682)
& VX74677 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__74682) )
| ? [Vvar__0___24Anonymous__74683] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74683)
& VX74677 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__74683) )
| ? [Vvar__0___24Anonymous__74684] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74684)
& VX74677 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__74684) )
| ? [Vvar__0___24Anonymous__74685] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74685)
& VX74677 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__74685) )
| ? [Vvar__0___24Anonymous__74686] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74686)
& VX74677 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__74686) )
| ? [Vvar__0___24Anonymous__74687] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__74687)
& VX74677 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__74687) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__66894,Vvar__1___24Anonymous__66895] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__66894)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__66895)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__66894,Vvar__1___24Anonymous__66895)
=> ( Vvar__1___24Anonymous__66895 = Vvar__0__n__66894
| ? [Vvar__1__m__66899] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__66899)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__66894,Vvar__1__m__66899)
& Vvar__1___24Anonymous__66895 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__66899) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__78538,Vvar__1__P__78539,VX78542] :
( cType___24t(Vvar__0__A__78538)
=> ( c_24__type__78552___24t(Vvar__0__A__78538,Vvar__1__P__78539,Vvar__1__P__78539)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__78538,Vvar__1__P__78539,VX78542)
=> ? [Vvar__2__x__78547] :
( t(Vvar__2__x__78547,Vvar__0__A__78538)
& p(happ(Vvar__1__P__78539,Vvar__2__x__78547))
& VX78542 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78538,Vvar__1__P__78539,Vvar__2__x__78547) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__95263,Vvar__1__P__95264,Vvar__2__Q__95267,VX95270] :
( cType___24t(Vvar__0__A__95263)
=> ( c_24__type__95287___24t(Vvar__0__A__95263,Vvar__1__P__95264,Vvar__2__Q__95267,Vvar__1__P__95264)
=> ( c_24__type__95295___24t(Vvar__0__A__95263,Vvar__1__P__95264,Vvar__2__Q__95267,Vvar__2__Q__95267)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__95263,Vvar__1__P__95264,Vvar__2__Q__95267,VX95270)
=> ? [Vvar__3__x__95278] :
( t(Vvar__3__x__95278,Vvar__0__A__95263)
& p(happ(Vvar__1__P__95264,Vvar__3__x__95278))
& p(happ(Vvar__2__Q__95267,Vvar__3__x__95278))
& VX95270 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__95263,Vvar__1__P__95264,Vvar__2__Q__95267,Vvar__3__x__95278) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__95341,Vvar__1__P__95342,VX95345] :
( cType___24t(Vvar__0__A__95341)
=> ( c_24__type__95355___24t(Vvar__0__A__95341,Vvar__1__P__95342,Vvar__1__P__95342)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__95341,Vvar__1__P__95342,VX95345)
=> ? [Vvar__2__x__95350] :
( t(Vvar__2__x__95350,Vvar__0__A__95341)
& ? [Vvar__3___24Anonymous__95351] :
( t(Vvar__3___24Anonymous__95351,happ(Vvar__1__P__95342,Vvar__2__x__95350))
& VX95345 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__95341,Vvar__1__P__95342,Vvar__2__x__95350,Vvar__3___24Anonymous__95351) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__95372,Vvar__1__P__95373,Vvar__2__Q__95376,VX95379] :
( cType___24t(Vvar__0__A__95372)
=> ( c_24__type__95396___24t(Vvar__0__A__95372,Vvar__1__P__95373,Vvar__2__Q__95376,Vvar__1__P__95373)
=> ( c_24__type__95404___24t(Vvar__0__A__95372,Vvar__1__P__95373,Vvar__2__Q__95376,Vvar__2__Q__95376)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__95372,Vvar__1__P__95373,Vvar__2__Q__95376,VX95379)
=> ? [Vvar__3__x__95387] :
( t(Vvar__3__x__95387,Vvar__0__A__95372)
& ? [Vvar__4___24Anonymous__95388] :
( t(Vvar__4___24Anonymous__95388,happ(Vvar__1__P__95373,Vvar__3__x__95387))
& ? [Vvar__5___24Anonymous__95389] :
( t(Vvar__5___24Anonymous__95389,happ(Vvar__2__Q__95376,Vvar__3__x__95387))
& VX95379 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__95372,Vvar__1__P__95373,Vvar__2__Q__95376,Vvar__3__x__95387,Vvar__4___24Anonymous__95388,Vvar__5___24Anonymous__95389) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__78603,Vvar__1__B__78604,VX78605] :
( cProp___24t(Vvar__0__A__78603)
=> ( cProp___24t(Vvar__1__B__78604)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__78603,Vvar__1__B__78604,VX78605)
=> ( ( p(Vvar__0__A__78603)
& VX78605 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__78603,Vvar__1__B__78604) )
| ( p(Vvar__1__B__78604)
& VX78605 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__78603,Vvar__1__B__78604) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__78687,Vvar__1__B__78688,VX78689] :
( cType___24t(Vvar__0__A__78687)
=> ( cProp___24t(Vvar__1__B__78688)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__78687,Vvar__1__B__78688,VX78689)
=> ( ? [Vvar__2___24Anonymous__78692] :
( t(Vvar__2___24Anonymous__78692,Vvar__0__A__78687)
& VX78689 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__78687,Vvar__1__B__78688,Vvar__2___24Anonymous__78692) )
| ( p(Vvar__1__B__78688)
& VX78689 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__78687,Vvar__1__B__78688) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__81026,Vvar__1__R__81027,Vvar__2__x__81032] :
( cType___24t(Vvar__0__A__81026)
=> ( c_24__type__81061___24t(Vvar__0__A__81026,Vvar__1__R__81027,Vvar__2__x__81032,Vvar__1__R__81027)
=> ( t(Vvar__2__x__81032,Vvar__0__A__81026)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__81026,Vvar__1__R__81027,Vvar__2__x__81032)
=> ( ! [Vvar__var__var__var__var__3__y__81042__81044__81046__81048__81050] :
( t(Vvar__var__var__var__var__3__y__81042__81044__81046__81048__81050,Vvar__0__A__81026)
=> ( p(happ(happ(Vvar__1__R__81027,Vvar__var__var__var__var__3__y__81042__81044__81046__81048__81050),Vvar__2__x__81032))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__81026,Vvar__1__R__81027,Vvar__var__var__var__var__3__y__81042__81044__81046__81048__81050) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__104605,Vvar__1__a__104606,Vvar__2___24Anonymous__104607,Vvar__3___24Anonymous__104608] :
( cType___24t(Vvar__0__A__104605)
=> ( t(Vvar__1__a__104606,Vvar__0__A__104605)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104605,Vvar__2___24Anonymous__104607)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104605,Vvar__3___24Anonymous__104608)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__104605,Vvar__1__a__104606,Vvar__2___24Anonymous__104607,Vvar__3___24Anonymous__104608)
=> ( ? [Vvar__2__l__104612] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104605,Vvar__2__l__104612)
& Vvar__3___24Anonymous__104608 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104605,Vvar__1__a__104606,Vvar__2__l__104612)
& Vvar__2___24Anonymous__104607 = Vvar__2__l__104612 )
| ? [Vvar__2__x__104615] :
( t(Vvar__2__x__104615,Vvar__0__A__104605)
& ? [Vvar__3__l__104616] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104605,Vvar__3__l__104616)
& ? [Vvar__4__l_27__104617] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104605,Vvar__4__l_27__104617)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__104605,Vvar__1__a__104606,Vvar__3__l__104616,Vvar__4__l_27__104617)
& Vvar__3___24Anonymous__104608 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104605,Vvar__2__x__104615,Vvar__4__l_27__104617)
& Vvar__2___24Anonymous__104607 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104605,Vvar__2__x__104615,Vvar__3__l__104616) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__104619,Vvar__1__P__104620,Vvar__2___24Anonymous__104623] :
( cType___24t(Vvar__0__A__104619)
=> ( c_24__type__104641___24t(Vvar__0__A__104619,Vvar__1__P__104620,Vvar__2___24Anonymous__104623,Vvar__1__P__104620)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104619,Vvar__2___24Anonymous__104623)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__104619,Vvar__1__P__104620,Vvar__2___24Anonymous__104623)
=> ( Vvar__2___24Anonymous__104623 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__104619)
| ? [Vvar__2__x__104633] :
( t(Vvar__2__x__104633,Vvar__0__A__104619)
& ? [Vvar__3__l__104634] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104619,Vvar__3__l__104634)
& p(happ(Vvar__1__P__104620,Vvar__2__x__104633))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__104619,Vvar__1__P__104620,Vvar__3__l__104634)
& Vvar__2___24Anonymous__104623 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104619,Vvar__2__x__104633,Vvar__3__l__104634) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__104643,Vvar__1__B__104644,Vvar__2__R__104645,Vvar__3___24Anonymous__104650,Vvar__4___24Anonymous__104651] :
( cType___24t(Vvar__0__A__104643)
=> ( cType___24t(Vvar__1__B__104644)
=> ( c_24__type__104688___24t(Vvar__0__A__104643,Vvar__1__B__104644,Vvar__2__R__104645,Vvar__3___24Anonymous__104650,Vvar__4___24Anonymous__104651,Vvar__2__R__104645)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104643,Vvar__3___24Anonymous__104650)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__104644,Vvar__4___24Anonymous__104651)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__104643,Vvar__1__B__104644,Vvar__2__R__104645,Vvar__3___24Anonymous__104650,Vvar__4___24Anonymous__104651)
=> ( ( Vvar__4___24Anonymous__104651 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__104644)
& Vvar__3___24Anonymous__104650 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__104643) )
| ? [Vvar__3__x__104667] :
( t(Vvar__3__x__104667,Vvar__0__A__104643)
& ? [Vvar__4__y__104668] :
( t(Vvar__4__y__104668,Vvar__1__B__104644)
& ? [Vvar__5__l__104669] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104643,Vvar__5__l__104669)
& ? [Vvar__6__l_27__104670] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__104644,Vvar__6__l_27__104670)
& p(happ(happ(Vvar__2__R__104645,Vvar__3__x__104667),Vvar__4__y__104668))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__104643,Vvar__1__B__104644,Vvar__2__R__104645,Vvar__5__l__104669,Vvar__6__l_27__104670)
& Vvar__4___24Anonymous__104651 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__104644,Vvar__4__y__104668,Vvar__6__l_27__104670)
& Vvar__3___24Anonymous__104650 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104643,Vvar__3__x__104667,Vvar__5__l__104669) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__104690,Vvar__1__R__104691,Vvar__2___24Anonymous__104696] :
( cType___24t(Vvar__0__A__104690)
=> ( c_24__type__104723___24t(Vvar__0__A__104690,Vvar__1__R__104691,Vvar__2___24Anonymous__104696,Vvar__1__R__104691)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104690,Vvar__2___24Anonymous__104696)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__104690,Vvar__1__R__104691,Vvar__2___24Anonymous__104696)
=> ( Vvar__2___24Anonymous__104696 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__104690)
| ? [Vvar__2__a__104710] :
( t(Vvar__2__a__104710,Vvar__0__A__104690)
& ? [Vvar__3__l__104711] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__104690,Vvar__3__l__104711)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__104690,happ(Vvar__1__R__104691,Vvar__2__a__104710),Vvar__3__l__104711)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__104690,Vvar__1__R__104691,Vvar__3__l__104711)
& Vvar__2___24Anonymous__104696 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__104690,Vvar__2__a__104710,Vvar__3__l__104711) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__75944,Vvar__1___24Anonymous__75945] :
( cType___24t(Vvar__0__A__75944)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__75944,Vvar__1___24Anonymous__75945)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__75944,Vvar__1___24Anonymous__75945)
=> ( Vvar__1___24Anonymous__75945 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__75944)
| ? [Vvar__1__x__75949] :
( t(Vvar__1__x__75949,Vvar__0__A__75944)
& ? [Vvar__2__l__75950] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__75944,Vvar__2__l__75950)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__75944,Vvar__1__x__75949,Vvar__2__l__75950)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__75944,Vvar__2__l__75950)
& Vvar__1___24Anonymous__75945 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__75944,Vvar__1__x__75949,Vvar__2__l__75950) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__110959,Vvar__1__eqA__110960,Vvar__2__x__110965,Vvar__3___24Anonymous__110966] :
( cType___24t(Vvar__0__A__110959)
=> ( c_24__type__110999___24t(Vvar__0__A__110959,Vvar__1__eqA__110960,Vvar__2__x__110965,Vvar__3___24Anonymous__110966,Vvar__1__eqA__110960)
=> ( t(Vvar__2__x__110965,Vvar__0__A__110959)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__110959,Vvar__3___24Anonymous__110966)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__110959,Vvar__1__eqA__110960,Vvar__2__x__110965,Vvar__3___24Anonymous__110966)
=> ( ? [Vvar__3__y__110975] :
( t(Vvar__3__y__110975,Vvar__0__A__110959)
& ? [Vvar__4__l__110976] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__110959,Vvar__4__l__110976)
& p(happ(happ(Vvar__1__eqA__110960,Vvar__2__x__110965),Vvar__3__y__110975))
& Vvar__3___24Anonymous__110966 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__110959,Vvar__3__y__110975,Vvar__4__l__110976) ) )
| ? [Vvar__3__y__110985] :
( t(Vvar__3__y__110985,Vvar__0__A__110959)
& ? [Vvar__4__l__110986] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__110959,Vvar__4__l__110986)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__110959,Vvar__1__eqA__110960,Vvar__2__x__110965,Vvar__4__l__110986)
& Vvar__3___24Anonymous__110966 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__110959,Vvar__3__y__110985,Vvar__4__l__110986) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__111001,Vvar__1__eqA__111002,Vvar__2___24Anonymous__111007] :
( cType___24t(Vvar__0__A__111001)
=> ( c_24__type__111034___24t(Vvar__0__A__111001,Vvar__1__eqA__111002,Vvar__2___24Anonymous__111007,Vvar__1__eqA__111002)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111001,Vvar__2___24Anonymous__111007)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__111001,Vvar__1__eqA__111002,Vvar__2___24Anonymous__111007)
=> ( Vvar__2___24Anonymous__111007 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111001)
| ? [Vvar__2__x__111021] :
( t(Vvar__2__x__111021,Vvar__0__A__111001)
& ? [Vvar__3__l__111022] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111001,Vvar__3__l__111022)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__111001,Vvar__1__eqA__111002,Vvar__2__x__111021,Vvar__3__l__111022)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__111001,Vvar__1__eqA__111002,Vvar__3__l__111022)
& Vvar__2___24Anonymous__111007 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111001,Vvar__2__x__111021,Vvar__3__l__111022) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__111036,Vvar__1__eqA__111037,Vvar__2___24Anonymous__111042,Vvar__3___24Anonymous__111043] :
( cType___24t(Vvar__0__A__111036)
=> ( c_24__type__111074___24t(Vvar__0__A__111036,Vvar__1__eqA__111037,Vvar__2___24Anonymous__111042,Vvar__3___24Anonymous__111043,Vvar__1__eqA__111037)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111036,Vvar__2___24Anonymous__111042)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111036,Vvar__3___24Anonymous__111043)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__111036,Vvar__1__eqA__111037,Vvar__2___24Anonymous__111042,Vvar__3___24Anonymous__111043)
=> ( ( Vvar__3___24Anonymous__111043 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111036)
& Vvar__2___24Anonymous__111042 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111036) )
| ? [Vvar__2__x__111057] :
( t(Vvar__2__x__111057,Vvar__0__A__111036)
& ? [Vvar__3__x_27__111058] :
( t(Vvar__3__x_27__111058,Vvar__0__A__111036)
& ? [Vvar__4__l__111059] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111036,Vvar__4__l__111059)
& ? [Vvar__5__l_27__111060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111036,Vvar__5__l_27__111060)
& p(happ(happ(Vvar__1__eqA__111037,Vvar__2__x__111057),Vvar__3__x_27__111058))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__111036,Vvar__1__eqA__111037,Vvar__4__l__111059,Vvar__5__l_27__111060)
& Vvar__3___24Anonymous__111043 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111036,Vvar__3__x_27__111058,Vvar__5__l_27__111060)
& Vvar__2___24Anonymous__111042 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111036,Vvar__2__x__111057,Vvar__4__l__111059) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__99447,Vvar__1__P__99448,Vvar__2__p__99451,Vvar__3__x__99452,Vvar__4__q__99453,Vvar__5___24Anonymous__99454] :
( cType___24t(Vvar__0__U__99447)
=> ( c_24__type__99469___24t(Vvar__0__U__99447,Vvar__1__P__99448,Vvar__2__p__99451,Vvar__3__x__99452,Vvar__4__q__99453,Vvar__5___24Anonymous__99454,Vvar__1__P__99448)
=> ( t(Vvar__2__p__99451,Vvar__0__U__99447)
=> ( t(Vvar__3__x__99452,happ(Vvar__1__P__99448,Vvar__2__p__99451))
=> ( t(Vvar__4__q__99453,Vvar__0__U__99447)
=> ( t(Vvar__5___24Anonymous__99454,happ(Vvar__1__P__99448,Vvar__4__q__99453))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__99447,Vvar__1__P__99448,Vvar__2__p__99451,Vvar__3__x__99452,Vvar__4__q__99453,Vvar__5___24Anonymous__99454)
=> ( Vvar__5___24Anonymous__99454 = Vvar__3__x__99452
& Vvar__4__q__99453 = Vvar__2__p__99451 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__99471,Vvar__1__P__99472,Vvar__2__p__99475,Vvar__3__x__99476,Vvar__4__q__99477,Vvar__5__y__99478] :
( cType___24t(Vvar__0__U__99471)
=> ( c_24__type__99497___24t(Vvar__0__U__99471,Vvar__1__P__99472,Vvar__2__p__99475,Vvar__3__x__99476,Vvar__4__q__99477,Vvar__5__y__99478,Vvar__1__P__99472)
=> ( t(Vvar__2__p__99475,Vvar__0__U__99471)
=> ( t(Vvar__3__x__99476,happ(Vvar__1__P__99472,Vvar__2__p__99475))
=> ( t(Vvar__4__q__99477,Vvar__0__U__99471)
=> ( t(Vvar__5__y__99478,happ(Vvar__1__P__99472,Vvar__4__q__99477))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__99471,Vvar__1__P__99472,Vvar__2__p__99475,Vvar__3__x__99476,Vvar__4__q__99477,Vvar__5__y__99478)
=> ( Vvar__4__q__99477 = Vvar__2__p__99475
& Vvar__3__x__99476 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__99471,Vvar__4__q__99477,Vvar__1__P__99472,Vvar__5__y__99478,Vvar__2__p__99475)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX775] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX775)
=> ( VX775 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__776] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__776)
& VX775 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__776) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX782] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX782)
=> ( VX782 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__783] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__783)
& VX782 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__783) )
| ? [Vvar__0___24Anonymous__784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__784)
& VX782 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__784) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX173] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX173)
=> ( ? [Vvar__0___24Anonymous__174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__174)
& VX173 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__174) )
| ? [Vvar__0___24Anonymous__175] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__175)
& VX173 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__175) )
| VX173 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__111765,VX111766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111765)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__111765,VX111766)
=> ( ( Vvar__0___24Anonymous__111765 = cCoq_2eNumbers_2eBinNums_2exH
& VX111766 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__111767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__111767)
& ? [Vvar__1___24Anonymous__111768] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__111767,Vvar__1___24Anonymous__111768)
& Vvar__0___24Anonymous__111765 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803___24a2(Vvar__0___24Anonymous__111765,Vvar__0__p__111767)
& VX111766 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__111767,Vvar__1___24Anonymous__111768) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__111828,Vvar__1__q__111829,Vvar__2___24Anonymous__111830] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__111828)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__111829)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__111830)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__111828,Vvar__1__q__111829,Vvar__2___24Anonymous__111830)
=> ( ( Vvar__0__p__111828 = Vvar__1__q__111829
& Vvar__2___24Anonymous__111830 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__111837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__111837)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__111829,Vvar__2__r__111837) = Vvar__0__p__111828
& Vvar__2___24Anonymous__111830 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__111837) )
| ? [Vvar__2__r__111841] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__111841)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__111828,Vvar__2__r__111841) = Vvar__1__q__111829
& Vvar__2___24Anonymous__111830 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.mask',axiom,
! [VX191832] :
( cCoq_2ePArith_2eBinPos_2ePos_2emask___24t(VX191832)
=> ( VX191832 = cCoq_2ePArith_2eBinPos_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__191833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__191833)
& VX191832 = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__191833) )
| VX191832 = cCoq_2ePArith_2eBinPos_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX83210] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX83210)
=> ( VX83210 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__83211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__83211)
& VX83210 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__83211) )
| VX83210 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX91526] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX91526)
=> ? [Vvar__0__Qnum__91527] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__91527)
& ? [Vvar__1__Qden__91528] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__91528)
& VX91526 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__91527,Vvar__1__Qden__91528) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX104762] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX104762)
=> ? [Vvar__0__neg__104763] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__104763)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__104763,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX104762 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__104763) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX104741] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX104741)
=> ? [Vvar__0__nonneg__104742] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__104742)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__104742)
& VX104741 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__104742) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX104755] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX104755)
=> ? [Vvar__0__nonpos__104756] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__104756)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__104756,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX104755 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__104756) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX104769] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX104769)
=> ? [Vvar__0__nonzero__104770] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__104770)
& Vvar__0__nonzero__104770 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX104769 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__104770) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX104748] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX104748)
=> ? [Vvar__0__pos__104749] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__104749)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__104749)
& VX104748 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__104749) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__102387,Vvar__1___24Anonymous__102388,VX102389] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__102387)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__102388)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__102387,Vvar__1___24Anonymous__102388,VX102389)
=> ( ( Vvar__0__x__102387 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__102388 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX102389 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__102387) )
| ? [Vvar__1__n__102393] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__102393)
& Vvar__0__x__102387 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__102393)
& Vvar__1___24Anonymous__102388 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24102413___24a3(Vvar__0__x__102387,Vvar__1___24Anonymous__102388,Vvar__1__n__102393)
& VX102389 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__102387,Vvar__1__n__102393) )
| ? [Vvar__1__n__102398] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__102398)
& Vvar__0__x__102387 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__102398))
& Vvar__1___24Anonymous__102388 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430___24a3(Vvar__0__x__102387,Vvar__1___24Anonymous__102388,Vvar__1__n__102398)
& VX102389 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__102387,Vvar__1__n__102398) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__104839,Vvar__1__R__104840] :
( cType___24t(Vvar__0__A__104839)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__104839,Vvar__1__R__104840)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__104839,Vvar__1__R__104840)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__104839,Vvar__1__R__104840)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__104839,Vvar__1__R__104840)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__104839,Vvar__1__R__104840)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__111173,Vvar__1__R__111174,Vvar__2__a__111179,Vvar__3___24Anonymous__111180] :
( cType___24t(Vvar__0__A__111173)
=> ( c_24__type__111210___24t(Vvar__0__A__111173,Vvar__1__R__111174,Vvar__2__a__111179,Vvar__3___24Anonymous__111180,Vvar__1__R__111174)
=> ( t(Vvar__2__a__111179,Vvar__0__A__111173)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111173,Vvar__3___24Anonymous__111180)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__111173,Vvar__1__R__111174,Vvar__2__a__111179,Vvar__3___24Anonymous__111180)
=> ( Vvar__3___24Anonymous__111180 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111173)
| ? [Vvar__3__b__111196] :
( t(Vvar__3__b__111196,Vvar__0__A__111173)
& ? [Vvar__4__l__111197] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111173,Vvar__4__l__111197)
& p(happ(happ(Vvar__1__R__111174,Vvar__2__a__111179),Vvar__3__b__111196))
& Vvar__3___24Anonymous__111180 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111173,Vvar__3__b__111196,Vvar__4__l__111197) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__111212,Vvar__1__R__111213,Vvar__2___24Anonymous__111218] :
( cType___24t(Vvar__0__A__111212)
=> ( c_24__type__111245___24t(Vvar__0__A__111212,Vvar__1__R__111213,Vvar__2___24Anonymous__111218,Vvar__1__R__111213)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111212,Vvar__2___24Anonymous__111218)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__111212,Vvar__1__R__111213,Vvar__2___24Anonymous__111218)
=> ( Vvar__2___24Anonymous__111218 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111212)
| ? [Vvar__2__a__111232] :
( t(Vvar__2__a__111232,Vvar__0__A__111212)
& ? [Vvar__3__l__111233] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111212,Vvar__3__l__111233)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__111212,Vvar__1__R__111213,Vvar__3__l__111233)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__111212,Vvar__1__R__111213,Vvar__2__a__111232,Vvar__3__l__111233)
& Vvar__2___24Anonymous__111218 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111212,Vvar__2__a__111232,Vvar__3__l__111233) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__111247,Vvar__1__R__111248,Vvar__2___24Anonymous__111253] :
( cType___24t(Vvar__0__A__111247)
=> ( c_24__type__111280___24t(Vvar__0__A__111247,Vvar__1__R__111248,Vvar__2___24Anonymous__111253,Vvar__1__R__111248)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111247,Vvar__2___24Anonymous__111253)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__111247,Vvar__1__R__111248,Vvar__2___24Anonymous__111253)
=> ( Vvar__2___24Anonymous__111253 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__111247)
| ? [Vvar__2__a__111267] :
( t(Vvar__2__a__111267,Vvar__0__A__111247)
& ? [Vvar__3__l__111268] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__111247,Vvar__3__l__111268)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__111247,Vvar__1__R__111248,Vvar__3__l__111268)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__111247,happ(Vvar__1__R__111248,Vvar__2__a__111267),Vvar__3__l__111268)
& Vvar__2___24Anonymous__111253 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__111247,Vvar__2__a__111267,Vvar__3__l__111268) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX66932] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX66932)
=> ? [Vvar__0___24Anonymous__66933] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__66933)
& ? [Vvar__1___24Anonymous__66934] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__66934)
& ? [Vvar__2___24Anonymous__66935] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__66935)
& ? [Vvar__3___24Anonymous__66936] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__66936)
& ? [Vvar__4___24Anonymous__66937] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__66937)
& ? [Vvar__5___24Anonymous__66938] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__66938)
& ? [Vvar__6___24Anonymous__66939] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__66939)
& ? [Vvar__7___24Anonymous__66940] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__66940)
& VX66932 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__66933,Vvar__1___24Anonymous__66934,Vvar__2___24Anonymous__66935,Vvar__3___24Anonymous__66936,Vvar__4___24Anonymous__66937,Vvar__5___24Anonymous__66938,Vvar__6___24Anonymous__66939,Vvar__7___24Anonymous__66940) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX82090] :
( cCoq_2eStrings_2eString_2estring___24t(VX82090)
=> ( VX82090 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__82091] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__82091)
& ? [Vvar__1___24Anonymous__82092] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__82092)
& VX82090 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__82091,Vvar__1___24Anonymous__82092) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061,VX102062] :
( cType___24t(Vvar__0__X__102049)
=> ( c_24__type__102122___24t(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061,Vvar__1__lt__102050)
=> ( c_24__type__102141___24t(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061,Vvar__2__eq__102055)
=> ( t(Vvar__3__x__102060,Vvar__0__X__102049)
=> ( t(Vvar__4__y__102061,Vvar__0__X__102049)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061,VX102062)
=> ( ( p(happ(happ(Vvar__1__lt__102050,Vvar__3__x__102060),Vvar__4__y__102061))
& VX102062 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061) )
| ( p(happ(happ(Vvar__2__eq__102055,Vvar__3__x__102060),Vvar__4__y__102061))
& VX102062 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061) )
| ( p(happ(happ(Vvar__1__lt__102050,Vvar__4__y__102061),Vvar__3__x__102060))
& VX102062 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__102049,Vvar__1__lt__102050,Vvar__2__eq__102055,Vvar__3__x__102060,Vvar__4__y__102061) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__111868,Vvar__1___24Anonymous__111869] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__111868)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__111869)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__111868,Vvar__1___24Anonymous__111869)
=> ( ? [Vvar__0__a__111871] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__111871)
& ? [Vvar__1__s__111872] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__111872)
& Vvar__1___24Anonymous__111869 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__111871,Vvar__1__s__111872)
& Vvar__0___24Anonymous__111868 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__111873] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__111873)
& ? [Vvar__1__s1__111874] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__111874)
& ? [Vvar__2__s2__111875] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__111875)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__111874,Vvar__2__s2__111875)
& Vvar__1___24Anonymous__111869 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__111873,Vvar__2__s2__111875)
& Vvar__0___24Anonymous__111868 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__111873,Vvar__1__s1__111874) ) ) )
| ? [Vvar__0__a__111877] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__111877)
& ? [Vvar__1__b__111878] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__111878)
& ? [Vvar__2__s1__111879] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__111879)
& ? [Vvar__3__s2__111880] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__111880)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__111877),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__111878))
& Vvar__1___24Anonymous__111869 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__111878,Vvar__3__s2__111880)
& Vvar__0___24Anonymous__111868 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__111877,Vvar__2__s1__111879) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX102241] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX102241)
=> ( VX102241 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX102241 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX102241 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__74902,VX74903] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74902)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__74902,VX74903)
=> ( ? [Vvar__0__n__74904] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74904)
& Vvar__0___24Anonymous__74902 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__74904)
& VX74903 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74904) )
| ? [Vvar__0__n__74905] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74905)
& ? [Vvar__1___24Anonymous__74906] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__74905,Vvar__1___24Anonymous__74906)
& Vvar__0___24Anonymous__74902 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__74905)
& VX74903 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74905,Vvar__1___24Anonymous__74906) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.Vector.t',axiom,
! [Vvar__0__A__191762,Vvar__1___24Anonymous__191763,VX191764] :
( cType___24t(Vvar__0__A__191762)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__191763)
=> ( cCoq_2eVectors_2eVector_2et___24t(Vvar__0__A__191762,Vvar__1___24Anonymous__191763,VX191764)
=> ( ( Vvar__1___24Anonymous__191763 = cCoq_2eInit_2eDatatypes_2eO
& VX191764 = cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__191762) )
| ? [Vvar__1__h__191767] :
( t(Vvar__1__h__191767,Vvar__0__A__191762)
& ? [Vvar__2__n__191768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__191768)
& ? [Vvar__3___24Anonymous__191769] :
( cCoq_2eVectors_2eVector_2et___24t(Vvar__0__A__191762,Vvar__2__n__191768,Vvar__3___24Anonymous__191769)
& Vvar__1___24Anonymous__191763 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__191768)
& VX191764 = cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__191762,Vvar__1__h__191767,Vvar__2__n__191768,Vvar__3___24Anonymous__191769) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__78971,Vvar__1___24Anonymous__78972,VX78973] :
( cType___24t(Vvar__0__A__78971)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__78972)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__78971,Vvar__1___24Anonymous__78972,VX78973)
=> ( ( Vvar__1___24Anonymous__78972 = cCoq_2eInit_2eDatatypes_2eO
& VX78973 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__78971) )
| ? [Vvar__1__h__78976] :
( t(Vvar__1__h__78976,Vvar__0__A__78971)
& ? [Vvar__2__n__78977] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__78977)
& ? [Vvar__3___24Anonymous__78978] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__78971,Vvar__2__n__78977,Vvar__3___24Anonymous__78978)
& Vvar__1___24Anonymous__78972 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__78977)
& VX78973 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__78971,Vvar__1__h__78976,Vvar__2__n__78977,Vvar__3___24Anonymous__78978) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__103928,Vvar__1__b__103929,Vvar__2__d__103930] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__103928)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__103929)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__103930)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__103928,Vvar__1__b__103929,Vvar__2__d__103930)
=> ? [Vvar__3__u__103935] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__103935)
& ? [Vvar__4__v__103936] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__103936)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__103935,Vvar__0__a__103928),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__103936,Vvar__1__b__103929)) = Vvar__2__d__103930
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__103903,Vvar__1__b__103904,VX103905] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__103903)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__103904)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__103903,Vvar__1__b__103904,VX103905)
=> ? [Vvar__2__u__103908] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__103908)
& ? [Vvar__3__v__103909] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__103909)
& ? [Vvar__4__d__103910] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__103910)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__103908,Vvar__0__a__103903),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__103909,Vvar__1__b__103904)) = Vvar__4__d__103910
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__103903,Vvar__1__b__103904,Vvar__4__d__103910)
& VX103905 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__103903,Vvar__1__b__103904,Vvar__2__u__103908,Vvar__3__v__103909,Vvar__4__d__103910) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__103875,Vvar__1__b__103876,Vvar__2__g__103877] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__103875)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__103876)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__103877)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__103875,Vvar__1__b__103876,Vvar__2__g__103877)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__103877,Vvar__0__a__103875)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__103877,Vvar__1__b__103876)
& ! [Vvar__var__var__var__var__5__x__103885__103888__103891__103894__103897] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__103885__103888__103891__103894__103897)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__103885__103888__103891__103894__103897,Vvar__0__a__103875)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__103885__103888__103891__103894__103897,Vvar__1__b__103876)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__103885__103888__103891__103894__103897,Vvar__2__g__103877) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__103938] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__103938)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__103938)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__103938))
& ! [Vvar__var__var__2__n__103943__103945__103947] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__103943__103945__103947)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__103943__103945__103947))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__103943__103945__103947,Vvar__0__p__103938)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__103943__103945__103947,Vvar__0__p__103938) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__111502,Vvar__1__p__111503,VX111504] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__111502)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__111503)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__111502,Vvar__1__p__111503,VX111504)
=> ? [Vvar__2__q__111507] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__111507)
& ? [Vvar__3__r__111508] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__111508)
& Vvar__0__x__111502 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__111507,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__111503)),Vvar__3__r__111508)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__111508))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__111508,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__111503)))
& VX111504 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__111502,Vvar__1__p__111503,Vvar__2__q__111507,Vvar__3__r__111508) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__81986,Vvar__1__F__81987] :
( cType___24t(Vvar__0__T__81986)
=> ( t(Vvar__1__F__81987,Vvar__0__T__81986)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__81986,Vvar__1__F__81987)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__104074,Vvar__1__F__104075] :
( cType___24t(Vvar__0__T__104074)
=> ( t(Vvar__1__F__104075,Vvar__0__T__104074)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__104074,Vvar__1__F__104075)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX99426] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX99426)
=> ( VX99426 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__99427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__99427)
& ? [Vvar__1___24Anonymous__99428] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__99428)
& VX99426 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__99427,Vvar__1___24Anonymous__99428) ) )
| ? [Vvar__0___24Anonymous__99429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__99429)
& ? [Vvar__1___24Anonymous__99430] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__99430)
& VX99426 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__99429,Vvar__1___24Anonymous__99430) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__99215,VX99216] :
( cType___24t(Vvar__0__C__99215)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,VX99216)
=> ( ? [Vvar__1___24Anonymous__99218] :
( t(Vvar__1___24Anonymous__99218,Vvar__0__C__99215)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__99215,Vvar__1___24Anonymous__99218) )
| ? [Vvar__1___24Anonymous__99220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__99220)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__99215,Vvar__1___24Anonymous__99220) )
| ? [Vvar__1___24Anonymous__99222] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__1___24Anonymous__99222)
& ? [Vvar__2___24Anonymous__99223] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__2___24Anonymous__99223)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__99215,Vvar__1___24Anonymous__99222,Vvar__2___24Anonymous__99223) ) )
| ? [Vvar__1___24Anonymous__99225] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__1___24Anonymous__99225)
& ? [Vvar__2___24Anonymous__99226] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__2___24Anonymous__99226)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__99215,Vvar__1___24Anonymous__99225,Vvar__2___24Anonymous__99226) ) )
| ? [Vvar__1___24Anonymous__99228] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__1___24Anonymous__99228)
& ? [Vvar__2___24Anonymous__99229] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__2___24Anonymous__99229)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__99215,Vvar__1___24Anonymous__99228,Vvar__2___24Anonymous__99229) ) )
| ? [Vvar__1___24Anonymous__99231] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__1___24Anonymous__99231)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__99215,Vvar__1___24Anonymous__99231) )
| ? [Vvar__1___24Anonymous__99233] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__99215,Vvar__1___24Anonymous__99233)
& ? [Vvar__2___24Anonymous__99234] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__99234)
& VX99216 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__99215,Vvar__1___24Anonymous__99233,Vvar__2___24Anonymous__99234) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__99379,VX99380] :
( cType___24t(Vvar__0__C__99379)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__99379,VX99380)
=> ( ? [Vvar__1___24Anonymous__99382] :
( t(Vvar__1___24Anonymous__99382,Vvar__0__C__99379)
& VX99380 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__99379,Vvar__1___24Anonymous__99382) )
| ? [Vvar__1___24Anonymous__99384] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__99384)
& ? [Vvar__2___24Anonymous__99385] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__99379,Vvar__2___24Anonymous__99385)
& VX99380 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__99379,Vvar__1___24Anonymous__99384,Vvar__2___24Anonymous__99385) ) )
| ? [Vvar__1___24Anonymous__99387] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__99379,Vvar__1___24Anonymous__99387)
& ? [Vvar__2___24Anonymous__99388] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__99388)
& ? [Vvar__3___24Anonymous__99389] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__99379,Vvar__3___24Anonymous__99389)
& VX99380 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__99379,Vvar__1___24Anonymous__99387,Vvar__2___24Anonymous__99388,Vvar__3___24Anonymous__99389) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002] :
( cType___24t(Vvar__0__R__100971)
=> ( t(Vvar__1__rO__100972,Vvar__0__R__100971)
=> ( t(Vvar__2__rI__100973,Vvar__0__R__100971)
=> ( c_24__type__101403___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__3__rplus__100974)
=> ( c_24__type__101504___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__4__rtimes__100979)
=> ( c_24__type__101605___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__5__rminus__100984)
=> ( c_24__type__101695___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__6__ropp__100989)
=> ( c_24__type__101796___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__7__req__100992)
=> ( c_24__type__101897___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__8__rle__100997)
=> ( c_24__type__101998___24t(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002,Vvar__9__rlt__101002)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992,Vvar__8__rle__100997,Vvar__9__rlt__101002)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__100971,Vvar__7__req__100992)
& ! [Vvar__var__var__var__var__11__x1__101046__101052__101157__101163__101169] :
( t(Vvar__var__var__var__var__11__x1__101046__101052__101157__101163__101169,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__12__x2__101047__101053__101158__101164__101170] :
( t(Vvar__var__var__var__var__12__x2__101047__101053__101158__101164__101170,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__11__x1__101046__101052__101157__101163__101169),Vvar__var__var__var__var__12__x2__101047__101053__101158__101164__101170))
=> ! [Vvar__var__var__var__var__14__y1__101048__101054__101159__101165__101171] :
( t(Vvar__var__var__var__var__14__y1__101048__101054__101159__101165__101171,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__15__y2__101049__101055__101160__101166__101172] :
( t(Vvar__var__var__var__var__15__y2__101049__101055__101160__101166__101172,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__14__y1__101048__101054__101159__101165__101171),Vvar__var__var__var__var__15__y2__101049__101055__101160__101166__101172))
=> p(happ(happ(Vvar__7__req__100992,happ(happ(Vvar__3__rplus__100974,Vvar__var__var__var__var__11__x1__101046__101052__101157__101163__101169),Vvar__var__var__var__var__14__y1__101048__101054__101159__101165__101171)),happ(happ(Vvar__3__rplus__100974,Vvar__var__var__var__var__12__x2__101047__101053__101158__101164__101170),Vvar__var__var__var__var__15__y2__101049__101055__101160__101166__101172))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__101059__101065__101175__101181__101187] :
( t(Vvar__var__var__var__var__12__x1__101059__101065__101175__101181__101187,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__13__x2__101060__101066__101176__101182__101188] :
( t(Vvar__var__var__var__var__13__x2__101060__101066__101176__101182__101188,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__12__x1__101059__101065__101175__101181__101187),Vvar__var__var__var__var__13__x2__101060__101066__101176__101182__101188))
=> ! [Vvar__var__var__var__var__15__y1__101061__101067__101177__101183__101189] :
( t(Vvar__var__var__var__var__15__y1__101061__101067__101177__101183__101189,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__16__y2__101062__101068__101178__101184__101190] :
( t(Vvar__var__var__var__var__16__y2__101062__101068__101178__101184__101190,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__15__y1__101061__101067__101177__101183__101189),Vvar__var__var__var__var__16__y2__101062__101068__101178__101184__101190))
=> p(happ(happ(Vvar__7__req__100992,happ(happ(Vvar__4__rtimes__100979,Vvar__var__var__var__var__12__x1__101059__101065__101175__101181__101187),Vvar__var__var__var__var__15__y1__101061__101067__101177__101183__101189)),happ(happ(Vvar__4__rtimes__100979,Vvar__var__var__var__var__13__x2__101060__101066__101176__101182__101188),Vvar__var__var__var__var__16__y2__101062__101068__101178__101184__101190))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__101072__101075__101193__101196__101199] :
( t(Vvar__var__var__var__var__13__x1__101072__101075__101193__101196__101199,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__14__x2__101073__101076__101194__101197__101200] :
( t(Vvar__var__var__var__var__14__x2__101073__101076__101194__101197__101200,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__13__x1__101072__101075__101193__101196__101199),Vvar__var__var__var__var__14__x2__101073__101076__101194__101197__101200))
=> p(happ(happ(Vvar__7__req__100992,happ(Vvar__6__ropp__100989,Vvar__var__var__var__var__13__x1__101072__101075__101193__101196__101199)),happ(Vvar__6__ropp__100989,Vvar__var__var__var__var__14__x2__101073__101076__101194__101197__101200))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__101079__101085__101202__101208__101214] :
( t(Vvar__var__var__var__var__14__x1__101079__101085__101202__101208__101214,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__15__x2__101080__101086__101203__101209__101215] :
( t(Vvar__var__var__var__var__15__x2__101080__101086__101203__101209__101215,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__14__x1__101079__101085__101202__101208__101214),Vvar__var__var__var__var__15__x2__101080__101086__101203__101209__101215))
=> ! [Vvar__var__var__var__var__17__y1__101081__101087__101204__101210__101216] :
( t(Vvar__var__var__var__var__17__y1__101081__101087__101204__101210__101216,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__18__y2__101082__101088__101205__101211__101217] :
( t(Vvar__var__var__var__var__18__y2__101082__101088__101205__101211__101217,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__17__y1__101081__101087__101204__101210__101216),Vvar__var__var__var__var__18__y2__101082__101088__101205__101211__101217))
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__14__x1__101079__101085__101202__101208__101214),Vvar__var__var__var__var__17__y1__101081__101087__101204__101210__101216))
<=> p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__15__x2__101080__101086__101203__101209__101215),Vvar__var__var__var__var__18__y2__101082__101088__101205__101211__101217)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__101092__101098__101220__101226__101232] :
( t(Vvar__var__var__var__var__15__x1__101092__101098__101220__101226__101232,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__16__x2__101093__101099__101221__101227__101233] :
( t(Vvar__var__var__var__var__16__x2__101093__101099__101221__101227__101233,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__15__x1__101092__101098__101220__101226__101232),Vvar__var__var__var__var__16__x2__101093__101099__101221__101227__101233))
=> ! [Vvar__var__var__var__var__18__y1__101094__101100__101222__101228__101234] :
( t(Vvar__var__var__var__var__18__y1__101094__101100__101222__101228__101234,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__19__y2__101095__101101__101223__101229__101235] :
( t(Vvar__var__var__var__var__19__y2__101095__101101__101223__101229__101235,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__18__y1__101094__101100__101222__101228__101234),Vvar__var__var__var__var__19__y2__101095__101101__101223__101229__101235))
=> ( p(happ(happ(Vvar__9__rlt__101002,Vvar__var__var__var__var__15__x1__101092__101098__101220__101226__101232),Vvar__var__var__var__var__18__y1__101094__101100__101222__101228__101234))
<=> p(happ(happ(Vvar__9__rlt__101002,Vvar__var__var__var__var__16__x2__101093__101099__101221__101227__101233),Vvar__var__var__var__var__19__y2__101095__101101__101223__101229__101235)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__100971,Vvar__1__rO__100972,Vvar__2__rI__100973,Vvar__3__rplus__100974,Vvar__4__rtimes__100979,Vvar__5__rminus__100984,Vvar__6__ropp__100989,Vvar__7__req__100992)
& ! [Vvar__var__var__var__17__n__101106__101107__101238__101239] :
( t(Vvar__var__var__var__17__n__101106__101107__101238__101239,Vvar__0__R__100971)
=> p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__17__n__101106__101107__101238__101239),Vvar__var__var__var__17__n__101106__101107__101238__101239)) )
& ! [Vvar__var__var__var__var__18__n__101109__101113__101240__101244__101248] :
( t(Vvar__var__var__var__var__18__n__101109__101113__101240__101244__101248,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__19__m__101110__101114__101241__101245__101249] :
( t(Vvar__var__var__var__var__19__m__101110__101114__101241__101245__101249,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__18__n__101109__101113__101240__101244__101248),Vvar__var__var__var__var__19__m__101110__101114__101241__101245__101249))
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__19__m__101110__101114__101241__101245__101249),Vvar__var__var__var__var__18__n__101109__101113__101240__101244__101248))
=> p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__18__n__101109__101113__101240__101244__101248),Vvar__var__var__var__var__19__m__101110__101114__101241__101245__101249)) ) ) ) )
& ! [Vvar__var__var__var__19__n__101118__101123__101252__101257] :
( t(Vvar__var__var__var__19__n__101118__101123__101252__101257,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__20__m__101119__101124__101253__101258] :
( t(Vvar__var__var__var__20__m__101119__101124__101253__101258,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__21__p__101120__101125__101254__101259] :
( t(Vvar__var__var__var__21__p__101120__101125__101254__101259,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__19__n__101118__101123__101252__101257),Vvar__var__var__var__20__m__101119__101124__101253__101258))
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__20__m__101119__101124__101253__101258),Vvar__var__var__var__21__p__101120__101125__101254__101259))
=> p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__19__n__101118__101123__101252__101257),Vvar__var__var__var__21__p__101120__101125__101254__101259)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__101129__101131__101262__101264__101266__101268] :
( t(Vvar__var__var__var__var__var__20__n__101129__101131__101262__101264__101266__101268,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__var__21__m__101130__101132__101263__101265__101267__101269] :
( t(Vvar__var__var__var__var__var__21__m__101130__101132__101263__101265__101267__101269,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__9__rlt__101002,Vvar__var__var__var__var__var__20__n__101129__101131__101262__101264__101266__101268),Vvar__var__var__var__var__var__21__m__101130__101132__101263__101265__101267__101269))
<=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__var__20__n__101129__101131__101262__101264__101266__101268),Vvar__var__var__var__var__var__21__m__101130__101132__101263__101265__101267__101269))
& ~ p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__var__20__n__101129__101131__101262__101264__101266__101268),Vvar__var__var__var__var__var__21__m__101130__101132__101263__101265__101267__101269)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__101134__101136__101270__101272__101274] :
( t(Vvar__var__var__var__var__21__n__101134__101136__101270__101272__101274,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__22__m__101135__101137__101271__101273__101275] :
( t(Vvar__var__var__var__var__22__m__101135__101137__101271__101273__101275,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__9__rlt__101002,Vvar__var__var__var__var__21__n__101134__101136__101270__101272__101274),Vvar__var__var__var__var__22__m__101135__101137__101271__101273__101275))
| p(happ(happ(Vvar__7__req__100992,Vvar__var__var__var__var__21__n__101134__101136__101270__101272__101274),Vvar__var__var__var__var__22__m__101135__101137__101271__101273__101275))
| p(happ(happ(Vvar__9__rlt__101002,Vvar__var__var__var__var__22__m__101135__101137__101271__101273__101275),Vvar__var__var__var__var__21__n__101134__101136__101270__101272__101274)) ) ) )
& ! [Vvar__var__var__var__var__22__n__101139__101143__101276__101280__101284] :
( t(Vvar__var__var__var__var__22__n__101139__101143__101276__101280__101284,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__23__m__101140__101144__101277__101281__101285] :
( t(Vvar__var__var__var__var__23__m__101140__101144__101277__101281__101285,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__24__p__101141__101145__101278__101282__101286] :
( t(Vvar__var__var__var__var__24__p__101141__101145__101278__101282__101286,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__8__rle__100997,Vvar__var__var__var__var__22__n__101139__101143__101276__101280__101284),Vvar__var__var__var__var__23__m__101140__101144__101277__101281__101285))
=> p(happ(happ(Vvar__8__rle__100997,happ(happ(Vvar__3__rplus__100974,Vvar__var__var__var__var__24__p__101141__101145__101278__101282__101286),Vvar__var__var__var__var__22__n__101139__101143__101276__101280__101284)),happ(happ(Vvar__3__rplus__100974,Vvar__var__var__var__var__24__p__101141__101145__101278__101282__101286),Vvar__var__var__var__var__23__m__101140__101144__101277__101281__101285))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__101148__101152__101288__101292__101296__101300] :
( t(Vvar__var__var__var__var__var__23__n__101148__101152__101288__101292__101296__101300,Vvar__0__R__100971)
=> ! [Vvar__var__var__var__var__var__24__m__101149__101153__101289__101293__101297__101301] :
( t(Vvar__var__var__var__var__var__24__m__101149__101153__101289__101293__101297__101301,Vvar__0__R__100971)
=> ( p(happ(happ(Vvar__9__rlt__101002,Vvar__1__rO__100972),Vvar__var__var__var__var__var__23__n__101148__101152__101288__101292__101296__101300))
=> ( p(happ(happ(Vvar__9__rlt__101002,Vvar__1__rO__100972),Vvar__var__var__var__var__var__24__m__101149__101153__101289__101293__101297__101301))
=> p(happ(happ(Vvar__9__rlt__101002,Vvar__1__rO__100972),happ(happ(Vvar__4__rtimes__100979,Vvar__var__var__var__var__var__23__n__101148__101152__101288__101292__101296__101300),Vvar__var__var__var__var__var__24__m__101149__101153__101289__101293__101297__101301))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__100992,Vvar__1__rO__100972),Vvar__2__rI__100973))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX102242] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX102242)
=> ( VX102242 = cCoq_2emicromega_2eRMicromega_2eC0
| VX102242 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__102243] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__102243)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__102243) )
| ? [Vvar__0__r__102244] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__102244)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__102244) )
| ? [Vvar__0__r1__102245] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__102245)
& ? [Vvar__1__r2__102246] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__102246)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__102245,Vvar__1__r2__102246) ) )
| ? [Vvar__0__r1__102247] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__102247)
& ? [Vvar__1__r2__102248] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__102248)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__102247,Vvar__1__r2__102248) ) )
| ? [Vvar__0__r1__102249] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__102249)
& ? [Vvar__1__r2__102250] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__102250)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__102249,Vvar__1__r2__102250) ) )
| ? [Vvar__0__r1__102251] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__102251)
& ? [Vvar__1__z__102252] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__102252)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__102251,Vvar__1__z__102252) ) )
| ? [Vvar__0__r__102253] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__102253)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__102253) )
| ? [Vvar__0__r__102254] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__102254)
& VX102242 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__102254) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__102478,VX102479] :
( cType___24t(Vvar__0__T__102478)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__102478,VX102479)
=> ? [Vvar__1__Flhs__102481] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__102478,Vvar__1__Flhs__102481)
& ? [Vvar__2__Fop__102482] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__102482)
& ? [Vvar__3__Frhs__102483] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__102478,Vvar__3__Frhs__102483)
& VX102479 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__102478,Vvar__1__Flhs__102481,Vvar__2__Fop__102482,Vvar__3__Frhs__102483) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX102476] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX102476)
=> ( VX102476 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX102476 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX102476 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX102476 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX102477] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX102477)
=> ( VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX102477 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__110144,VX110145] :
( cType___24t(Vvar__0__C__110144)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,VX110145)
=> ( ? [Vvar__1___24Anonymous__110147] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__110147)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__110144,Vvar__1___24Anonymous__110147) )
| ? [Vvar__1___24Anonymous__110149] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__110144,Vvar__1___24Anonymous__110149)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__110144,Vvar__1___24Anonymous__110149) )
| ? [Vvar__1___24Anonymous__110151] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__110144,Vvar__1___24Anonymous__110151)
& ? [Vvar__2___24Anonymous__110152] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,Vvar__2___24Anonymous__110152)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__110144,Vvar__1___24Anonymous__110151,Vvar__2___24Anonymous__110152) ) )
| ? [Vvar__1___24Anonymous__110154] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,Vvar__1___24Anonymous__110154)
& ? [Vvar__2___24Anonymous__110155] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,Vvar__2___24Anonymous__110155)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__110144,Vvar__1___24Anonymous__110154,Vvar__2___24Anonymous__110155) ) )
| ? [Vvar__1___24Anonymous__110157] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,Vvar__1___24Anonymous__110157)
& ? [Vvar__2___24Anonymous__110158] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__110144,Vvar__2___24Anonymous__110158)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__110144,Vvar__1___24Anonymous__110157,Vvar__2___24Anonymous__110158) ) )
| ? [Vvar__1___24Anonymous__110160] :
( t(Vvar__1___24Anonymous__110160,Vvar__0__C__110144)
& VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__110144,Vvar__1___24Anonymous__110160) )
| VX110145 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__110144) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920] :
( cType___24t(Vvar__0__R__104851)
=> ( t(Vvar__1__rO__104852,Vvar__0__R__104851)
=> ( t(Vvar__2__rI__104853,Vvar__0__R__104851)
=> ( c_24__type__105384___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__3__rplus__104854)
=> ( c_24__type__105730___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__4__rtimes__104859)
=> ( c_24__type__106076___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__5__rminus__104864)
=> ( c_24__type__106399___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__6__ropp__104869)
=> ( c_24__type__106745___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__7__req__104872)
=> ( c_24__type__107091___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__8__rle__104877)
=> ( cType___24t(Vvar__9__C__104882)
=> ( t(Vvar__10__cO__104883,Vvar__9__C__104882)
=> ( t(Vvar__11__cI__104884,Vvar__9__C__104882)
=> ( c_24__type__107437___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__12__cplus__104885)
=> ( c_24__type__107783___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__13__ctimes__104890)
=> ( c_24__type__108129___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__14__cminus__104895)
=> ( c_24__type__108452___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__15__copp__104900)
=> ( c_24__type__108798___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__16__ceqb__104903)
=> ( c_24__type__109144___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__17__cleb__104908)
=> ( c_24__type__109467___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__18__phi__104913)
=> ( cType___24t(Vvar__19__E__104916)
=> ( c_24__type__109790___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__20__pow__phi__104917)
=> ( c_24__type__110136___24t(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920,Vvar__21__rpow__104920)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__8__rle__104877,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__17__cleb__104908,Vvar__18__phi__104913,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__104851,Vvar__1__rO__104852,Vvar__2__rI__104853,Vvar__3__rplus__104854,Vvar__4__rtimes__104859,Vvar__5__rminus__104864,Vvar__6__ropp__104869,Vvar__7__req__104872,Vvar__9__C__104882,Vvar__10__cO__104883,Vvar__11__cI__104884,Vvar__12__cplus__104885,Vvar__13__ctimes__104890,Vvar__14__cminus__104895,Vvar__15__copp__104900,Vvar__16__ceqb__104903,Vvar__18__phi__104913)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__104851,Vvar__2__rI__104853,Vvar__4__rtimes__104859,Vvar__7__req__104872,Vvar__19__E__104916,Vvar__20__pow__phi__104917,Vvar__21__rpow__104920)
& ! [Vvar__var__var__var__var__var__24__x__105003__105006__105016__105019__105022__105025] :
( t(Vvar__var__var__var__var__var__24__x__105003__105006__105016__105019__105022__105025,Vvar__9__C__104882)
=> ! [Vvar__var__var__var__var__var__25__y__105004__105007__105017__105020__105023__105026] :
( t(Vvar__var__var__var__var__var__25__y__105004__105007__105017__105020__105023__105026,Vvar__9__C__104882)
=> ( happ(happ(Vvar__16__ceqb__104903,Vvar__var__var__var__var__var__24__x__105003__105006__105016__105019__105022__105025),Vvar__var__var__var__var__var__25__y__105004__105007__105017__105020__105023__105026) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__104872,happ(Vvar__18__phi__104913,Vvar__var__var__var__var__var__24__x__105003__105006__105016__105019__105022__105025)),happ(Vvar__18__phi__104913,Vvar__var__var__var__var__var__25__y__105004__105007__105017__105020__105023__105026))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__105010__105013__105028__105031__105034__105037] :
( t(Vvar__var__var__var__var__var__25__x__105010__105013__105028__105031__105034__105037,Vvar__9__C__104882)
=> ! [Vvar__var__var__var__var__var__26__y__105011__105014__105029__105032__105035__105038] :
( t(Vvar__var__var__var__var__var__26__y__105011__105014__105029__105032__105035__105038,Vvar__9__C__104882)
=> ( happ(happ(Vvar__17__cleb__104908,Vvar__var__var__var__var__var__25__x__105010__105013__105028__105031__105034__105037),Vvar__var__var__var__var__var__26__y__105011__105014__105029__105032__105035__105038) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__104877,happ(Vvar__18__phi__104913,Vvar__var__var__var__var__var__25__x__105010__105013__105028__105031__105034__105037)),happ(Vvar__18__phi__104913,Vvar__var__var__var__var__var__26__y__105011__105014__105029__105032__105035__105038))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,VX103436] :
( cType___24t(Vvar__0__TA__103432)
=> ( cType___24t(Vvar__1__TX__103433)
=> ( cType___24t(Vvar__2__AA__103434)
=> ( cType___24t(Vvar__3__AF__103435)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,VX103436)
=> ( VX103436 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435)
| VX103436 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435)
| ? [Vvar__4___24Anonymous__103449] :
( t(Vvar__4___24Anonymous__103449,Vvar__1__TX__103433)
& VX103436 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103449) )
| ? [Vvar__4___24Anonymous__103454] :
( t(Vvar__4___24Anonymous__103454,Vvar__0__TA__103432)
& ? [Vvar__5___24Anonymous__103455] :
( t(Vvar__5___24Anonymous__103455,Vvar__2__AA__103434)
& VX103436 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103454,Vvar__5___24Anonymous__103455) ) )
| ? [Vvar__4___24Anonymous__103460] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103460)
& ? [Vvar__5___24Anonymous__103461] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__5___24Anonymous__103461)
& VX103436 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103460,Vvar__5___24Anonymous__103461) ) )
| ? [Vvar__4___24Anonymous__103466] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103466)
& ? [Vvar__5___24Anonymous__103467] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__5___24Anonymous__103467)
& VX103436 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103466,Vvar__5___24Anonymous__103467) ) )
| ? [Vvar__4___24Anonymous__103472] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103472)
& VX103436 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103472) )
| ? [Vvar__4___24Anonymous__103477] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103477)
& ? [Vvar__5___24Anonymous__103478] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__103435,Vvar__5___24Anonymous__103478)
& ? [Vvar__6___24Anonymous__103479] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__6___24Anonymous__103479)
& VX103436 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__103432,Vvar__1__TX__103433,Vvar__2__AA__103434,Vvar__3__AF__103435,Vvar__4___24Anonymous__103477,Vvar__5___24Anonymous__103478,Vvar__6___24Anonymous__103479) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__111388,VX111389] :
( cType___24t(Vvar__0__A__111388)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__111388,VX111389)
=> ( VX111389 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__111388)
| ? [Vvar__1___24Anonymous__111392] :
( t(Vvar__1___24Anonymous__111392,Vvar__0__A__111388)
& VX111389 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__111388,Vvar__1___24Anonymous__111392) )
| ? [Vvar__1___24Anonymous__111394] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__111388,Vvar__1___24Anonymous__111394)
& ? [Vvar__2___24Anonymous__111395] :
( t(Vvar__2___24Anonymous__111395,Vvar__0__A__111388)
& ? [Vvar__3___24Anonymous__111396] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__111388,Vvar__3___24Anonymous__111396)
& VX111389 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__111388,Vvar__1___24Anonymous__111394,Vvar__2___24Anonymous__111395,Vvar__3___24Anonymous__111396) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__111557] :
( cProp___24t(Vvar__0___24Anonymous__111557)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__111557)
=> ( ? [Vvar__0__P__111559] :
( cProp___24t(Vvar__0__P__111559)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__111559)
& Vvar__0___24Anonymous__111557 = Vvar__0__P__111559 )
| ? [Vvar__0__s__111561] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__111561)
& Vvar__0___24Anonymous__111557 = c_24__prop__111570___24a2(Vvar__0___24Anonymous__111557,Vvar__0__s__111561) )
| ? [Vvar__0__s1__111563] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__111563)
& ? [Vvar__1__s2__111564] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__111564)
& Vvar__0___24Anonymous__111557 = c_24__prop__111571___24a3(Vvar__0___24Anonymous__111557,Vvar__0__s1__111563,Vvar__1__s2__111564) ) )
| ? [Vvar__0__s1__111567] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__111567)
& ? [Vvar__1__s2__111568] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__111568)
& Vvar__0___24Anonymous__111557 = c_24__prop__111572___24a3(Vvar__0___24Anonymous__111557,Vvar__0__s1__111567,Vvar__1__s2__111568) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__103953] :
( cProp___24t(Vvar__0___24Anonymous__103953)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__103953)
=> ( ? [Vvar__0__S__103955] :
( cType___24t(Vvar__0__S__103955)
& ? [Vvar__1__x__103956] :
( t(Vvar__1__x__103956,Vvar__0__S__103955)
& ? [Vvar__2__y__103957] :
( t(Vvar__2__y__103957,Vvar__0__S__103955)
& Vvar__0___24Anonymous__103953 = c_24__prop__103977___24a4(Vvar__0___24Anonymous__103953,Vvar__0__S__103955,Vvar__1__x__103956,Vvar__2__y__103957) ) ) )
| ? [Vvar__0__x__103958] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__103958)
& ? [Vvar__1__y__103959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__103959)
& Vvar__0___24Anonymous__103953 = c_24__prop__103978___24a3(Vvar__0___24Anonymous__103953,Vvar__0__x__103958,Vvar__1__y__103959) ) )
| ? [Vvar__0__x__103960] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__103960)
& ? [Vvar__1__s__103961] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__103961)
& Vvar__0___24Anonymous__103953 = c_24__prop__103979___24a3(Vvar__0___24Anonymous__103953,Vvar__0__x__103960,Vvar__1__s__103961) ) )
| Vvar__0___24Anonymous__103953 = c_24True
| Vvar__0___24Anonymous__103953 = c_24False
| ? [Vvar__0__P__103962] :
( cProp___24t(Vvar__0__P__103962)
& ? [Vvar__1__Q__103963] :
( cProp___24t(Vvar__1__Q__103963)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__103962)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__103963)
& Vvar__0___24Anonymous__103953 = c_24__prop__103980___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103962,Vvar__1__Q__103963) ) )
| ? [Vvar__0__P__103966] :
( cProp___24t(Vvar__0__P__103966)
& ? [Vvar__1__Q__103967] :
( cProp___24t(Vvar__1__Q__103967)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__103966)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__103967)
& Vvar__0___24Anonymous__103953 = c_24__prop__103981___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103966,Vvar__1__Q__103967) ) )
| ? [Vvar__0__P__103970] :
( cProp___24t(Vvar__0__P__103970)
& ? [Vvar__1__Q__103971] :
( cProp___24t(Vvar__1__Q__103971)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__103970)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__103971)
& Vvar__0___24Anonymous__103953 = c_24__prop__103982___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103970,Vvar__1__Q__103971) ) )
| ? [Vvar__0__P__103975] :
( cProp___24t(Vvar__0__P__103975)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__103975)
& Vvar__0___24Anonymous__103953 = c_24__prop__103983___24a2(Vvar__0___24Anonymous__103953,Vvar__0__P__103975) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.ct',axiom,
! [Vvar__0___24Anonymous__191877,Vvar__1___24Anonymous__191878,Vvar__2___24Anonymous__191879] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__191877)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__191878)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__191879)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2ect___24a3(Vvar__0___24Anonymous__191877,Vvar__1___24Anonymous__191878,Vvar__2___24Anonymous__191879)
=> ( ? [Vvar__0__x__191881] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__191881)
& Vvar__2___24Anonymous__191879 = Vvar__0__x__191881
& Vvar__1___24Anonymous__191878 = Vvar__0__x__191881
& Vvar__0___24Anonymous__191877 = Vvar__0__x__191881 )
| ? [Vvar__0__x__191882] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__191882)
& Vvar__2___24Anonymous__191879 = Vvar__0__x__191882
& Vvar__1___24Anonymous__191878 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__191877 = Vvar__0__x__191882 )
| ? [Vvar__0__x__191883] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__191883)
& Vvar__2___24Anonymous__191879 = Vvar__0__x__191883
& Vvar__1___24Anonymous__191878 = Vvar__0__x__191883
& Vvar__0___24Anonymous__191877 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__191884] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__191884)
& Vvar__2___24Anonymous__191879 = Vvar__0__x__191884
& Vvar__1___24Anonymous__191878 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__191877 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__191885] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__191885)
& Vvar__2___24Anonymous__191879 = Vvar__0__x__191885
& Vvar__1___24Anonymous__191878 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__191877 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.tree',axiom,
! [VX191864] :
( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(VX191864)
=> ( VX191864 = cCoq_2emicromega_2eZMicromega_2eVars_2eLeaf
| ? [Vvar__0___24Anonymous__191865] :
( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(Vvar__0___24Anonymous__191865)
& ? [Vvar__1___24Anonymous__191866] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__191866)
& ? [Vvar__2___24Anonymous__191867] :
( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(Vvar__2___24Anonymous__191867)
& VX191864 = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__191865,Vvar__1___24Anonymous__191866,Vvar__2___24Anonymous__191867) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX81100] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX81100)
=> ( VX81100 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__81101] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__81101)
& ? [Vvar__1___24Anonymous__81102] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__81102)
& VX81100 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__81101,Vvar__1___24Anonymous__81102) ) )
| ? [Vvar__0___24Anonymous__81103] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__81103)
& ? [Vvar__1___24Anonymous__81104] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__81104)
& VX81100 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__81103,Vvar__1___24Anonymous__81104) ) )
| ? [Vvar__0___24Anonymous__81105] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__81105)
& ? [Vvar__1___24Anonymous__81106] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__81106)
& ? [Vvar__2___24Anonymous__81107] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__81107)
& VX81100 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__81105,Vvar__1___24Anonymous__81106,Vvar__2___24Anonymous__81107) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
! [Vvar__0__x__111425,Vvar__1___24Anonymous__111426] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__111425)
=> ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__111426)
=> ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__111425,Vvar__1___24Anonymous__111426)
=> ( ? [Vvar__1__c__111429] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__111429)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__111425,Vvar__1__c__111429)
& Vvar__1___24Anonymous__111426 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__111429) )
| ? [Vvar__1__p__111432] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__111432)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__111425,Vvar__1__p__111432)
& ? [Vvar__3__j__111434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__111434)
& Vvar__1___24Anonymous__111426 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__111434,Vvar__1__p__111432) ) )
| ? [Vvar__1__p__111436] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__111436)
& ? [Vvar__2__q__111437] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__111437)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__111425,Vvar__1__p__111436)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__111425,Vvar__2__q__111437)
& ? [Vvar__5__j__111440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__111440)
& Vvar__1___24Anonymous__111426 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__111436,Vvar__5__j__111440,Vvar__2__q__111437) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__111441,Vvar__1__env__111442,Vvar__2__env_27__111445,Vvar__3__x__111448] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__111441)
=> ( c_24__type__111469___24t(Vvar__0__fr__111441,Vvar__1__env__111442,Vvar__2__env_27__111445,Vvar__3__x__111448,Vvar__1__env__111442)
=> ( c_24__type__111478___24t(Vvar__0__fr__111441,Vvar__1__env__111442,Vvar__2__env_27__111445,Vvar__3__x__111448,Vvar__2__env_27__111445)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__111448)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__111441,Vvar__1__env__111442,Vvar__2__env_27__111445,Vvar__3__x__111448)
=> ( happ(Vvar__1__env__111442,Vvar__3__x__111448) = happ(Vvar__2__env_27__111445,Vvar__3__x__111448)
& happ(Vvar__1__env__111442,Vvar__3__x__111448) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__111445,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__111441,Vvar__3__x__111448))),happ(Vvar__2__env_27__111445,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__111441,Vvar__3__x__111448))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__111445,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__111441,Vvar__3__x__111448))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__111445,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__111441,Vvar__3__x__111448))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__89967,VX89968] :
( cType___24t(Vvar__0__C__89967)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,VX89968)
=> ( VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__89967)
| VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__89967)
| ? [Vvar__1___24Anonymous__89972] :
( t(Vvar__1___24Anonymous__89972,Vvar__0__C__89967)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__89967,Vvar__1___24Anonymous__89972) )
| ? [Vvar__1___24Anonymous__89974] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__89974)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__89967,Vvar__1___24Anonymous__89974) )
| ? [Vvar__1___24Anonymous__89976] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89976)
& ? [Vvar__2___24Anonymous__89977] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__2___24Anonymous__89977)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__89967,Vvar__1___24Anonymous__89976,Vvar__2___24Anonymous__89977) ) )
| ? [Vvar__1___24Anonymous__89979] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89979)
& ? [Vvar__2___24Anonymous__89980] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__2___24Anonymous__89980)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__89967,Vvar__1___24Anonymous__89979,Vvar__2___24Anonymous__89980) ) )
| ? [Vvar__1___24Anonymous__89982] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89982)
& ? [Vvar__2___24Anonymous__89983] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__2___24Anonymous__89983)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__89967,Vvar__1___24Anonymous__89982,Vvar__2___24Anonymous__89983) ) )
| ? [Vvar__1___24Anonymous__89985] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89985)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__89967,Vvar__1___24Anonymous__89985) )
| ? [Vvar__1___24Anonymous__89987] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89987)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__89967,Vvar__1___24Anonymous__89987) )
| ? [Vvar__1___24Anonymous__89989] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89989)
& ? [Vvar__2___24Anonymous__89990] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__2___24Anonymous__89990)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__89967,Vvar__1___24Anonymous__89989,Vvar__2___24Anonymous__89990) ) )
| ? [Vvar__1___24Anonymous__89992] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__89967,Vvar__1___24Anonymous__89992)
& ? [Vvar__2___24Anonymous__89993] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__89993)
& VX89968 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__89967,Vvar__1___24Anonymous__89992,Vvar__2___24Anonymous__89993) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528] :
( cType___24t(Vvar__0__R__99499)
=> ( t(Vvar__1__rO__99500,Vvar__0__R__99499)
=> ( t(Vvar__2__rI__99501,Vvar__0__R__99499)
=> ( c_24__type__99693___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__3__radd__99502)
=> ( c_24__type__99786___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__4__rmul__99507)
=> ( c_24__type__99879___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__5__rsub__99512)
=> ( c_24__type__99961___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__6__ropp__99517)
=> ( c_24__type__100054___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__7__rdiv__99520)
=> ( c_24__type__100136___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__8__rinv__99525)
=> ( c_24__type__100229___24t(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528,Vvar__9__req__99528)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__7__rdiv__99520,Vvar__8__rinv__99525,Vvar__9__req__99528)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__99499,Vvar__1__rO__99500,Vvar__2__rI__99501,Vvar__3__radd__99502,Vvar__4__rmul__99507,Vvar__5__rsub__99512,Vvar__6__ropp__99517,Vvar__9__req__99528)
& ~ p(happ(happ(Vvar__9__req__99528,Vvar__2__rI__99501),Vvar__1__rO__99500))
& ! [Vvar__var__var__var__var__var__var__12__p__99571__99573__99580__99582__99584__99586__99588] :
( t(Vvar__var__var__var__var__var__var__12__p__99571__99573__99580__99582__99584__99586__99588,Vvar__0__R__99499)
=> ! [Vvar__var__var__var__var__var__var__13__q__99572__99574__99581__99583__99585__99587__99589] :
( t(Vvar__var__var__var__var__var__var__13__q__99572__99574__99581__99583__99585__99587__99589,Vvar__0__R__99499)
=> p(happ(happ(Vvar__9__req__99528,happ(happ(Vvar__7__rdiv__99520,Vvar__var__var__var__var__var__var__12__p__99571__99573__99580__99582__99584__99586__99588),Vvar__var__var__var__var__var__var__13__q__99572__99574__99581__99583__99585__99587__99589)),happ(happ(Vvar__4__rmul__99507,Vvar__var__var__var__var__var__var__12__p__99571__99573__99580__99582__99584__99586__99588),happ(Vvar__8__rinv__99525,Vvar__var__var__var__var__var__var__13__q__99572__99574__99581__99583__99585__99587__99589)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__99576__99578__99590__99592__99594__99596__99598__99600] :
( t(Vvar__var__var__var__var__var__var__var__13__p__99576__99578__99590__99592__99594__99596__99598__99600,Vvar__0__R__99499)
=> ( ~ p(happ(happ(Vvar__9__req__99528,Vvar__var__var__var__var__var__var__var__13__p__99576__99578__99590__99592__99594__99596__99598__99600),Vvar__1__rO__99500))
=> p(happ(happ(Vvar__9__req__99528,happ(happ(Vvar__4__rmul__99507,happ(Vvar__8__rinv__99525,Vvar__var__var__var__var__var__var__var__13__p__99576__99578__99590__99592__99594__99596__99598__99600)),Vvar__var__var__var__var__var__var__var__13__p__99576__99578__99590__99592__99594__99596__99598__99600)),Vvar__2__rI__99501)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264] :
( cType___24t(Vvar__0__R__100235)
=> ( t(Vvar__1__rO__100236,Vvar__0__R__100235)
=> ( t(Vvar__2__rI__100237,Vvar__0__R__100235)
=> ( c_24__type__100429___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__3__radd__100238)
=> ( c_24__type__100522___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__4__rmul__100243)
=> ( c_24__type__100615___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__5__rsub__100248)
=> ( c_24__type__100697___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__6__ropp__100253)
=> ( c_24__type__100790___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__7__rdiv__100256)
=> ( c_24__type__100872___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__8__rinv__100261)
=> ( c_24__type__100965___24t(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264,Vvar__9__req__100264)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__7__rdiv__100256,Vvar__8__rinv__100261,Vvar__9__req__100264)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__100235,Vvar__1__rO__100236,Vvar__2__rI__100237,Vvar__3__radd__100238,Vvar__4__rmul__100243,Vvar__5__rsub__100248,Vvar__6__ropp__100253,Vvar__9__req__100264)
& ~ p(happ(happ(Vvar__9__req__100264,Vvar__2__rI__100237),Vvar__1__rO__100236))
& ! [Vvar__var__var__var__var__var__var__12__p__100307__100309__100316__100318__100320__100322__100324] :
( t(Vvar__var__var__var__var__var__var__12__p__100307__100309__100316__100318__100320__100322__100324,Vvar__0__R__100235)
=> ! [Vvar__var__var__var__var__var__var__13__q__100308__100310__100317__100319__100321__100323__100325] :
( t(Vvar__var__var__var__var__var__var__13__q__100308__100310__100317__100319__100321__100323__100325,Vvar__0__R__100235)
=> p(happ(happ(Vvar__9__req__100264,happ(happ(Vvar__7__rdiv__100256,Vvar__var__var__var__var__var__var__12__p__100307__100309__100316__100318__100320__100322__100324),Vvar__var__var__var__var__var__var__13__q__100308__100310__100317__100319__100321__100323__100325)),happ(happ(Vvar__4__rmul__100243,Vvar__var__var__var__var__var__var__12__p__100307__100309__100316__100318__100320__100322__100324),happ(Vvar__8__rinv__100261,Vvar__var__var__var__var__var__var__13__q__100308__100310__100317__100319__100321__100323__100325)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__100312__100314__100326__100328__100330__100332__100334__100336] :
( t(Vvar__var__var__var__var__var__var__var__13__p__100312__100314__100326__100328__100330__100332__100334__100336,Vvar__0__R__100235)
=> ( ~ p(happ(happ(Vvar__9__req__100264,Vvar__var__var__var__var__var__var__var__13__p__100312__100314__100326__100328__100330__100332__100334__100336),Vvar__1__rO__100236))
=> p(happ(happ(Vvar__9__req__100264,happ(happ(Vvar__4__rmul__100243,happ(Vvar__8__rinv__100261,Vvar__var__var__var__var__var__var__var__13__p__100312__100314__100326__100328__100330__100332__100334__100336)),Vvar__var__var__var__var__var__var__var__13__p__100312__100314__100326__100328__100330__100332__100334__100336)),Vvar__2__rI__100237)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__90585,VX90586] :
( cType___24t(Vvar__0__C__90585)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__90585,VX90586)
=> ? [Vvar__1__num__90588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__90585,Vvar__1__num__90588)
& ? [Vvar__2__denum__90589] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__90585,Vvar__2__denum__90589)
& ? [Vvar__3__condition__90590] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__90585),Vvar__3__condition__90590)
& VX90586 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__90585,Vvar__1__num__90588,Vvar__2__denum__90589,Vvar__3__condition__90590) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__104160,VX104161] :
( cType___24t(Vvar__0__C__104160)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__104160,VX104161)
=> ? [Vvar__1__rsplit__left__104163] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__104160,Vvar__1__rsplit__left__104163)
& ? [Vvar__2__rsplit__common__104164] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__104160,Vvar__2__rsplit__common__104164)
& ? [Vvar__3__rsplit__right__104165] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__104160,Vvar__3__rsplit__right__104165)
& VX104161 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__104160,Vvar__1__rsplit__left__104163,Vvar__2__rsplit__common__104164,Vvar__3__rsplit__right__104165) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195] :
( cType___24t(Vvar__0__R__104174)
=> ( t(Vvar__1__rO__104175,Vvar__0__R__104174)
=> ( t(Vvar__2__rI__104176,Vvar__0__R__104174)
=> ( c_24__type__104322___24t(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195,Vvar__3__radd__104177)
=> ( c_24__type__104385___24t(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195,Vvar__4__rmul__104182)
=> ( c_24__type__104448___24t(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195,Vvar__5__rdiv__104187)
=> ( c_24__type__104502___24t(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195,Vvar__6__rinv__104192)
=> ( c_24__type__104565___24t(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195,Vvar__7__req__104195)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__5__rdiv__104187,Vvar__6__rinv__104192,Vvar__7__req__104195)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__104174,Vvar__1__rO__104175,Vvar__2__rI__104176,Vvar__3__radd__104177,Vvar__4__rmul__104182,Vvar__7__req__104195)
& ~ p(happ(happ(Vvar__7__req__104195,Vvar__2__rI__104176),Vvar__1__rO__104175))
& ! [Vvar__var__var__var__var__var__var__10__p__104230__104232__104239__104241__104243__104245__104247] :
( t(Vvar__var__var__var__var__var__var__10__p__104230__104232__104239__104241__104243__104245__104247,Vvar__0__R__104174)
=> ! [Vvar__var__var__var__var__var__var__11__q__104231__104233__104240__104242__104244__104246__104248] :
( t(Vvar__var__var__var__var__var__var__11__q__104231__104233__104240__104242__104244__104246__104248,Vvar__0__R__104174)
=> p(happ(happ(Vvar__7__req__104195,happ(happ(Vvar__5__rdiv__104187,Vvar__var__var__var__var__var__var__10__p__104230__104232__104239__104241__104243__104245__104247),Vvar__var__var__var__var__var__var__11__q__104231__104233__104240__104242__104244__104246__104248)),happ(happ(Vvar__4__rmul__104182,Vvar__var__var__var__var__var__var__10__p__104230__104232__104239__104241__104243__104245__104247),happ(Vvar__6__rinv__104192,Vvar__var__var__var__var__var__var__11__q__104231__104233__104240__104242__104244__104246__104248)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__104235__104237__104249__104251__104253__104255__104257__104259] :
( t(Vvar__var__var__var__var__var__var__var__11__p__104235__104237__104249__104251__104253__104255__104257__104259,Vvar__0__R__104174)
=> ( ~ p(happ(happ(Vvar__7__req__104195,Vvar__var__var__var__var__var__var__var__11__p__104235__104237__104249__104251__104253__104255__104257__104259),Vvar__1__rO__104175))
=> p(happ(happ(Vvar__7__req__104195,happ(happ(Vvar__4__rmul__104182,happ(Vvar__6__rinv__104192,Vvar__var__var__var__var__var__var__var__11__p__104235__104237__104249__104251__104253__104255__104257__104259)),Vvar__var__var__var__var__var__var__var__11__p__104235__104237__104249__104251__104253__104255__104257__104259)),Vvar__2__rI__104176)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX104574] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX104574)
=> ? [Vvar__0__hypo__type__104575] :
( cType___24t(Vvar__0__hypo__type__104575)
& ? [Vvar__1__hypo__proof__104576] :
( t(Vvar__1__hypo__proof__104576,Vvar__0__hypo__type__104575)
& VX104574 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__104575,Vvar__1__hypo__proof__104576) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX234] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX234)
=> ( VX234 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__235] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__235)
& ? [Vvar__1___24Anonymous__236] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__236)
& VX234 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__235,Vvar__1___24Anonymous__236) ) )
| ? [Vvar__0___24Anonymous__237] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__237)
& ? [Vvar__1___24Anonymous__238] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__238)
& VX234 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__237,Vvar__1___24Anonymous__238) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__255,VX256] :
( cType___24t(Vvar__0__C__255)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,VX256)
=> ( VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__255)
| VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__255)
| ? [Vvar__1___24Anonymous__260] :
( t(Vvar__1___24Anonymous__260,Vvar__0__C__255)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__255,Vvar__1___24Anonymous__260) )
| ? [Vvar__1___24Anonymous__262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__262)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__255,Vvar__1___24Anonymous__262) )
| ? [Vvar__1___24Anonymous__264] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__1___24Anonymous__264)
& ? [Vvar__2___24Anonymous__265] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__2___24Anonymous__265)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__255,Vvar__1___24Anonymous__264,Vvar__2___24Anonymous__265) ) )
| ? [Vvar__1___24Anonymous__267] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__1___24Anonymous__267)
& ? [Vvar__2___24Anonymous__268] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__2___24Anonymous__268)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__255,Vvar__1___24Anonymous__267,Vvar__2___24Anonymous__268) ) )
| ? [Vvar__1___24Anonymous__270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__1___24Anonymous__270)
& ? [Vvar__2___24Anonymous__271] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__2___24Anonymous__271)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__255,Vvar__1___24Anonymous__270,Vvar__2___24Anonymous__271) ) )
| ? [Vvar__1___24Anonymous__273] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__1___24Anonymous__273)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__255,Vvar__1___24Anonymous__273) )
| ? [Vvar__1___24Anonymous__275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__255,Vvar__1___24Anonymous__275)
& ? [Vvar__2___24Anonymous__276] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__276)
& VX256 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__255,Vvar__1___24Anonymous__275,Vvar__2___24Anonymous__276) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__187,VX188] :
( cType___24t(Vvar__0__C__187)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__187,VX188)
=> ( ? [Vvar__1___24Anonymous__190] :
( t(Vvar__1___24Anonymous__190,Vvar__0__C__187)
& VX188 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__187,Vvar__1___24Anonymous__190) )
| ? [Vvar__1___24Anonymous__192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__192)
& ? [Vvar__2___24Anonymous__193] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__187,Vvar__2___24Anonymous__193)
& VX188 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__187,Vvar__1___24Anonymous__192,Vvar__2___24Anonymous__193) ) )
| ? [Vvar__1___24Anonymous__195] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__187,Vvar__1___24Anonymous__195)
& ? [Vvar__2___24Anonymous__196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__196)
& ? [Vvar__3___24Anonymous__197] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__187,Vvar__3___24Anonymous__197)
& VX188 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__187,Vvar__1___24Anonymous__195,Vvar__2___24Anonymous__196,Vvar__3___24Anonymous__197) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938] :
( cType___24t(Vvar__0__R__91917)
=> ( t(Vvar__1__rO__91918,Vvar__0__R__91917)
=> ( t(Vvar__2__rI__91919,Vvar__0__R__91917)
=> ( c_24__type__92166___24t(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938,Vvar__3__radd__91920)
=> ( c_24__type__92229___24t(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938,Vvar__4__rmul__91925)
=> ( c_24__type__92292___24t(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938,Vvar__5__rsub__91930)
=> ( c_24__type__92346___24t(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938,Vvar__6__ropp__91935)
=> ( c_24__type__92409___24t(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938,Vvar__7__req__91938)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__91917,Vvar__1__rO__91918,Vvar__2__rI__91919,Vvar__3__radd__91920,Vvar__4__rmul__91925,Vvar__5__rsub__91930,Vvar__6__ropp__91935,Vvar__7__req__91938)
=> ( ! [Vvar__var__var__var__var__var__8__x__91971__91972__92025__92026__92027__92028] :
( t(Vvar__var__var__var__var__var__8__x__91971__91972__92025__92026__92027__92028,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__3__radd__91920,Vvar__1__rO__91918),Vvar__var__var__var__var__var__8__x__91971__91972__92025__92026__92027__92028)),Vvar__var__var__var__var__var__8__x__91971__91972__92025__92026__92027__92028)) )
& ! [Vvar__var__var__var__var__9__x__91974__91976__92029__92031__92033] :
( t(Vvar__var__var__var__var__9__x__91974__91976__92029__92031__92033,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__10__y__91975__91977__92030__92032__92034] :
( t(Vvar__var__var__var__var__10__y__91975__91977__92030__92032__92034,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__9__x__91974__91976__92029__92031__92033),Vvar__var__var__var__var__10__y__91975__91977__92030__92032__92034)),happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__10__y__91975__91977__92030__92032__92034),Vvar__var__var__var__var__9__x__91974__91976__92029__92031__92033))) ) )
& ! [Vvar__var__var__var__var__10__x__91979__91982__92035__92038__92041] :
( t(Vvar__var__var__var__var__10__x__91979__91982__92035__92038__92041,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__11__y__91980__91983__92036__92039__92042] :
( t(Vvar__var__var__var__var__11__y__91980__91983__92036__92039__92042,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__12__z__91981__91984__92037__92040__92043] :
( t(Vvar__var__var__var__var__12__z__91981__91984__92037__92040__92043,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__10__x__91979__91982__92035__92038__92041),happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__11__y__91980__91983__92036__92039__92042),Vvar__var__var__var__var__12__z__91981__91984__92037__92040__92043))),happ(happ(Vvar__3__radd__91920,happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__10__x__91979__91982__92035__92038__92041),Vvar__var__var__var__var__11__y__91980__91983__92036__92039__92042)),Vvar__var__var__var__var__12__z__91981__91984__92037__92040__92043))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__91986__91987__92044__92045__92046__92047] :
( t(Vvar__var__var__var__var__var__11__x__91986__91987__92044__92045__92046__92047,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__4__rmul__91925,Vvar__2__rI__91919),Vvar__var__var__var__var__var__11__x__91986__91987__92044__92045__92046__92047)),Vvar__var__var__var__var__var__11__x__91986__91987__92044__92045__92046__92047)) )
& ! [Vvar__var__var__var__var__var__12__x__91989__91990__92048__92049__92050__92051] :
( t(Vvar__var__var__var__var__var__12__x__91989__91990__92048__92049__92050__92051,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__4__rmul__91925,Vvar__1__rO__91918),Vvar__var__var__var__var__var__12__x__91989__91990__92048__92049__92050__92051)),Vvar__1__rO__91918)) )
& ! [Vvar__var__var__var__var__13__x__91992__91994__92052__92054__92056] :
( t(Vvar__var__var__var__var__13__x__91992__91994__92052__92054__92056,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__14__y__91993__91995__92053__92055__92057] :
( t(Vvar__var__var__var__var__14__y__91993__91995__92053__92055__92057,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__13__x__91992__91994__92052__92054__92056),Vvar__var__var__var__var__14__y__91993__91995__92053__92055__92057)),happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__14__y__91993__91995__92053__92055__92057),Vvar__var__var__var__var__13__x__91992__91994__92052__92054__92056))) ) )
& ! [Vvar__var__var__var__var__14__x__91997__92000__92058__92061__92064] :
( t(Vvar__var__var__var__var__14__x__91997__92000__92058__92061__92064,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__15__y__91998__92001__92059__92062__92065] :
( t(Vvar__var__var__var__var__15__y__91998__92001__92059__92062__92065,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__16__z__91999__92002__92060__92063__92066] :
( t(Vvar__var__var__var__var__16__z__91999__92002__92060__92063__92066,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__14__x__91997__92000__92058__92061__92064),happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__15__y__91998__92001__92059__92062__92065),Vvar__var__var__var__var__16__z__91999__92002__92060__92063__92066))),happ(happ(Vvar__4__rmul__91925,happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__14__x__91997__92000__92058__92061__92064),Vvar__var__var__var__var__15__y__91998__92001__92059__92062__92065)),Vvar__var__var__var__var__16__z__91999__92002__92060__92063__92066))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__92004__92007__92067__92070__92073__92076] :
( t(Vvar__var__var__var__var__var__15__x__92004__92007__92067__92070__92073__92076,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__var__16__y__92005__92008__92068__92071__92074__92077] :
( t(Vvar__var__var__var__var__var__16__y__92005__92008__92068__92071__92074__92077,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__var__17__z__92006__92009__92069__92072__92075__92078] :
( t(Vvar__var__var__var__var__var__17__z__92006__92009__92069__92072__92075__92078,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__4__rmul__91925,happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__var__15__x__92004__92007__92067__92070__92073__92076),Vvar__var__var__var__var__var__16__y__92005__92008__92068__92071__92074__92077)),Vvar__var__var__var__var__var__17__z__92006__92009__92069__92072__92075__92078)),happ(happ(Vvar__3__radd__91920,happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__var__15__x__92004__92007__92067__92070__92073__92076),Vvar__var__var__var__var__var__17__z__92006__92009__92069__92072__92075__92078)),happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__var__16__y__92005__92008__92068__92071__92074__92077),Vvar__var__var__var__var__var__17__z__92006__92009__92069__92072__92075__92078)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__92011__92013__92079__92081__92083__92085] :
( t(Vvar__var__var__var__var__var__16__x__92011__92013__92079__92081__92083__92085,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__var__17__y__92012__92014__92080__92082__92084__92086] :
( t(Vvar__var__var__var__var__var__17__y__92012__92014__92080__92082__92084__92086,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(Vvar__6__ropp__91935,happ(happ(Vvar__4__rmul__91925,Vvar__var__var__var__var__var__16__x__92011__92013__92079__92081__92083__92085),Vvar__var__var__var__var__var__17__y__92012__92014__92080__92082__92084__92086))),happ(happ(Vvar__4__rmul__91925,happ(Vvar__6__ropp__91935,Vvar__var__var__var__var__var__16__x__92011__92013__92079__92081__92083__92085)),Vvar__var__var__var__var__var__17__y__92012__92014__92080__92082__92084__92086))) ) )
& ! [Vvar__var__var__var__var__var__17__x__92016__92018__92087__92089__92091__92093] :
( t(Vvar__var__var__var__var__var__17__x__92016__92018__92087__92089__92091__92093,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__var__18__y__92017__92019__92088__92090__92092__92094] :
( t(Vvar__var__var__var__var__var__18__y__92017__92019__92088__92090__92092__92094,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(Vvar__6__ropp__91935,happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__var__17__x__92016__92018__92087__92089__92091__92093),Vvar__var__var__var__var__var__18__y__92017__92019__92088__92090__92092__92094))),happ(happ(Vvar__3__radd__91920,happ(Vvar__6__ropp__91935,Vvar__var__var__var__var__var__17__x__92016__92018__92087__92089__92091__92093)),happ(Vvar__6__ropp__91935,Vvar__var__var__var__var__var__18__y__92017__92019__92088__92090__92092__92094)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__92021__92023__92095__92097__92099__92101__92103] :
( t(Vvar__var__var__var__var__var__var__18__x__92021__92023__92095__92097__92099__92101__92103,Vvar__0__R__91917)
=> ! [Vvar__var__var__var__var__var__var__19__y__92022__92024__92096__92098__92100__92102__92104] :
( t(Vvar__var__var__var__var__var__var__19__y__92022__92024__92096__92098__92100__92102__92104,Vvar__0__R__91917)
=> p(happ(happ(Vvar__7__req__91938,happ(happ(Vvar__5__rsub__91930,Vvar__var__var__var__var__var__var__18__x__92021__92023__92095__92097__92099__92101__92103),Vvar__var__var__var__var__var__var__19__y__92022__92024__92096__92098__92100__92102__92104)),happ(happ(Vvar__3__radd__91920,Vvar__var__var__var__var__var__var__18__x__92021__92023__92095__92097__92099__92101__92103),happ(Vvar__6__ropp__91935,Vvar__var__var__var__var__var__var__19__y__92022__92024__92096__92098__92100__92102__92104)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544] :
( cType___24t(Vvar__0__R__110524)
=> ( c_24__type__110664___24t(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__1__req__110525)
=> ( cType___24t(Vvar__2__C__110530)
=> ( c_24__type__110714___24t(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__3__cadd__110531)
=> ( c_24__type__110764___24t(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__4__cmul__110536)
=> ( c_24__type__110806___24t(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__5__phi__110541)
=> ( c_24__type__110856___24t(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__6__cdiv__110544)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__110576__110581__110586__110591__110596__110601__110606__110611] :
( t(Vvar__var__var__var__var__var__var__var__7__a__110576__110581__110586__110591__110596__110601__110606__110611,Vvar__2__C__110530)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__110577__110582__110587__110592__110597__110602__110607__110612] :
( t(Vvar__var__var__var__var__var__var__var__8__b__110577__110582__110587__110592__110597__110602__110607__110612,Vvar__2__C__110530)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_24110919___24a9(Vvar__0__R__110524,Vvar__1__req__110525,Vvar__2__C__110530,Vvar__3__cadd__110531,Vvar__4__cmul__110536,Vvar__5__phi__110541,Vvar__6__cdiv__110544,Vvar__var__var__var__var__var__var__var__7__a__110576__110581__110586__110591__110596__110601__110606__110611,Vvar__var__var__var__var__var__var__var__8__b__110577__110582__110587__110592__110597__110602__110607__110612) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218] :
( cType___24t(Vvar__0__R__103202)
=> ( t(Vvar__1__rI__103203,Vvar__0__R__103202)
=> ( c_24__type__103304___24t(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218,Vvar__2__rmul__103204)
=> ( c_24__type__103348___24t(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218,Vvar__3__req__103209)
=> ( cType___24t(Vvar__4__Cpow__103214)
=> ( c_24__type__103384___24t(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218,Vvar__5__Cp__phi__103215)
=> ( c_24__type__103428___24t(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218,Vvar__6__rpow__103218)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__3__req__103209,Vvar__4__Cpow__103214,Vvar__5__Cp__phi__103215,Vvar__6__rpow__103218)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__103246__103248__103250__103252__103254__103256__103258__103260] :
( t(Vvar__var__var__var__var__var__var__var__7__r__103246__103248__103250__103252__103254__103256__103258__103260,Vvar__0__R__103202)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__103247__103249__103251__103253__103255__103257__103259__103261] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__103247__103249__103251__103253__103255__103257__103259__103261)
=> p(happ(happ(Vvar__3__req__103209,happ(happ(Vvar__6__rpow__103218,Vvar__var__var__var__var__var__var__var__7__r__103246__103248__103250__103252__103254__103256__103258__103260),happ(Vvar__5__Cp__phi__103215,Vvar__var__var__var__var__var__var__var__8__n__103247__103249__103251__103253__103255__103257__103259__103261))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__103202,Vvar__1__rI__103203,Vvar__2__rmul__103204,Vvar__var__var__var__var__var__var__var__7__r__103246__103248__103250__103252__103254__103256__103258__103260,Vvar__var__var__var__var__var__var__var__8__n__103247__103249__103251__103253__103255__103257__103259__103261))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447] :
( cType___24t(Vvar__0__R__92433)
=> ( c_24__type__92538___24t(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447,Vvar__1__radd__92434)
=> ( c_24__type__92568___24t(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447,Vvar__2__rmul__92439)
=> ( c_24__type__92592___24t(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447,Vvar__3__ropp__92444)
=> ( c_24__type__92622___24t(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447,Vvar__4__req__92447)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__92652___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__92433,c_24__type__92676___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447),Vvar__4__req__92447,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__92433,Vvar__0__R__92433,Vvar__4__req__92447,Vvar__4__req__92447)),Vvar__1__radd__92434)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__92709___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__92433,c_24__type__92733___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447),Vvar__4__req__92447,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__92433,Vvar__0__R__92433,Vvar__4__req__92447,Vvar__4__req__92447)),Vvar__2__rmul__92439)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__92760___24a5(Vvar__0__R__92433,Vvar__1__radd__92434,Vvar__2__rmul__92439,Vvar__3__ropp__92444,Vvar__4__req__92447),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__92433,Vvar__0__R__92433,Vvar__4__req__92447,Vvar__4__req__92447),Vvar__3__ropp__92444)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX82892] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX82892)
=> ( VX82892 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__82893] :
( cType___24t(Vvar__0__R__82893)
& ? [Vvar__1__req__82894] :
( c_24__type__75779___24t(Vvar__0__R__82893,Vvar__1__req__82894)
& ? [Vvar__2__reqb__82899] :
( c_24__type__716___24t(Vvar__0__R__82893,Vvar__2__reqb__82899)
& ! [Vvar__var__3__x__82905__82908] :
( t(Vvar__var__3__x__82905__82908,Vvar__0__R__82893)
=> ! [Vvar__var__4__y__82906__82909] :
( t(Vvar__var__4__y__82906__82909,Vvar__0__R__82893)
=> ( happ(happ(Vvar__2__reqb__82899,Vvar__var__3__x__82905__82908),Vvar__var__4__y__82906__82909) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__82894,Vvar__var__3__x__82905__82908),Vvar__var__4__y__82906__82909)) ) ) )
& VX82892 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__82893,Vvar__1__req__82894,Vvar__2__reqb__82899) ) ) )
| ? [Vvar__0__R__82911] :
( cType___24t(Vvar__0__R__82911)
& ? [Vvar__1__rO__82912] :
( t(Vvar__1__rO__82912,Vvar__0__R__82911)
& ? [Vvar__2__rI__82913] :
( t(Vvar__2__rI__82913,Vvar__0__R__82911)
& ? [Vvar__3__radd__82914] :
( c_24__type__702___24t(Vvar__0__R__82911,Vvar__3__radd__82914)
& ? [Vvar__4__rmul__82919] :
( c_24__type__702___24t(Vvar__0__R__82911,Vvar__4__rmul__82919)
& ? [Vvar__5__rsub__82924] :
( c_24__type__702___24t(Vvar__0__R__82911,Vvar__5__rsub__82924)
& ? [Vvar__6__ropp__82929] :
( c_24__type__711___24t(Vvar__0__R__82911,Vvar__6__ropp__82929)
& ? [Vvar__7__req__82932] :
( c_24__type__75779___24t(Vvar__0__R__82911,Vvar__7__req__82932)
& ? [Vvar__8__C__82937] :
( cType___24t(Vvar__8__C__82937)
& ? [Vvar__9__cO__82938] :
( t(Vvar__9__cO__82938,Vvar__8__C__82937)
& ? [Vvar__10__cI__82939] :
( t(Vvar__10__cI__82939,Vvar__8__C__82937)
& ? [Vvar__11__cadd__82940] :
( c_24__type__76704___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__11__cadd__82940)
& ? [Vvar__12__cmul__82945] :
( c_24__type__76704___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__12__cmul__82945)
& ? [Vvar__13__csub__82950] :
( c_24__type__76704___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__13__csub__82950)
& ? [Vvar__14__copp__82955] :
( c_24__type__76718___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__14__copp__82955)
& ? [Vvar__15__ceqb__82958] :
( c_24__type__76725___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__15__ceqb__82958)
& ? [Vvar__16__phi__82963] :
( c_24__type__76407___24t(Vvar__0__R__82911,Vvar__8__C__82937,Vvar__16__phi__82963)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__82911,Vvar__1__rO__82912,Vvar__2__rI__82913,Vvar__3__radd__82914,Vvar__4__rmul__82919,Vvar__5__rsub__82924,Vvar__6__ropp__82929,Vvar__7__req__82932,Vvar__8__C__82937,Vvar__9__cO__82938,Vvar__10__cI__82939,Vvar__11__cadd__82940,Vvar__12__cmul__82945,Vvar__13__csub__82950,Vvar__14__copp__82955,Vvar__15__ceqb__82958,Vvar__16__phi__82963)
& VX82892 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__82911,Vvar__1__rO__82912,Vvar__2__rI__82913,Vvar__3__radd__82914,Vvar__4__rmul__82919,Vvar__5__rsub__82924,Vvar__6__ropp__82929,Vvar__7__req__82932,Vvar__8__C__82937,Vvar__9__cO__82938,Vvar__10__cI__82939,Vvar__11__cadd__82940,Vvar__12__cmul__82945,Vvar__13__csub__82950,Vvar__14__copp__82955,Vvar__15__ceqb__82958,Vvar__16__phi__82963) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815] :
( cType___24t(Vvar__0__R__92763)
=> ( t(Vvar__1__rO__92764,Vvar__0__R__92763)
=> ( t(Vvar__2__rI__92765,Vvar__0__R__92763)
=> ( c_24__type__93159___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__3__radd__92766)
=> ( c_24__type__93372___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__4__rmul__92771)
=> ( c_24__type__93585___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__5__rsub__92776)
=> ( c_24__type__93780___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__6__ropp__92781)
=> ( c_24__type__93993___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__7__req__92784)
=> ( cType___24t(Vvar__8__C__92789)
=> ( t(Vvar__9__cO__92790,Vvar__8__C__92789)
=> ( t(Vvar__10__cI__92791,Vvar__8__C__92789)
=> ( c_24__type__94206___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__11__cadd__92792)
=> ( c_24__type__94419___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__12__cmul__92797)
=> ( c_24__type__94632___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__13__csub__92802)
=> ( c_24__type__94827___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__14__copp__92807)
=> ( c_24__type__95040___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__15__ceqb__92810)
=> ( c_24__type__95235___24t(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815,Vvar__16__phi__92815)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__92763,Vvar__1__rO__92764,Vvar__2__rI__92765,Vvar__3__radd__92766,Vvar__4__rmul__92771,Vvar__5__rsub__92776,Vvar__6__ropp__92781,Vvar__7__req__92784,Vvar__8__C__92789,Vvar__9__cO__92790,Vvar__10__cI__92791,Vvar__11__cadd__92792,Vvar__12__cmul__92797,Vvar__13__csub__92802,Vvar__14__copp__92807,Vvar__15__ceqb__92810,Vvar__16__phi__92815)
=> ( p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,Vvar__9__cO__92790)),Vvar__1__rO__92764))
& p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,Vvar__10__cI__92791)),Vvar__2__rI__92765))
& ! [Vvar__var__var__var__var__var__var__19__x__92877__92879__92901__92903__92905__92907__92909] :
( t(Vvar__var__var__var__var__var__var__19__x__92877__92879__92901__92903__92905__92907__92909,Vvar__8__C__92789)
=> ! [Vvar__var__var__var__var__var__var__20__y__92878__92880__92902__92904__92906__92908__92910] :
( t(Vvar__var__var__var__var__var__var__20__y__92878__92880__92902__92904__92906__92908__92910,Vvar__8__C__92789)
=> p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,happ(happ(Vvar__11__cadd__92792,Vvar__var__var__var__var__var__var__19__x__92877__92879__92901__92903__92905__92907__92909),Vvar__var__var__var__var__var__var__20__y__92878__92880__92902__92904__92906__92908__92910))),happ(happ(Vvar__3__radd__92766,happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__19__x__92877__92879__92901__92903__92905__92907__92909)),happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__20__y__92878__92880__92902__92904__92906__92908__92910)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__92882__92884__92911__92913__92915__92917__92919] :
( t(Vvar__var__var__var__var__var__var__20__x__92882__92884__92911__92913__92915__92917__92919,Vvar__8__C__92789)
=> ! [Vvar__var__var__var__var__var__var__21__y__92883__92885__92912__92914__92916__92918__92920] :
( t(Vvar__var__var__var__var__var__var__21__y__92883__92885__92912__92914__92916__92918__92920,Vvar__8__C__92789)
=> p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,happ(happ(Vvar__13__csub__92802,Vvar__var__var__var__var__var__var__20__x__92882__92884__92911__92913__92915__92917__92919),Vvar__var__var__var__var__var__var__21__y__92883__92885__92912__92914__92916__92918__92920))),happ(happ(Vvar__5__rsub__92776,happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__20__x__92882__92884__92911__92913__92915__92917__92919)),happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__21__y__92883__92885__92912__92914__92916__92918__92920)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__92887__92889__92921__92923__92925__92927__92929] :
( t(Vvar__var__var__var__var__var__var__21__x__92887__92889__92921__92923__92925__92927__92929,Vvar__8__C__92789)
=> ! [Vvar__var__var__var__var__var__var__22__y__92888__92890__92922__92924__92926__92928__92930] :
( t(Vvar__var__var__var__var__var__var__22__y__92888__92890__92922__92924__92926__92928__92930,Vvar__8__C__92789)
=> p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,happ(happ(Vvar__12__cmul__92797,Vvar__var__var__var__var__var__var__21__x__92887__92889__92921__92923__92925__92927__92929),Vvar__var__var__var__var__var__var__22__y__92888__92890__92922__92924__92926__92928__92930))),happ(happ(Vvar__4__rmul__92771,happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__21__x__92887__92889__92921__92923__92925__92927__92929)),happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__22__y__92888__92890__92922__92924__92926__92928__92930)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__92892__92893__92931__92932__92933__92934__92935] :
( t(Vvar__var__var__var__var__var__var__22__x__92892__92893__92931__92932__92933__92934__92935,Vvar__8__C__92789)
=> p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,happ(Vvar__14__copp__92807,Vvar__var__var__var__var__var__var__22__x__92892__92893__92931__92932__92933__92934__92935))),happ(Vvar__6__ropp__92781,happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__var__22__x__92892__92893__92931__92932__92933__92934__92935)))) )
& ! [Vvar__var__var__var__var__var__23__x__92895__92898__92936__92939__92942__92945] :
( t(Vvar__var__var__var__var__var__23__x__92895__92898__92936__92939__92942__92945,Vvar__8__C__92789)
=> ! [Vvar__var__var__var__var__var__24__y__92896__92899__92937__92940__92943__92946] :
( t(Vvar__var__var__var__var__var__24__y__92896__92899__92937__92940__92943__92946,Vvar__8__C__92789)
=> ( happ(happ(Vvar__15__ceqb__92810,Vvar__var__var__var__var__var__23__x__92895__92898__92936__92939__92942__92945),Vvar__var__var__var__var__var__24__y__92896__92899__92937__92940__92943__92946) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__92784,happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__23__x__92895__92898__92936__92939__92942__92945)),happ(Vvar__16__phi__92815,Vvar__var__var__var__var__var__24__y__92896__92899__92937__92940__92943__92946))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513] :
( cType___24t(Vvar__0__R__102492)
=> ( t(Vvar__1__rO__102493,Vvar__0__R__102492)
=> ( t(Vvar__2__rI__102494,Vvar__0__R__102492)
=> ( c_24__type__102716___24t(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513,Vvar__3__radd__102495)
=> ( c_24__type__102779___24t(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513,Vvar__4__rmul__102500)
=> ( c_24__type__102842___24t(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513,Vvar__5__rsub__102505)
=> ( c_24__type__102896___24t(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513,Vvar__6__ropp__102510)
=> ( c_24__type__102959___24t(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513,Vvar__7__req__102513)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__102492,Vvar__1__rO__102493,Vvar__2__rI__102494,Vvar__3__radd__102495,Vvar__4__rmul__102500,Vvar__5__rsub__102505,Vvar__6__ropp__102510,Vvar__7__req__102513)
=> ( ! [Vvar__var__var__var__var__var__8__x__102546__102547__102590__102591__102592__102593] :
( t(Vvar__var__var__var__var__var__8__x__102546__102547__102590__102591__102592__102593,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__3__radd__102495,Vvar__1__rO__102493),Vvar__var__var__var__var__var__8__x__102546__102547__102590__102591__102592__102593)),Vvar__var__var__var__var__var__8__x__102546__102547__102590__102591__102592__102593)) )
& ! [Vvar__var__var__var__var__9__x__102549__102551__102594__102596__102598] :
( t(Vvar__var__var__var__var__9__x__102549__102551__102594__102596__102598,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__10__y__102550__102552__102595__102597__102599] :
( t(Vvar__var__var__var__var__10__y__102550__102552__102595__102597__102599,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__9__x__102549__102551__102594__102596__102598),Vvar__var__var__var__var__10__y__102550__102552__102595__102597__102599)),happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__10__y__102550__102552__102595__102597__102599),Vvar__var__var__var__var__9__x__102549__102551__102594__102596__102598))) ) )
& ! [Vvar__var__var__var__var__10__x__102554__102557__102600__102603__102606] :
( t(Vvar__var__var__var__var__10__x__102554__102557__102600__102603__102606,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__11__y__102555__102558__102601__102604__102607] :
( t(Vvar__var__var__var__var__11__y__102555__102558__102601__102604__102607,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__12__z__102556__102559__102602__102605__102608] :
( t(Vvar__var__var__var__var__12__z__102556__102559__102602__102605__102608,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__10__x__102554__102557__102600__102603__102606),happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__11__y__102555__102558__102601__102604__102607),Vvar__var__var__var__var__12__z__102556__102559__102602__102605__102608))),happ(happ(Vvar__3__radd__102495,happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__10__x__102554__102557__102600__102603__102606),Vvar__var__var__var__var__11__y__102555__102558__102601__102604__102607)),Vvar__var__var__var__var__12__z__102556__102559__102602__102605__102608))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__102561__102562__102609__102610__102611__102612] :
( t(Vvar__var__var__var__var__var__11__x__102561__102562__102609__102610__102611__102612,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__4__rmul__102500,Vvar__2__rI__102494),Vvar__var__var__var__var__var__11__x__102561__102562__102609__102610__102611__102612)),Vvar__var__var__var__var__var__11__x__102561__102562__102609__102610__102611__102612)) )
& ! [Vvar__var__var__var__var__12__x__102564__102566__102613__102615__102617] :
( t(Vvar__var__var__var__var__12__x__102564__102566__102613__102615__102617,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__13__y__102565__102567__102614__102616__102618] :
( t(Vvar__var__var__var__var__13__y__102565__102567__102614__102616__102618,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__12__x__102564__102566__102613__102615__102617),Vvar__var__var__var__var__13__y__102565__102567__102614__102616__102618)),happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__13__y__102565__102567__102614__102616__102618),Vvar__var__var__var__var__12__x__102564__102566__102613__102615__102617))) ) )
& ! [Vvar__var__var__var__var__13__x__102569__102572__102619__102622__102625] :
( t(Vvar__var__var__var__var__13__x__102569__102572__102619__102622__102625,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__14__y__102570__102573__102620__102623__102626] :
( t(Vvar__var__var__var__var__14__y__102570__102573__102620__102623__102626,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__15__z__102571__102574__102621__102624__102627] :
( t(Vvar__var__var__var__var__15__z__102571__102574__102621__102624__102627,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__13__x__102569__102572__102619__102622__102625),happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__14__y__102570__102573__102620__102623__102626),Vvar__var__var__var__var__15__z__102571__102574__102621__102624__102627))),happ(happ(Vvar__4__rmul__102500,happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__13__x__102569__102572__102619__102622__102625),Vvar__var__var__var__var__14__y__102570__102573__102620__102623__102626)),Vvar__var__var__var__var__15__z__102571__102574__102621__102624__102627))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__102576__102579__102628__102631__102634__102637] :
( t(Vvar__var__var__var__var__var__14__x__102576__102579__102628__102631__102634__102637,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__var__15__y__102577__102580__102629__102632__102635__102638] :
( t(Vvar__var__var__var__var__var__15__y__102577__102580__102629__102632__102635__102638,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__var__16__z__102578__102581__102630__102633__102636__102639] :
( t(Vvar__var__var__var__var__var__16__z__102578__102581__102630__102633__102636__102639,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__4__rmul__102500,happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__var__14__x__102576__102579__102628__102631__102634__102637),Vvar__var__var__var__var__var__15__y__102577__102580__102629__102632__102635__102638)),Vvar__var__var__var__var__var__16__z__102578__102581__102630__102633__102636__102639)),happ(happ(Vvar__3__radd__102495,happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__var__14__x__102576__102579__102628__102631__102634__102637),Vvar__var__var__var__var__var__16__z__102578__102581__102630__102633__102636__102639)),happ(happ(Vvar__4__rmul__102500,Vvar__var__var__var__var__var__15__y__102577__102580__102629__102632__102635__102638),Vvar__var__var__var__var__var__16__z__102578__102581__102630__102633__102636__102639)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__102583__102585__102640__102642__102644__102646__102648] :
( t(Vvar__var__var__var__var__var__var__15__x__102583__102585__102640__102642__102644__102646__102648,Vvar__0__R__102492)
=> ! [Vvar__var__var__var__var__var__var__16__y__102584__102586__102641__102643__102645__102647__102649] :
( t(Vvar__var__var__var__var__var__var__16__y__102584__102586__102641__102643__102645__102647__102649,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__5__rsub__102505,Vvar__var__var__var__var__var__var__15__x__102583__102585__102640__102642__102644__102646__102648),Vvar__var__var__var__var__var__var__16__y__102584__102586__102641__102643__102645__102647__102649)),happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__var__var__15__x__102583__102585__102640__102642__102644__102646__102648),happ(Vvar__6__ropp__102510,Vvar__var__var__var__var__var__var__16__y__102584__102586__102641__102643__102645__102647__102649)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__102588__102589__102650__102651__102652__102653__102654] :
( t(Vvar__var__var__var__var__var__var__16__x__102588__102589__102650__102651__102652__102653__102654,Vvar__0__R__102492)
=> p(happ(happ(Vvar__7__req__102513,happ(happ(Vvar__3__radd__102495,Vvar__var__var__var__var__var__var__16__x__102588__102589__102650__102651__102652__102653__102654),happ(Vvar__6__ropp__102510,Vvar__var__var__var__var__var__var__16__x__102588__102589__102650__102651__102652__102653__102654))),Vvar__1__rO__102493)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360] :
( cType___24t(Vvar__0__R__77324)
=> ( t(Vvar__1__rO__77325,Vvar__0__R__77324)
=> ( t(Vvar__2__rI__77326,Vvar__0__R__77324)
=> ( c_24__type__77577___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__3__radd__77327)
=> ( c_24__type__77702___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__4__rmul__77332)
=> ( c_24__type__77827___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__5__req__77337)
=> ( cType___24t(Vvar__6__C__77342)
=> ( t(Vvar__7__cO__77343,Vvar__6__C__77342)
=> ( t(Vvar__8__cI__77344,Vvar__6__C__77342)
=> ( c_24__type__77952___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__9__cadd__77345)
=> ( c_24__type__78077___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__10__cmul__77350)
=> ( c_24__type__78202___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__11__ceqb__77355)
=> ( c_24__type__78313___24t(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360,Vvar__12__phi__77360)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__77324,Vvar__1__rO__77325,Vvar__2__rI__77326,Vvar__3__radd__77327,Vvar__4__rmul__77332,Vvar__5__req__77337,Vvar__6__C__77342,Vvar__7__cO__77343,Vvar__8__cI__77344,Vvar__9__cadd__77345,Vvar__10__cmul__77350,Vvar__11__ceqb__77355,Vvar__12__phi__77360)
=> ( p(happ(happ(Vvar__5__req__77337,happ(Vvar__12__phi__77360,Vvar__7__cO__77343)),Vvar__1__rO__77325))
& p(happ(happ(Vvar__5__req__77337,happ(Vvar__12__phi__77360,Vvar__8__cI__77344)),Vvar__2__rI__77326))
& ! [Vvar__var__var__var__var__var__var__15__x__77406__77408__77422__77424__77426__77428__77430] :
( t(Vvar__var__var__var__var__var__var__15__x__77406__77408__77422__77424__77426__77428__77430,Vvar__6__C__77342)
=> ! [Vvar__var__var__var__var__var__var__16__y__77407__77409__77423__77425__77427__77429__77431] :
( t(Vvar__var__var__var__var__var__var__16__y__77407__77409__77423__77425__77427__77429__77431,Vvar__6__C__77342)
=> p(happ(happ(Vvar__5__req__77337,happ(Vvar__12__phi__77360,happ(happ(Vvar__9__cadd__77345,Vvar__var__var__var__var__var__var__15__x__77406__77408__77422__77424__77426__77428__77430),Vvar__var__var__var__var__var__var__16__y__77407__77409__77423__77425__77427__77429__77431))),happ(happ(Vvar__3__radd__77327,happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__var__15__x__77406__77408__77422__77424__77426__77428__77430)),happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__var__16__y__77407__77409__77423__77425__77427__77429__77431)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__77411__77413__77432__77434__77436__77438__77440] :
( t(Vvar__var__var__var__var__var__var__16__x__77411__77413__77432__77434__77436__77438__77440,Vvar__6__C__77342)
=> ! [Vvar__var__var__var__var__var__var__17__y__77412__77414__77433__77435__77437__77439__77441] :
( t(Vvar__var__var__var__var__var__var__17__y__77412__77414__77433__77435__77437__77439__77441,Vvar__6__C__77342)
=> p(happ(happ(Vvar__5__req__77337,happ(Vvar__12__phi__77360,happ(happ(Vvar__10__cmul__77350,Vvar__var__var__var__var__var__var__16__x__77411__77413__77432__77434__77436__77438__77440),Vvar__var__var__var__var__var__var__17__y__77412__77414__77433__77435__77437__77439__77441))),happ(happ(Vvar__4__rmul__77332,happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__var__16__x__77411__77413__77432__77434__77436__77438__77440)),happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__var__17__y__77412__77414__77433__77435__77437__77439__77441)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__77416__77419__77442__77445__77448__77451] :
( t(Vvar__var__var__var__var__var__17__x__77416__77419__77442__77445__77448__77451,Vvar__6__C__77342)
=> ! [Vvar__var__var__var__var__var__18__y__77417__77420__77443__77446__77449__77452] :
( t(Vvar__var__var__var__var__var__18__y__77417__77420__77443__77446__77449__77452,Vvar__6__C__77342)
=> ( happ(happ(Vvar__11__ceqb__77355,Vvar__var__var__var__var__var__17__x__77416__77419__77442__77445__77448__77451),Vvar__var__var__var__var__var__18__y__77417__77420__77443__77446__77449__77452) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__77337,happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__17__x__77416__77419__77442__77445__77448__77451)),happ(Vvar__12__phi__77360,Vvar__var__var__var__var__var__18__y__77417__77420__77443__77446__77449__77452))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__77035,Vvar__1__rO__77036,Vvar__2__rI__77037,Vvar__3__radd__77038,Vvar__4__rmul__77043,Vvar__5__req__77048] :
( cType___24t(Vvar__0__R__77035)
=> ( t(Vvar__1__rO__77036,Vvar__0__R__77035)
=> ( t(Vvar__2__rI__77037,Vvar__0__R__77035)
=> ( c_24__type__77203___24t(Vvar__0__R__77035,Vvar__1__rO__77036,Vvar__2__rI__77037,Vvar__3__radd__77038,Vvar__4__rmul__77043,Vvar__5__req__77048,Vvar__3__radd__77038)
=> ( c_24__type__77242___24t(Vvar__0__R__77035,Vvar__1__rO__77036,Vvar__2__rI__77037,Vvar__3__radd__77038,Vvar__4__rmul__77043,Vvar__5__req__77048,Vvar__4__rmul__77043)
=> ( c_24__type__77281___24t(Vvar__0__R__77035,Vvar__1__rO__77036,Vvar__2__rI__77037,Vvar__3__radd__77038,Vvar__4__rmul__77043,Vvar__5__req__77048,Vvar__5__req__77048)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__77035,Vvar__1__rO__77036,Vvar__2__rI__77037,Vvar__3__radd__77038,Vvar__4__rmul__77043,Vvar__5__req__77048)
=> ( ! [Vvar__var__var__var__var__var__6__n__77073__77074__77112__77113__77114__77115] :
( t(Vvar__var__var__var__var__var__6__n__77073__77074__77112__77113__77114__77115,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__3__radd__77038,Vvar__1__rO__77036),Vvar__var__var__var__var__var__6__n__77073__77074__77112__77113__77114__77115)),Vvar__var__var__var__var__var__6__n__77073__77074__77112__77113__77114__77115)) )
& ! [Vvar__var__var__var__var__7__n__77076__77078__77116__77118__77120] :
( t(Vvar__var__var__var__var__7__n__77076__77078__77116__77118__77120,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__8__m__77077__77079__77117__77119__77121] :
( t(Vvar__var__var__var__var__8__m__77077__77079__77117__77119__77121,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__7__n__77076__77078__77116__77118__77120),Vvar__var__var__var__var__8__m__77077__77079__77117__77119__77121)),happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__8__m__77077__77079__77117__77119__77121),Vvar__var__var__var__var__7__n__77076__77078__77116__77118__77120))) ) )
& ! [Vvar__var__var__var__var__8__n__77081__77084__77122__77125__77128] :
( t(Vvar__var__var__var__var__8__n__77081__77084__77122__77125__77128,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__9__m__77082__77085__77123__77126__77129] :
( t(Vvar__var__var__var__var__9__m__77082__77085__77123__77126__77129,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__10__p__77083__77086__77124__77127__77130] :
( t(Vvar__var__var__var__var__10__p__77083__77086__77124__77127__77130,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__8__n__77081__77084__77122__77125__77128),happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__9__m__77082__77085__77123__77126__77129),Vvar__var__var__var__var__10__p__77083__77086__77124__77127__77130))),happ(happ(Vvar__3__radd__77038,happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__8__n__77081__77084__77122__77125__77128),Vvar__var__var__var__var__9__m__77082__77085__77123__77126__77129)),Vvar__var__var__var__var__10__p__77083__77086__77124__77127__77130))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__77088__77089__77131__77132__77133__77134] :
( t(Vvar__var__var__var__var__var__9__n__77088__77089__77131__77132__77133__77134,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__4__rmul__77043,Vvar__2__rI__77037),Vvar__var__var__var__var__var__9__n__77088__77089__77131__77132__77133__77134)),Vvar__var__var__var__var__var__9__n__77088__77089__77131__77132__77133__77134)) )
& ! [Vvar__var__var__var__var__var__10__n__77091__77092__77135__77136__77137__77138] :
( t(Vvar__var__var__var__var__var__10__n__77091__77092__77135__77136__77137__77138,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__4__rmul__77043,Vvar__1__rO__77036),Vvar__var__var__var__var__var__10__n__77091__77092__77135__77136__77137__77138)),Vvar__1__rO__77036)) )
& ! [Vvar__var__var__var__var__11__n__77094__77096__77139__77141__77143] :
( t(Vvar__var__var__var__var__11__n__77094__77096__77139__77141__77143,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__12__m__77095__77097__77140__77142__77144] :
( t(Vvar__var__var__var__var__12__m__77095__77097__77140__77142__77144,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__11__n__77094__77096__77139__77141__77143),Vvar__var__var__var__var__12__m__77095__77097__77140__77142__77144)),happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__12__m__77095__77097__77140__77142__77144),Vvar__var__var__var__var__11__n__77094__77096__77139__77141__77143))) ) )
& ! [Vvar__var__var__var__var__12__n__77099__77102__77145__77148__77151] :
( t(Vvar__var__var__var__var__12__n__77099__77102__77145__77148__77151,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__13__m__77100__77103__77146__77149__77152] :
( t(Vvar__var__var__var__var__13__m__77100__77103__77146__77149__77152,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__14__p__77101__77104__77147__77150__77153] :
( t(Vvar__var__var__var__var__14__p__77101__77104__77147__77150__77153,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__12__n__77099__77102__77145__77148__77151),happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__13__m__77100__77103__77146__77149__77152),Vvar__var__var__var__var__14__p__77101__77104__77147__77150__77153))),happ(happ(Vvar__4__rmul__77043,happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__12__n__77099__77102__77145__77148__77151),Vvar__var__var__var__var__13__m__77100__77103__77146__77149__77152)),Vvar__var__var__var__var__14__p__77101__77104__77147__77150__77153))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__77106__77109__77154__77157__77160__77163] :
( t(Vvar__var__var__var__var__var__13__n__77106__77109__77154__77157__77160__77163,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__var__14__m__77107__77110__77155__77158__77161__77164] :
( t(Vvar__var__var__var__var__var__14__m__77107__77110__77155__77158__77161__77164,Vvar__0__R__77035)
=> ! [Vvar__var__var__var__var__var__15__p__77108__77111__77156__77159__77162__77165] :
( t(Vvar__var__var__var__var__var__15__p__77108__77111__77156__77159__77162__77165,Vvar__0__R__77035)
=> p(happ(happ(Vvar__5__req__77048,happ(happ(Vvar__4__rmul__77043,happ(happ(Vvar__3__radd__77038,Vvar__var__var__var__var__var__13__n__77106__77109__77154__77157__77160__77163),Vvar__var__var__var__var__var__14__m__77107__77110__77155__77158__77161__77164)),Vvar__var__var__var__var__var__15__p__77108__77111__77156__77159__77162__77165)),happ(happ(Vvar__3__radd__77038,happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__var__13__n__77106__77109__77154__77157__77160__77163),Vvar__var__var__var__var__var__15__p__77108__77111__77156__77159__77162__77165)),happ(happ(Vvar__4__rmul__77043,Vvar__var__var__var__var__var__14__m__77107__77110__77155__77158__77161__77164),Vvar__var__var__var__var__var__15__p__77108__77111__77156__77159__77162__77165)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__110430,Vvar__1__copp__110431,Vvar__2__ceqb__110434,Vvar__3__get__sign__110439] :
( cType___24t(Vvar__0__C__110430)
=> ( c_24__type__110486___24t(Vvar__0__C__110430,Vvar__1__copp__110431,Vvar__2__ceqb__110434,Vvar__3__get__sign__110439,Vvar__1__copp__110431)
=> ( c_24__type__110505___24t(Vvar__0__C__110430,Vvar__1__copp__110431,Vvar__2__ceqb__110434,Vvar__3__get__sign__110439,Vvar__2__ceqb__110434)
=> ( c_24__type__110519___24t(Vvar__0__C__110430,Vvar__1__copp__110431,Vvar__2__ceqb__110434,Vvar__3__get__sign__110439,Vvar__3__get__sign__110439)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__110430,Vvar__1__copp__110431,Vvar__2__ceqb__110434,Vvar__3__get__sign__110439)
=> ( ! [Vvar__var__var__var__var__var__4__c__110456__110459__110462__110465__110468__110471] :
( t(Vvar__var__var__var__var__var__4__c__110456__110459__110462__110465__110468__110471,Vvar__0__C__110430)
=> ! [Vvar__var__var__var__var__var__5__c_27__110457__110460__110463__110466__110469__110472] :
( t(Vvar__var__var__var__var__var__5__c_27__110457__110460__110463__110466__110469__110472,Vvar__0__C__110430)
=> ( happ(Vvar__3__get__sign__110439,Vvar__var__var__var__var__var__4__c__110456__110459__110462__110465__110468__110471) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__110430,Vvar__var__var__var__var__var__5__c_27__110457__110460__110463__110466__110469__110472)
=> happ(happ(Vvar__2__ceqb__110434,Vvar__var__var__var__var__var__4__c__110456__110459__110462__110465__110468__110471),happ(Vvar__1__copp__110431,Vvar__var__var__var__var__var__5__c_27__110457__110460__110463__110466__110469__110472)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990] :
( cType___24t(Vvar__0__R__102979)
=> ( c_24__type__103065___24t(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990,Vvar__1__radd__102980)
=> ( c_24__type__103088___24t(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990,Vvar__2__rmul__102985)
=> ( c_24__type__103111___24t(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990,Vvar__3__req__102990)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__103134___24a4(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__102979,c_24__type__103152___24a4(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990),Vvar__3__req__102990,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__102979,Vvar__0__R__102979,Vvar__3__req__102990,Vvar__3__req__102990)),Vvar__1__radd__102980)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__103178___24a4(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__102979,c_24__type__103196___24a4(Vvar__0__R__102979,Vvar__1__radd__102980,Vvar__2__rmul__102985,Vvar__3__req__102990),Vvar__3__req__102990,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__102979,Vvar__0__R__102979,Vvar__3__req__102990,Vvar__3__req__102990)),Vvar__2__rmul__102985)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX104790] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX104790)
=> ( VX104790 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX104790 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_LF.Basics.NatPlayground.nat',axiom,
! [VX111682] :
( cLF_2eBasics_2eNatPlayground_2enat___24t(VX111682)
=> ( VX111682 = cLF_2eBasics_2eNatPlayground_2eO
| ? [Vvar__0__n__111683] :
( cLF_2eBasics_2eNatPlayground_2enat___24t(Vvar__0__n__111683)
& VX111682 = cLF_2eBasics_2eNatPlayground_2eS___24a1(Vvar__0__n__111683) ) ) ) ).
fof('$_inversion_LF.Basics.NatPlayground.nat\'',axiom,
! [VX111687] :
( cLF_2eBasics_2eNatPlayground_2enat_27___24t(VX111687)
=> ( VX111687 = cLF_2eBasics_2eNatPlayground_2estop
| ? [Vvar__0__foo__111688] :
( cLF_2eBasics_2eNatPlayground_2enat_27___24t(Vvar__0__foo__111688)
& VX111687 = cLF_2eBasics_2eNatPlayground_2etick___24a1(Vvar__0__foo__111688) ) ) ) ).
fof('$_inversion_LF.Basics.bin',axiom,
! [VX104000] :
( cLF_2eBasics_2ebin___24t(VX104000)
=> ( VX104000 = cLF_2eBasics_2eZ
| ? [Vvar__0__n__104001] :
( cLF_2eBasics_2ebin___24t(Vvar__0__n__104001)
& VX104000 = cLF_2eBasics_2eA___24a1(Vvar__0__n__104001) )
| ? [Vvar__0__n__104002] :
( cLF_2eBasics_2ebin___24t(Vvar__0__n__104002)
& VX104000 = cLF_2eBasics_2eB___24a1(Vvar__0__n__104002) ) ) ) ).
fof('$_inversion_LF.Basics.bit',axiom,
! [VX82290] :
( cLF_2eBasics_2ebit___24t(VX82290)
=> ( VX82290 = cLF_2eBasics_2eB0
| VX82290 = cLF_2eBasics_2eB1 ) ) ).
fof('$_inversion_LF.Basics.bool',axiom,
! [VX66856] :
( cLF_2eBasics_2ebool___24t(VX66856)
=> ( VX66856 = cLF_2eBasics_2etrue
| VX66856 = cLF_2eBasics_2efalse ) ) ).
fof('$_inversion_LF.Basics.color',axiom,
! [VX82279] :
( cLF_2eBasics_2ecolor___24t(VX82279)
=> ( VX82279 = cLF_2eBasics_2eblack
| VX82279 = cLF_2eBasics_2ewhite
| ? [Vvar__0__p__82280] :
( cLF_2eBasics_2ergb___24t(Vvar__0__p__82280)
& VX82279 = cLF_2eBasics_2eprimary___24a1(Vvar__0__p__82280) ) ) ) ).
fof('$_inversion_LF.Basics.day',axiom,
! [VX103999] :
( cLF_2eBasics_2eday___24t(VX103999)
=> ( VX103999 = cLF_2eBasics_2emonday
| VX103999 = cLF_2eBasics_2etuesday
| VX103999 = cLF_2eBasics_2ewednesday
| VX103999 = cLF_2eBasics_2ethursday
| VX103999 = cLF_2eBasics_2efriday
| VX103999 = cLF_2eBasics_2esaturday
| VX103999 = cLF_2eBasics_2esunday ) ) ).
fof('$_inversion_LF.Basics.nybble',axiom,
! [VX82291] :
( cLF_2eBasics_2enybble___24t(VX82291)
=> ? [Vvar__0__b0__82292] :
( cLF_2eBasics_2ebit___24t(Vvar__0__b0__82292)
& ? [Vvar__1__b1__82293] :
( cLF_2eBasics_2ebit___24t(Vvar__1__b1__82293)
& ? [Vvar__2__b2__82294] :
( cLF_2eBasics_2ebit___24t(Vvar__2__b2__82294)
& ? [Vvar__3__b3__82295] :
( cLF_2eBasics_2ebit___24t(Vvar__3__b3__82295)
& VX82291 = cLF_2eBasics_2ebits___24a4(Vvar__0__b0__82292,Vvar__1__b1__82293,Vvar__2__b2__82294,Vvar__3__b3__82295) ) ) ) ) ) ).
fof('$_inversion_LF.Basics.rgb',axiom,
! [VX82278] :
( cLF_2eBasics_2ergb___24t(VX82278)
=> ( VX82278 = cLF_2eBasics_2ered
| VX82278 = cLF_2eBasics_2egreen
| VX82278 = cLF_2eBasics_2eblue ) ) ).
fof('$_inversion_LF.Lists.NatList.natlist',axiom,
! [VX40] :
( cLF_2eLists_2eNatList_2enatlist___24t(VX40)
=> ( VX40 = cLF_2eLists_2eNatList_2enil
| ? [Vvar__0__n__41] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__41)
& ? [Vvar__1__l__42] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vvar__1__l__42)
& VX40 = cLF_2eLists_2eNatList_2econs___24a2(Vvar__0__n__41,Vvar__1__l__42) ) ) ) ) ).
fof('$_inversion_LF.Lists.NatList.natoption',axiom,
! [VX66747] :
( cLF_2eLists_2eNatList_2enatoption___24t(VX66747)
=> ( ? [Vvar__0__n__66748] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__66748)
& VX66747 = cLF_2eLists_2eNatList_2eSome___24a1(Vvar__0__n__66748) )
| VX66747 = cLF_2eLists_2eNatList_2eNone ) ) ).
fof('$_inversion_LF.Lists.NatList.natprod',axiom,
! [VX103986] :
( cLF_2eLists_2eNatList_2enatprod___24t(VX103986)
=> ? [Vvar__0__n1__103987] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__103987)
& ? [Vvar__1__n2__103988] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__103988)
& VX103986 = cLF_2eLists_2eNatList_2epair___24a2(Vvar__0__n1__103987,Vvar__1__n2__103988) ) ) ) ).
fof('$_inversion_LF.Lists.PartialMap.partial_map',axiom,
! [VX82450] :
( cLF_2eLists_2ePartialMap_2epartial__map___24t(VX82450)
=> ( VX82450 = cLF_2eLists_2ePartialMap_2eempty
| ? [Vvar__0__i__82451] :
( cLF_2eLists_2eid___24t(Vvar__0__i__82451)
& ? [Vvar__1__v__82452] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__v__82452)
& ? [Vvar__2__m__82453] :
( cLF_2eLists_2ePartialMap_2epartial__map___24t(Vvar__2__m__82453)
& VX82450 = cLF_2eLists_2ePartialMap_2erecord___24a3(Vvar__0__i__82451,Vvar__1__v__82452,Vvar__2__m__82453) ) ) ) ) ) ).
fof('$_inversion_LF.Lists.baz',axiom,
! [VX82357] :
( cLF_2eLists_2ebaz___24t(VX82357)
=> ( ? [Vvar__0__x__82358] :
( cLF_2eLists_2ebaz___24t(Vvar__0__x__82358)
& VX82357 = cLF_2eLists_2eBaz1___24a1(Vvar__0__x__82358) )
| ? [Vvar__0__y__82359] :
( cLF_2eLists_2ebaz___24t(Vvar__0__y__82359)
& ? [Vvar__1__b__82360] :
( cLF_2eBasics_2ebool___24t(Vvar__1__b__82360)
& VX82357 = cLF_2eLists_2eBaz2___24a2(Vvar__0__y__82359,Vvar__1__b__82360) ) ) ) ) ).
fof('$_inversion_LF.Lists.id',axiom,
! [VX82346] :
( cLF_2eLists_2eid___24t(VX82346)
=> ? [Vvar__0__n__82347] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__82347)
& VX82346 = cLF_2eLists_2eId___24a1(Vvar__0__n__82347) ) ) ).
fof('$_inversion_Poly.MumbleGrumble.grumble',axiom,
! [Vvar__0__X__111584,VX111585] :
( cType___24t(Vvar__0__X__111584)
=> ( cPoly_2eMumbleGrumble_2egrumble___24t(Vvar__0__X__111584,VX111585)
=> ( ? [Vvar__1__m__111587] :
( cPoly_2eMumbleGrumble_2emumble___24t(Vvar__1__m__111587)
& VX111585 = cPoly_2eMumbleGrumble_2ed___24a2(Vvar__0__X__111584,Vvar__1__m__111587) )
| ? [Vvar__1__x__111589] :
( t(Vvar__1__x__111589,Vvar__0__X__111584)
& VX111585 = cPoly_2eMumbleGrumble_2ee___24a2(Vvar__0__X__111584,Vvar__1__x__111589) ) ) ) ) ).
fof('$_inversion_Poly.MumbleGrumble.mumble',axiom,
! [VX111573] :
( cPoly_2eMumbleGrumble_2emumble___24t(VX111573)
=> ( VX111573 = cPoly_2eMumbleGrumble_2ea
| ? [Vvar__0__x__111574] :
( cPoly_2eMumbleGrumble_2emumble___24t(Vvar__0__x__111574)
& ? [Vvar__1__y__111575] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__y__111575)
& VX111573 = cPoly_2eMumbleGrumble_2eb___24a2(Vvar__0__x__111574,Vvar__1__y__111575) ) )
| VX111573 = cPoly_2eMumbleGrumble_2ec ) ) ).
fof('$_inversion_Poly.OptionPlayground.option',axiom,
! [Vvar__0__X__153804,VX153805] :
( cType___24t(Vvar__0__X__153804)
=> ( cPoly_2eOptionPlayground_2eoption___24t(Vvar__0__X__153804,VX153805)
=> ( ? [Vvar__1__x__153807] :
( t(Vvar__1__x__153807,Vvar__0__X__153804)
& VX153805 = cPoly_2eOptionPlayground_2eSome___24a2(Vvar__0__X__153804,Vvar__1__x__153807) )
| VX153805 = cPoly_2eOptionPlayground_2eNone___24a1(Vvar__0__X__153804) ) ) ) ).
fof('$_inversion_Poly.boollist',axiom,
! [VX82535] :
( cPoly_2eboollist___24t(VX82535)
=> ( VX82535 = cPoly_2ebool__nil
| ? [Vvar__0__b__82536] :
( cLF_2eBasics_2ebool___24t(Vvar__0__b__82536)
& ? [Vvar__1__l__82537] :
( cPoly_2eboollist___24t(Vvar__1__l__82537)
& VX82535 = cPoly_2ebool__cons___24a2(Vvar__0__b__82536,Vvar__1__l__82537) ) ) ) ) ).
fof('$_inversion_Poly.list',axiom,
! [Vvar__0__X__146,VX147] :
( cType___24t(Vvar__0__X__146)
=> ( cPoly_2elist___24t(Vvar__0__X__146,VX147)
=> ( VX147 = cPoly_2enil___24a1(Vvar__0__X__146)
| ? [Vvar__1__x__150] :
( t(Vvar__1__x__150,Vvar__0__X__146)
& ? [Vvar__2__l__151] :
( cPoly_2elist___24t(Vvar__0__X__146,Vvar__2__l__151)
& VX147 = cPoly_2econs___24a3(Vvar__0__X__146,Vvar__1__x__150,Vvar__2__l__151) ) ) ) ) ) ).
fof('$_inversion_Poly.list\'',axiom,
! [Vvar__0__X__111913,VX111914] :
( cType___24t(Vvar__0__X__111913)
=> ( cPoly_2elist_27___24t(Vvar__0__X__111913,VX111914)
=> ( VX111914 = cPoly_2enil_27___24a1(Vvar__0__X__111913)
| ? [Vvar__1__x__111917] :
( t(Vvar__1__x__111917,Vvar__0__X__111913)
& ? [Vvar__2__l__111918] :
( cPoly_2elist_27___24t(Vvar__0__X__111913,Vvar__2__l__111918)
& VX111914 = cPoly_2econs_27___24a3(Vvar__0__X__111913,Vvar__1__x__111917,Vvar__2__l__111918) ) ) ) ) ) ).
fof('$_inversion_Poly.prod',axiom,
! [Vvar__0__X__142548,Vvar__1__Y__142549,VX142550] :
( cType___24t(Vvar__0__X__142548)
=> ( cType___24t(Vvar__1__Y__142549)
=> ( cPoly_2eprod___24t(Vvar__0__X__142548,Vvar__1__Y__142549,VX142550)
=> ? [Vvar__2__x__142553] :
( t(Vvar__2__x__142553,Vvar__0__X__142548)
& ? [Vvar__3__y__142554] :
( t(Vvar__3__y__142554,Vvar__1__Y__142549)
& VX142550 = cPoly_2epair___24a4(Vvar__0__X__142548,Vvar__1__Y__142549,Vvar__2__x__142553,Vvar__3__y__142554) ) ) ) ) ) ).
fof('$_lam_104135',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__104135___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_111642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__111642___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_111748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__111748___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__111749] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__111749)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__111749)
& c_24__lam__111748___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__111749) ) ) ) ).
fof('$_lam_111755',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__111755___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__111756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__111756)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__111756)
& c_24__lam__111755___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__111756) ) ) ) ).
fof('$_lam_111759',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__111759___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__111760] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__111760)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__111760)
& c_24__lam__111759___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_82206',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__82206___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_prop_103977',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__S__103955,Vvar__1__x__103956,Vvar__2__y__103957] :
( p(c_24__prop__103977___24a4(Vvar__0___24Anonymous__103953,Vvar__0__S__103955,Vvar__1__x__103956,Vvar__2__y__103957))
<=> Vvar__1__x__103956 = Vvar__2__y__103957 ) ).
fof('$_prop_103978',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__x__103958,Vvar__1__y__103959] :
( p(c_24__prop__103978___24a3(Vvar__0___24Anonymous__103953,Vvar__0__x__103958,Vvar__1__y__103959))
<=> Vvar__0__x__103958 = Vvar__1__y__103959 ) ).
fof('$_prop_103979',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__x__103960,Vvar__1__s__103961] :
( p(c_24__prop__103979___24a3(Vvar__0___24Anonymous__103953,Vvar__0__x__103960,Vvar__1__s__103961))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__103960,Vvar__1__s__103961) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_103980',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__P__103962,Vvar__1__Q__103963] :
( p(c_24__prop__103980___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103962,Vvar__1__Q__103963))
<=> ( p(Vvar__0__P__103962)
& p(Vvar__1__Q__103963) ) ) ).
fof('$_prop_103981',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__P__103966,Vvar__1__Q__103967] :
( p(c_24__prop__103981___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103966,Vvar__1__Q__103967))
<=> ( p(Vvar__0__P__103966)
| p(Vvar__1__Q__103967) ) ) ).
fof('$_prop_103982',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__P__103970,Vvar__1__Q__103971] :
( p(c_24__prop__103982___24a3(Vvar__0___24Anonymous__103953,Vvar__0__P__103970,Vvar__1__Q__103971))
<=> ( p(Vvar__0__P__103970)
=> p(Vvar__1__Q__103971) ) ) ).
fof('$_prop_103983',axiom,
! [Vvar__0___24Anonymous__103953,Vvar__0__P__103975] :
( p(c_24__prop__103983___24a2(Vvar__0___24Anonymous__103953,Vvar__0__P__103975))
<=> ~ p(Vvar__0__P__103975) ) ).
fof('$_prop_111570',axiom,
! [Vvar__0___24Anonymous__111557,Vvar__0__s__111561] :
( p(c_24__prop__111570___24a2(Vvar__0___24Anonymous__111557,Vvar__0__s__111561))
<=> ! [Vvar__1__a__111562] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__111562)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__111562,Vvar__0__s__111561) ) ) ).
fof('$_prop_111571',axiom,
! [Vvar__0___24Anonymous__111557,Vvar__0__s1__111563,Vvar__1__s2__111564] :
( p(c_24__prop__111571___24a3(Vvar__0___24Anonymous__111557,Vvar__0__s1__111563,Vvar__1__s2__111564))
<=> ! [Vvar__2__a__111565] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__111565)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__111565,Vvar__0__s1__111563)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__111565,Vvar__1__s2__111564) ) ) ) ).
fof('$_prop_111572',axiom,
! [Vvar__0___24Anonymous__111557,Vvar__0__s1__111567,Vvar__1__s2__111568] :
( p(c_24__prop__111572___24a3(Vvar__0___24Anonymous__111557,Vvar__0__s1__111567,Vvar__1__s2__111568))
<=> ! [Vvar__2__a__111569] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__111569)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__111569,Vvar__0__s1__111567)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__111569,Vvar__1__s2__111568) ) ) ) ).
fof('$_prop_111662',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__111662___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_37',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__37___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_98187',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__98187___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_99129',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__99129___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_type_100054',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100055] :
( c_24__type__100054___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100055)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__100055,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_100136',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__100137] :
( c_24__type__100136___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__100137)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__100137,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_100229',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100230] :
( c_24__type__100229___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100230)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__100230,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_100429',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__100430] :
( c_24__type__100429___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__100430)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__100430,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_100522',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100523] :
( c_24__type__100522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100523)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__100523,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_100615',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__100616] :
( c_24__type__100615___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__100616)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__100616,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_100697',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100698] :
( c_24__type__100697___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100698)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__100698,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_100790',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__100791] :
( c_24__type__100790___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__100791)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__100791,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_100872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100873] :
( c_24__type__100872___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__100873)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__100873,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_100965',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__100966] :
( c_24__type__100965___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__100966)
<=> ! [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__100966,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_101403',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101404] :
( c_24__type__101403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101404)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__101404,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_101504',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__101505] :
( c_24__type__101504___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__101505)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__101505,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_101605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101606] :
( c_24__type__101605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101606)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__101606,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_101695',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__101696] :
( c_24__type__101695___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__101696)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__101696,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_101796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101797] :
( c_24__type__101796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101797)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__101797,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_101897',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__101898] :
( c_24__type__101897___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__101898)
<=> ! [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__101898,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_101998',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101999] :
( c_24__type__101998___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__101999)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__101999,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_102122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__102123] :
( c_24__type__102122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__102123)
<=> ! [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__102123,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_102141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__102142] :
( c_24__type__102141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__102142)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__102142,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_102161',axiom,
! [Vvar__102162] :
( c_24__type__102161___24t(Vvar__102162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___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__102162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_102442',axiom,
! [Vvar__102443] :
( c_24__type__102442___24t(Vvar__102443)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__102443,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_102716',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__102717] :
( c_24__type__102716___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__102717)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__102717,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_102779',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__102780] :
( c_24__type__102779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__102780)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__102780,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_102842',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__102843] :
( c_24__type__102842___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__102843)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__102843,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_102896',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__102897] :
( c_24__type__102896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__102897)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__102897,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_102959',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__102960] :
( c_24__type__102959___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__102960)
<=> ! [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__102960,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_103065',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103066] :
( c_24__type__103065___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103066)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__103066,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103088',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103089] :
( c_24__type__103088___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103089)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__103089,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103112] :
( c_24__type__103111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103112)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__103112,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_103134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103135] :
( c_24__type__103134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103135)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__103135,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103153] :
( c_24__type__103152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103153)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__103153,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_103178',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103179] :
( c_24__type__103178___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103179)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__103179,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103197] :
( c_24__type__103196___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__103197)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__103197,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_103304',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103305] :
( c_24__type__103304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103305)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__103305,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103349] :
( c_24__type__103348___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103349)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__103349,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_103384',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103385] :
( c_24__type__103384___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103385)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__103385,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_103428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103429] :
( c_24__type__103428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__103429)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__103429,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_103486',axiom,
! [Vvar__103487] :
( c_24__type__103486___24t(Vvar__103487)
<=> ! [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__103487,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_104011',axiom,
! [Vvar__104012] :
( c_24__type__104011___24t(Vvar__104012)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eBasics_2ebin___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__104012,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104013',axiom,
! [Vvar__104014] :
( c_24__type__104013___24t(Vvar__104014)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__104014,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104019',axiom,
! [Vvar__104020] :
( c_24__type__104019___24t(Vvar__104020)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__104020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104028',axiom,
! [Vvar__104029] :
( c_24__type__104028___24t(Vvar__104029)
<=> ! [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__104029,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104033',axiom,
! [Vvar__104034] :
( c_24__type__104033___24t(Vvar__104034)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__104034,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104035',axiom,
! [Vvar__104036] :
( c_24__type__104035___24t(Vvar__104036)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__104036,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104080',axiom,
! [Vvar__104081] :
( c_24__type__104080___24t(Vvar__104081)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__104081,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104083',axiom,
! [Vvar__104084] :
( c_24__type__104083___24t(Vvar__104084)
<=> ! [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__104084,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104086',axiom,
! [Vvar__104087] :
( c_24__type__104086___24t(Vvar__104087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__104087,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104091',axiom,
! [Vvar__104092] :
( c_24__type__104091___24t(Vvar__104092)
<=> ! [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__104092,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104099',axiom,
! [Vvar__104100] :
( c_24__type__104099___24t(Vvar__104100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__104100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_104102',axiom,
! [Vvar__104103] :
( c_24__type__104102___24t(Vvar__104103)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__104103,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104113',axiom,
! [Vvar__104114] :
( c_24__type__104113___24t(Vvar__104114)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(happ(happ(Vvar__104114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_104122',axiom,
! [Vvar__104123] :
( c_24__type__104122___24t(Vvar__104123)
<=> ! [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__104123,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_104129',axiom,
! [Vvar__104130] :
( c_24__type__104129___24t(Vvar__104130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__89942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__104130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__104151] :
( c_24__type__104150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__104151)
<=> ! [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__104151,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_104153',axiom,
! [Vvar__104154] :
( c_24__type__104153___24t(Vvar__104154)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__104154,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104158',axiom,
! [Vvar__104159] :
( c_24__type__104158___24t(Vvar__104159)
<=> ! [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__104159,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_104322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104323] :
( c_24__type__104322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104323)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__104323,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_104385',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__104386] :
( c_24__type__104385___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__104386)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__104386,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_104448',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104449] :
( c_24__type__104448___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104449)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__104449,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_104502',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__104503] :
( c_24__type__104502___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__104503)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__104503,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_104565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104566] :
( c_24__type__104565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__104566)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__104566,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_104571',axiom,
! [Vvar__104572] :
( c_24__type__104571___24t(Vvar__104572)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cLF_2eBasics_2ebin___24t(happ(Vvar__104572,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104603',axiom,
! [Vvar__104604] :
( c_24__type__104603___24t(Vvar__104604)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__104604,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_104641',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104642] :
( c_24__type__104641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104642)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__104642,Vv__CANONICAL__3)) ) ) ).
fof('$_type_104688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__104689] :
( c_24__type__104688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__104689)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__104689,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_104723',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104724] :
( c_24__type__104723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__104724)
<=> ! [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__104724,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_104725',axiom,
! [Vvar__104726] :
( c_24__type__104725___24t(Vvar__104726)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__104726,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104734',axiom,
! [Vvar__104735] :
( c_24__type__104734___24t(Vvar__104735)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__104735,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104739',axiom,
! [Vvar__104740] :
( c_24__type__104739___24t(Vvar__104740)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__104740,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104776',axiom,
! [Vvar__104777] :
( c_24__type__104776___24t(Vvar__104777)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__104777,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104778',axiom,
! [Vvar__104779] :
( c_24__type__104778___24t(Vvar__104779)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__104779,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104781',axiom,
! [Vvar__104782] :
( c_24__type__104781___24t(Vvar__104782)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__104782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104785',axiom,
! [Vvar__104786] :
( c_24__type__104785___24t(Vvar__104786)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__104786,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104787',axiom,
! [Vvar__104788] :
( c_24__type__104787___24t(Vvar__104788)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__104788,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104792',axiom,
! [Vvar__104793] :
( c_24__type__104792___24t(Vvar__104793)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__104793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104810',axiom,
! [Vvar__104811] :
( c_24__type__104810___24t(Vvar__104811)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___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__104811,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_104836',axiom,
! [Vvar__104837] :
( c_24__type__104836___24t(Vvar__104837)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__104837,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_105384',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__105385] :
( c_24__type__105384___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__105385)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__105385,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_105730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__105731] :
( c_24__type__105730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__105731)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__105731,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_106076',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__106077] :
( c_24__type__106076___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__106077)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__106077,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_106399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__106400] :
( c_24__type__106399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__106400)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__106400,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_106745',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__106746] :
( c_24__type__106745___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__106746)
<=> ! [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__106746,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_107091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__107092] :
( c_24__type__107091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__107092)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__107092,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_107437',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__107438] :
( c_24__type__107437___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__107438)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__107438,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_107783',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__107784] :
( c_24__type__107783___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__107784)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__107784,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_108129',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__108130] :
( c_24__type__108129___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__108130)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__108130,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_108452',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__108453] :
( c_24__type__108452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__108453)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__108453,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_108798',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__108799] :
( c_24__type__108798___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__108799)
<=> ! [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__108799,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_109144',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__109145] :
( c_24__type__109144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__109145)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__109145,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_109467',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__109468] :
( c_24__type__109467___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__109468)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__109468,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_109790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__109791] :
( c_24__type__109790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__109791)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__109791,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_110136',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__110137] :
( c_24__type__110136___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__110137)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__110137,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_110291',axiom,
! [Vvar__110292] :
( c_24__type__110291___24t(Vvar__110292)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__110292,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_110296',axiom,
! [Vvar__110297] :
( c_24__type__110296___24t(Vvar__110297)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__110297,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_110304',axiom,
! [Vvar__110305] :
( c_24__type__110304___24t(Vvar__110305)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__110305,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_110306',axiom,
! [Vvar__110307] :
( c_24__type__110306___24t(Vvar__110307)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__110307,Vv__CANONICAL__0)) ) ) ).
fof('$_type_110311',axiom,
! [Vvar__110312] :
( c_24__type__110311___24t(Vvar__110312)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__110312,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_110329',axiom,
! [Vvar__110330] :
( c_24__type__110329___24t(Vvar__110330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__702___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)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__110330,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_110486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110487] :
( c_24__type__110486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110487)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__110487,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_110505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110506] :
( c_24__type__110505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110506)
<=> ! [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__110506,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_110519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110520] :
( c_24__type__110519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__110520)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__110520,Vv__CANONICAL__4)) ) ) ).
fof('$_type_110664',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110665] :
( c_24__type__110664___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110665)
<=> ! [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__110665,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_110714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110715] :
( c_24__type__110714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110715)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__110715,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_110764',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110765] :
( c_24__type__110764___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110765)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__110765,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_110806',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110807] :
( c_24__type__110806___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110807)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__110807,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_110856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110857] :
( c_24__type__110856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__110857)
<=> ! [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__110857,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_110932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__110933] :
( c_24__type__110932___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__110933)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__110933,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_110999',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111000] :
( c_24__type__110999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111000)
<=> ! [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__111000,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_111034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111035] :
( c_24__type__111034___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111035)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__111035,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_111074',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111075] :
( c_24__type__111074___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111075)
<=> ! [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__111075,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_111107',axiom,
! [Vvar__111108] :
( c_24__type__111107___24t(Vvar__111108)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__111117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__78464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__111108,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_111117',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111118] :
( c_24__type__111117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111118)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__111118,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_111210',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111211] :
( c_24__type__111210___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111211)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__111211,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_111245',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111246] :
( c_24__type__111245___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111246)
<=> ! [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__111246,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_111280',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111281] :
( c_24__type__111280___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__111281)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__111281,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_111289',axiom,
! [Vvar__111290] :
( c_24__type__111289___24t(Vvar__111290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___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__111290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_111310',axiom,
! [Vvar__111311] :
( c_24__type__111310___24t(Vvar__111311)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__111311,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_111328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111329] :
( c_24__type__111328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__111329)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__111329,Vv__CANONICAL__2)) ) ) ).
fof('$_type_111334',axiom,
! [Vvar__111335] :
( c_24__type__111334___24t(Vvar__111335)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__111335,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_111338',axiom,
! [Vvar__111339] :
( c_24__type__111338___24t(Vvar__111339)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__111339,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_111341',axiom,
! [Vvar__111342] :
( c_24__type__111341___24t(Vvar__111342)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__111342,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111350',axiom,
! [Vvar__111351] :
( c_24__type__111350___24t(Vvar__111351)
<=> ! [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__111351,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_111368',axiom,
! [Vvar__111369] :
( c_24__type__111368___24t(Vvar__111369)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__111369,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_111385',axiom,
! [Vvar__111386] :
( c_24__type__111385___24t(Vvar__111386)
<=> ! [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__111386,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_111469',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111470] :
( c_24__type__111469___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111470)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__111470,Vv__CANONICAL__4)) ) ) ).
fof('$_type_111478',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111479] :
( c_24__type__111478___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__111479)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__111479,Vv__CANONICAL__4)) ) ) ).
fof('$_type_111524',axiom,
! [Vvar__111525] :
( c_24__type__111524___24t(Vvar__111525)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__111525,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111605',axiom,
! [Vvar__111606] :
( c_24__type__111605___24t(Vvar__111606)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__111606,Vv__CANONICAL__0)) ) ) ).
fof('$_type_111654',axiom,
! [Vvar__111655] :
( c_24__type__111654___24t(Vvar__111655)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__111659___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__111655,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_111659',axiom,
! [Vv__CANONICAL__0,Vvar__111660] :
( c_24__type__111659___24t(Vv__CANONICAL__0,Vvar__111660)
<=> ! [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__111660,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_111665',axiom,
! [Vvar__111666] :
( c_24__type__111665___24t(Vvar__111666)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__82195___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__82195___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__111666,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111672',axiom,
! [Vvar__111673] :
( c_24__type__111672___24t(Vvar__111673)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cLF_2eLists_2eNatList_2enatprod___24t(happ(happ(Vvar__111673,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111677',axiom,
! [Vvar__111678] :
( c_24__type__111677___24t(Vvar__111678)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatprod___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__111678,Vv__CANONICAL__0)) ) ) ).
fof('$_type_111715',axiom,
! [Vvar__111716] :
( c_24__type__111715___24t(Vvar__111716)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(happ(Vvar__111716,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_111762',axiom,
! [Vvar__111763] :
( c_24__type__111762___24t(Vvar__111763)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__111763,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111844',axiom,
! [Vvar__111845] :
( c_24__type__111844___24t(Vvar__111845)
<=> ! [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__111845,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111849',axiom,
! [Vvar__111850] :
( c_24__type__111849___24t(Vvar__111850)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__111850,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_111866',axiom,
! [Vvar__111867] :
( c_24__type__111866___24t(Vvar__111867)
<=> ! [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__111867,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_111906',axiom,
! [Vvar__111907] :
( c_24__type__111906___24t(Vvar__111907)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__111907,Vv__CANONICAL__0)) ) ) ).
fof('$_type_111910',axiom,
! [Vvar__111911] :
( c_24__type__111910___24t(Vvar__111911)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__98635___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__98635___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__111911,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_123905',axiom,
! [Vvar__123906] :
( c_24__type__123905___24t(Vvar__123906)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__66373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__123906,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_13',axiom,
! [Vvar__14] :
( c_24__type__13___24t(Vvar__14)
<=> ! [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__14,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_135730',axiom,
! [Vvar__135731] :
( c_24__type__135730___24t(Vvar__135731)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__135731,Vv__CANONICAL__0)) ) ) ).
fof('$_type_136247',axiom,
! [Vvar__136248] :
( c_24__type__136247___24t(Vvar__136248)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__95362___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__136248,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_136864',axiom,
! [Vvar__136865] :
( c_24__type__136864___24t(Vvar__136865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__136865,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_137555',axiom,
! [Vvar__137556] :
( c_24__type__137555___24t(Vvar__137556)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2enatoption___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__137556,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_142570',axiom,
! [Vvar__142571] :
( c_24__type__142570___24t(Vvar__142571)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cPoly_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__142571,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_152',axiom,
! [Vvar__153] :
( c_24__type__152___24t(Vvar__153)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__153,Vv__CANONICAL__0)) ) ) ).
fof('$_type_152866',axiom,
! [Vvar__152867] :
( c_24__type__152866___24t(Vvar__152867)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__152867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_154264',axiom,
! [Vvar__154265] :
( c_24__type__154264___24t(Vvar__154265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__154265,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_166',axiom,
! [Vvar__167] :
( c_24__type__166___24t(Vvar__167)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cPoly_2elist___24t(Vv__CANONICAL__0,happ(Vvar__167,Vv__CANONICAL__0)) ) ) ).
fof('$_type_171',axiom,
! [Vvar__172] :
( c_24__type__171___24t(Vvar__172)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cPoly_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cPoly_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__172,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_184',axiom,
! [Vvar__185] :
( c_24__type__184___24t(Vvar__185)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__185,Vv__CANONICAL__0)) ) ) ).
fof('$_type_184436',axiom,
! [Vvar__184437] :
( c_24__type__184436___24t(Vvar__184437)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___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)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__184437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_184467',axiom,
! [Vvar__184468] :
( c_24__type__184467___24t(Vvar__184468)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__184468,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_184498',axiom,
! [Vvar__184499] :
( c_24__type__184498___24t(Vvar__184499)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___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)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__184499,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_191699',axiom,
! [Vvar__191700] :
( c_24__type__191699___24t(Vvar__191700)
<=> ! [Vv__CANONICAL__0] :
( cPoly_2eExercises_2eChurch_2ecnat___24t(Vv__CANONICAL__0)
=> cPoly_2eExercises_2eChurch_2ecnat___24t(happ(Vvar__191700,Vv__CANONICAL__0)) ) ) ).
fof('$_type_192795',axiom,
! [Vvar__192796] :
( c_24__type__192795___24t(Vvar__192796)
<=> ! [Vv__CANONICAL__0] :
( cPoly_2eExercises_2eChurch_2ecnat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cPoly_2eExercises_2eChurch_2ecnat___24t(Vv__CANONICAL__1)
=> cPoly_2eExercises_2eChurch_2ecnat___24t(happ(happ(Vvar__192796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25',axiom,
! [Vvar__26] :
( c_24__type__25___24t(Vvar__26)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35',axiom,
! [Vvar__36] :
( c_24__type__35___24t(Vvar__36)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__36,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38',axiom,
! [Vvar__39] :
( c_24__type__38___24t(Vvar__39)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__39,Vv__CANONICAL__0)) ) ) ).
fof('$_type_478',axiom,
! [Vvar__479] :
( c_24__type__478___24t(Vvar__479)
<=> ! [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__479,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_481',axiom,
! [Vvar__482] :
( c_24__type__481___24t(Vvar__482)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__482,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_486',axiom,
! [Vvar__487] :
( c_24__type__486___24t(Vvar__487)
<=> ! [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__487,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50',axiom,
! [Vvar__51] :
( c_24__type__50___24t(Vvar__51)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__1)
=> cLF_2eLists_2eNatList_2enatlist___24t(happ(happ(Vvar__51,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_53',axiom,
! [Vvar__54] :
( c_24__type__53___24t(Vvar__54)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__54,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_56',axiom,
! [Vvar__57] :
( c_24__type__56___24t(Vvar__57)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__1)
=> cLF_2eLists_2eNatList_2ebag___24t(happ(happ(Vvar__57,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6',axiom,
! [Vvar__7] :
( c_24__type__6___24t(Vvar__7)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66353',axiom,
! [Vvar__66354] :
( c_24__type__66353___24t(Vvar__66354)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__66354,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66355',axiom,
! [Vvar__66356] :
( c_24__type__66355___24t(Vvar__66356)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__66356,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66374] :
( c_24__type__66373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__66374)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__66374,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_66383',axiom,
! [Vvar__66384] :
( c_24__type__66383___24t(Vvar__66384)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__66384,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66411',axiom,
! [Vvar__66412] :
( c_24__type__66411___24t(Vvar__66412)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__66412,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66416',axiom,
! [Vvar__66417] :
( c_24__type__66416___24t(Vvar__66417)
<=> ! [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__66417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_66425',axiom,
! [Vvar__66426] :
( c_24__type__66425___24t(Vvar__66426)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__66426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66430',axiom,
! [Vvar__66431] :
( c_24__type__66430___24t(Vvar__66431)
<=> ! [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__66431,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66434',axiom,
! [Vvar__66435] :
( c_24__type__66434___24t(Vvar__66435)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__66435,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66563',axiom,
! [Vvar__66564] :
( c_24__type__66563___24t(Vvar__66564)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__716___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__66564,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_66745',axiom,
! [Vvar__66746] :
( c_24__type__66745___24t(Vvar__66746)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__66746,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66752',axiom,
! [Vvar__66753] :
( c_24__type__66752___24t(Vvar__66753)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cLF_2eLists_2eNatList_2enatoption___24t(happ(Vvar__66753,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66754',axiom,
! [Vvar__66755] :
( c_24__type__66754___24t(Vvar__66755)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__0)
=> cLF_2eLists_2eNatList_2enatoption___24t(happ(Vvar__66755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66769',axiom,
! [Vvar__66770] :
( c_24__type__66769___24t(Vvar__66770)
<=> ! [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__66770,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66773',axiom,
! [Vvar__66774] :
( c_24__type__66773___24t(Vvar__66774)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__66774,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66863',axiom,
! [Vvar__66864] :
( c_24__type__66863___24t(Vvar__66864)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cLF_2eBasics_2ebool___24t(happ(happ(Vvar__66864,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66866',axiom,
! [Vvar__66867] :
( c_24__type__66866___24t(Vvar__66867)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__66867,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66902',axiom,
! [Vvar__66903] :
( c_24__type__66902___24t(Vvar__66903)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__66903,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66906',axiom,
! [Vvar__66907] :
( c_24__type__66906___24t(Vvar__66907)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__66907,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66917',axiom,
! [Vvar__66918] :
( c_24__type__66917___24t(Vvar__66918)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__66918,Vv__CANONICAL__0)) ) ) ).
fof('$_type_66921',axiom,
! [Vvar__66922] :
( c_24__type__66921___24t(Vvar__66922)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__35___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__35___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__66922,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66924',axiom,
! [Vvar__66925] :
( c_24__type__66924___24t(Vvar__66925)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__1)
=> cLF_2eLists_2eNatList_2enatlist___24t(happ(happ(Vvar__66925,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66927',axiom,
! [Vvar__66928] :
( c_24__type__66927___24t(Vvar__66928)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__1)
=> cLF_2eBasics_2ebool___24t(happ(happ(Vvar__66928,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66985',axiom,
! [Vvar__66986] :
( c_24__type__66985___24t(Vvar__66986)
<=> ! [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__66986,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('$_type_67111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67112] :
( c_24__type__67111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__67112)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__67112,Vv__CANONICAL__3)) ) ) ).
fof('$_type_67146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__67147] :
( c_24__type__67146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__67147)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__67147,Vv__CANONICAL__5)) ) ) ).
fof('$_type_67154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__67155] :
( c_24__type__67154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__67155)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__67155,Vv__CANONICAL__5)) ) ) ).
fof('$_type_67173',axiom,
! [Vvar__67174] :
( c_24__type__67173___24t(Vvar__67174)
<=> ! [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__67174,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_67175',axiom,
! [Vvar__67176] :
( c_24__type__67175___24t(Vvar__67176)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__67176,Vv__CANONICAL__0)) ) ) ).
fof('$_type_702',axiom,
! [Vv__CANONICAL__0,Vvar__703] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vvar__703)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__703,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_711',axiom,
! [Vv__CANONICAL__0,Vvar__712] :
( c_24__type__711___24t(Vv__CANONICAL__0,Vvar__712)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__712,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_716',axiom,
! [Vv__CANONICAL__0,Vvar__717] :
( c_24__type__716___24t(Vv__CANONICAL__0,Vvar__717)
<=> ! [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__717,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_729',axiom,
! [Vvar__730] :
( c_24__type__729___24t(Vvar__730)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__730,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_736',axiom,
! [Vvar__737] :
( c_24__type__736___24t(Vvar__737)
<=> ! [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__737,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74590',axiom,
! [Vvar__74591] :
( c_24__type__74590___24t(Vvar__74591)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__74591,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74607',axiom,
! [Vv__CANONICAL__0,Vvar__74608] :
( c_24__type__74607___24t(Vv__CANONICAL__0,Vvar__74608)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__74608,Vv__CANONICAL__1)) ) ) ).
fof('$_type_74620',axiom,
! [Vvar__74621] :
( c_24__type__74620___24t(Vvar__74621)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__67175___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__74625___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__74621,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_74625',axiom,
! [Vv__CANONICAL__0,Vvar__74626] :
( c_24__type__74625___24t(Vv__CANONICAL__0,Vvar__74626)
<=> ! [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__74626,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_74643',axiom,
! [Vv__CANONICAL__0,Vvar__74644] :
( c_24__type__74643___24t(Vv__CANONICAL__0,Vvar__74644)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__74644,Vv__CANONICAL__1)) ) ) ).
fof('$_type_74656',axiom,
! [Vvar__74657] :
( c_24__type__74656___24t(Vvar__74657)
<=> ! [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__74657,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_750',axiom,
! [Vvar__751] :
( c_24__type__750___24t(Vvar__751)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__751,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_75779',axiom,
! [Vv__CANONICAL__0,Vvar__75780] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vvar__75780)
<=> ! [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__75780,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_75794',axiom,
! [Vvar__75795] :
( c_24__type__75794___24t(Vvar__75795)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__75795,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_75900',axiom,
! [Vvar__75901] :
( c_24__type__75900___24t(Vvar__75901)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75907___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__75901,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_75907',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75908] :
( c_24__type__75907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75908)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__75908,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_75935',axiom,
! [Vvar__75936] :
( c_24__type__75935___24t(Vvar__75936)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75942___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__75936,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_75942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75943] :
( c_24__type__75942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75943)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__75943,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_75966',axiom,
! [Vvar__75967] :
( c_24__type__75966___24t(Vvar__75967)
<=> ! [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__75967,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_760',axiom,
! [Vvar__761] :
( c_24__type__760___24t(Vvar__761)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__761,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76003',axiom,
! [Vvar__76004] :
( c_24__type__76003___24t(Vvar__76004)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__76004,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_76072',axiom,
! [Vvar__76073] :
( c_24__type__76072___24t(Vvar__76073)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__76073,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76075',axiom,
! [Vv__CANONICAL__0,Vvar__76076] :
( c_24__type__76075___24t(Vv__CANONICAL__0,Vvar__76076)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__76076,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_76169',axiom,
! [Vvar__76170] :
( c_24__type__76169___24t(Vvar__76170)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__76170,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76180',axiom,
! [Vvar__76181] :
( c_24__type__76180___24t(Vvar__76181)
<=> ! [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__76181,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76408] :
( c_24__type__76407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76408)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__76408,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_765',axiom,
! [Vvar__766] :
( c_24__type__765___24t(Vvar__766)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__766,Vv__CANONICAL__0)) ) ) ).
fof('$_type_76704',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76705] :
( c_24__type__76704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76705)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__76705,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_76718',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76719] :
( c_24__type__76718___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76719)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__76719,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_76725',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76726] :
( c_24__type__76725___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76726)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__76726,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_77030',axiom,
! [Vvar__77031] :
( c_24__type__77030___24t(Vvar__77031)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__702___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__77031,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_77203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77204] :
( c_24__type__77203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77204)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__77204,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_77242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77243] :
( c_24__type__77242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77243)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__77243,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_77281',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77282] :
( c_24__type__77281___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__77282)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__77282,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_77577',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__77578] :
( c_24__type__77577___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__77578)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__77578,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_77702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__77703] :
( c_24__type__77702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__77703)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__77703,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_77827',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__77828] :
( c_24__type__77827___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__77828)
<=> ! [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__77828,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_77952',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__77953] :
( c_24__type__77952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__77953)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__77953,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_780',axiom,
! [Vvar__781] :
( c_24__type__780___24t(Vvar__781)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__781,Vv__CANONICAL__0)) ) ) ).
fof('$_type_78077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__78078] :
( c_24__type__78077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__78078)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__78078,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_78202',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__78203] :
( c_24__type__78202___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__78203)
<=> ! [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__78203,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_78313',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__78314] :
( c_24__type__78313___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__78314)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__78314,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_78373',axiom,
! [Vvar__78374] :
( c_24__type__78373___24t(Vvar__78374)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__78374,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_78384',axiom,
! [Vvar__78385] :
( c_24__type__78384___24t(Vvar__78385)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__78385,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_78454',axiom,
! [Vvar__78455] :
( c_24__type__78454___24t(Vvar__78455)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__78464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__78455,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_78464',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78465] :
( c_24__type__78464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78465)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__78465,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_78521',axiom,
! [Vvar__78522] :
( c_24__type__78521___24t(Vvar__78522)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__78531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__78464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__78522,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_78531',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78532] :
( c_24__type__78531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78532)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__78532,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_78552',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78553] :
( c_24__type__78552___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78553)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__78553,Vv__CANONICAL__2)) ) ) ).
fof('$_type_78556',axiom,
! [Vvar__78557] :
( c_24__type__78556___24t(Vvar__78557)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__78557,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78559',axiom,
! [Vv__CANONICAL__0,Vvar__78560] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vvar__78560)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__78560,Vv__CANONICAL__1)) ) ) ).
fof('$_type_78576',axiom,
! [Vvar__78577] :
( c_24__type__78576___24t(Vvar__78577)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__78577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_78593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78594] :
( c_24__type__78593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78594)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__78594,Vv__CANONICAL__2)) ) ) ).
fof('$_type_78599',axiom,
! [Vvar__78600] :
( c_24__type__78599___24t(Vvar__78600)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__78600,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_78613',axiom,
! [Vvar__78614] :
( c_24__type__78613___24t(Vvar__78614)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__78614,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78636',axiom,
! [Vvar__78637] :
( c_24__type__78636___24t(Vvar__78637)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__78637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_78641',axiom,
! [Vvar__78642] :
( c_24__type__78641___24t(Vvar__78642)
<=> ! [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__78642,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_78697',axiom,
! [Vvar__78698] :
( c_24__type__78697___24t(Vvar__78698)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__78698,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78720',axiom,
! [Vvar__78721] :
( c_24__type__78720___24t(Vvar__78721)
<=> ! [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__78721,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78725',axiom,
! [Vvar__78726] :
( c_24__type__78725___24t(Vvar__78726)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__78726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_78980',axiom,
! [Vvar__78981] :
( c_24__type__78980___24t(Vvar__78981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__78981,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_78997',axiom,
! [Vvar__78998] :
( c_24__type__78997___24t(Vvar__78998)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__78998,Vv__CANONICAL__0)) ) ) ).
fof('$_type_79005',axiom,
! [Vvar__79006] :
( c_24__type__79005___24t(Vvar__79006)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__79006,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_793',axiom,
! [Vvar__794] :
( c_24__type__793___24t(Vvar__794)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__794,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8',axiom,
! [Vvar__9] :
( c_24__type__8___24t(Vvar__9)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9,Vv__CANONICAL__0)) ) ) ).
fof('$_type_81061',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81062] :
( c_24__type__81061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81062)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__81062,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_81074',axiom,
! [Vvar__81075] :
( c_24__type__81074___24t(Vvar__81075)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__75779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__81075,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81086',axiom,
! [Vvar__81087] :
( c_24__type__81086___24t(Vvar__81087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__81089___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__81087,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_81089',axiom,
! [Vv__CANONICAL__0,Vvar__81090] :
( c_24__type__81089___24t(Vv__CANONICAL__0,Vvar__81090)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__81090,Vv__CANONICAL__1)) ) ) ).
fof('$_type_81173',axiom,
! [Vvar__81174] :
( c_24__type__81173___24t(Vvar__81174)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__81174,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_81490',axiom,
! [Vvar__81491] :
( c_24__type__81490___24t(Vvar__81491)
<=> ! [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__81491,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81498',axiom,
! [Vvar__81499] :
( c_24__type__81498___24t(Vvar__81499)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__81499,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81652',axiom,
! [Vvar__81653] :
( c_24__type__81652___24t(Vvar__81653)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__81653,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_81678',axiom,
! [Vvar__81679] :
( c_24__type__81678___24t(Vvar__81679)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__81679,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81683',axiom,
! [Vvar__81684] :
( c_24__type__81683___24t(Vvar__81684)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__0)
=> cLF_2eLists_2eNatList_2enatlist___24t(happ(Vvar__81684,Vv__CANONICAL__0)) ) ) ).
fof('$_type_81687',axiom,
! [Vvar__81688] :
( c_24__type__81687___24t(Vvar__81688)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__1)
=> cLF_2eLists_2eNatList_2ebag___24t(happ(happ(Vvar__81688,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81691',axiom,
! [Vvar__81692] :
( c_24__type__81691___24t(Vvar__81692)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2ebag___24t(Vv__CANONICAL__1)
=> cLF_2eBasics_2ebool___24t(happ(happ(Vvar__81692,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81698',axiom,
! [Vvar__81699] :
( c_24__type__81698___24t(Vvar__81699)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eLists_2eNatList_2enatlist___24t(Vv__CANONICAL__1)
=> cLF_2eBasics_2ebool___24t(happ(happ(Vvar__81699,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81725',axiom,
! [Vvar__81726] :
( c_24__type__81725___24t(Vvar__81726)
<=> ! [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__81726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81731',axiom,
! [Vvar__81732] :
( c_24__type__81731___24t(Vvar__81732)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__81732,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81745',axiom,
! [Vvar__81746] :
( c_24__type__81745___24t(Vvar__81746)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__702___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__81746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_81755',axiom,
! [Vvar__81756] :
( c_24__type__81755___24t(Vvar__81756)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__81756,Vv__CANONICAL__0)) ) ) ).
fof('$_type_81758',axiom,
! [Vvar__81759] :
( c_24__type__81758___24t(Vvar__81759)
<=> ! [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__81759,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81795',axiom,
! [Vvar__81796] :
( c_24__type__81795___24t(Vvar__81796)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__81796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81901',axiom,
! [Vvar__81902] :
( c_24__type__81901___24t(Vvar__81902)
<=> ! [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__81902,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81904',axiom,
! [Vvar__81905] :
( c_24__type__81904___24t(Vvar__81905)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__81905,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_81906',axiom,
! [Vvar__81907] :
( c_24__type__81906___24t(Vvar__81907)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__81907,Vv__CANONICAL__0)) ) ) ).
fof('$_type_81920',axiom,
! [Vvar__81921] :
( c_24__type__81920___24t(Vvar__81921)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__81921,Vv__CANONICAL__0)) ) ) ).
fof('$_type_81949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81950] :
( c_24__type__81949___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__81950)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__81950,Vv__CANONICAL__3)) ) ) ).
fof('$_type_81960',axiom,
! [Vvar__81961] :
( c_24__type__81960___24t(Vvar__81961)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__81961,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_81972',axiom,
! [Vvar__81973] :
( c_24__type__81972___24t(Vvar__81973)
<=> ! [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__81973,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_81984',axiom,
! [Vvar__81985] :
( c_24__type__81984___24t(Vvar__81985)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__81985,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_82020',axiom,
! [Vvar__82021] :
( c_24__type__82020___24t(Vvar__82021)
<=> ! [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__82021,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_82195',axiom,
! [Vvar__82196] :
( c_24__type__82195___24t(Vvar__82196)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__82196,Vv__CANONICAL__0)) ) ) ).
fof('$_type_82218',axiom,
! [Vvar__82219] :
( c_24__type__82218___24t(Vvar__82219)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__82223___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__82219,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_82223',axiom,
! [Vv__CANONICAL__0,Vvar__82224] :
( c_24__type__82223___24t(Vv__CANONICAL__0,Vvar__82224)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__82224,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_82249',axiom,
! [Vvar__82250] :
( c_24__type__82249___24t(Vvar__82250)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__82250,Vv__CANONICAL__0)) ) ) ).
fof('$_type_82269',axiom,
! [Vvar__82270] :
( c_24__type__82269___24t(Vvar__82270)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eBasics_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eBasics_2ebool___24t(Vv__CANONICAL__1)
=> cLF_2eBasics_2ebool___24t(happ(happ(Vvar__82270,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_82276',axiom,
! [Vvar__82277] :
( c_24__type__82276___24t(Vvar__82277)
<=> ! [Vv__CANONICAL__0] :
( cLF_2eBasics_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLF_2eBasics_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cLF_2eBasics_2ebool___24t(Vv__CANONICAL__2)
=> cLF_2eBasics_2ebool___24t(happ(happ(happ(Vvar__82277,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_82716',axiom,
! [Vvar__82717] :
( c_24__type__82716___24t(Vvar__82717)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__82717,Vv__CANONICAL__0)) ) ) ).
fof('$_type_82745',axiom,
! [Vvar__82746] :
( c_24__type__82745___24t(Vvar__82746)
<=> ! [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__82746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_82890',axiom,
! [Vvar__82891] :
( c_24__type__82890___24t(Vvar__82891)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__82891,Vv__CANONICAL__0)) ) ) ).
fof('$_type_83216',axiom,
! [Vvar__83217] :
( c_24__type__83216___24t(Vvar__83217)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__83217,Vv__CANONICAL__0)) ) ) ).
fof('$_type_84006',axiom,
! [Vvar__84007] :
( c_24__type__84006___24t(Vvar__84007)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__84007,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_84011',axiom,
! [Vvar__84012] :
( c_24__type__84011___24t(Vvar__84012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__84012,Vv__CANONICAL__0)) ) ) ).
fof('$_type_84015',axiom,
! [Vvar__84016] :
( c_24__type__84015___24t(Vvar__84016)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__84016,Vv__CANONICAL__0)) ) ) ).
fof('$_type_84029',axiom,
! [Vvar__84030] :
( c_24__type__84029___24t(Vvar__84030)
<=> ! [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__84030,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_89935',axiom,
! [Vvar__89936] :
( c_24__type__89935___24t(Vvar__89936)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__89936,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_89942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__89943] :
( c_24__type__89942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__89943)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__89943) ) ) ).
fof('$_type_90295',axiom,
! [Vvar__90296] :
( c_24__type__90295___24t(Vvar__90296)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__90296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_90298',axiom,
! [Vvar__90299] :
( c_24__type__90298___24t(Vvar__90299)
<=> ! [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__90299,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_91337',axiom,
! [Vvar__91338] :
( c_24__type__91337___24t(Vvar__91338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__91338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_91424',axiom,
! [Vvar__91425] :
( c_24__type__91424___24t(Vvar__91425)
<=> ! [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__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__711___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__91425,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('$_type_91468',axiom,
! [Vvar__91469] :
( c_24__type__91468___24t(Vvar__91469)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__91469,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_91477',axiom,
! [Vvar__91478] :
( c_24__type__91477___24t(Vvar__91478)
<=> ! [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__91478,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_91534',axiom,
! [Vvar__91535] :
( c_24__type__91534___24t(Vvar__91535)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__91535,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_91894',axiom,
! [Vvar__91895] :
( c_24__type__91894___24t(Vvar__91895)
<=> ! [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__91895,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_91912',axiom,
! [Vvar__91913] :
( c_24__type__91912___24t(Vvar__91913)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__91913,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_92166',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__92167] :
( c_24__type__92166___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__92167)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92167,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92229',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__92230] :
( c_24__type__92229___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__92230)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92230,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92292',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__92293] :
( c_24__type__92292___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__92293)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92293,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__92347] :
( c_24__type__92346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__92347)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__92347,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_92409',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__92410] :
( c_24__type__92409___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__92410)
<=> ! [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__92410,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_92538',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92539] :
( c_24__type__92538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92539)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92539,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92568',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92569] :
( c_24__type__92568___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92569)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92569,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92593] :
( c_24__type__92592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92593)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__92593,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_92622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92623] :
( c_24__type__92622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92623)
<=> ! [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__92623,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_92652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92653] :
( c_24__type__92652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92653)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92653,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92676',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92677] :
( c_24__type__92676___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92677)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__92677,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_92709',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92710] :
( c_24__type__92709___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92710)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__92710,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92733',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92734] :
( c_24__type__92733___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92734)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__92734,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_92760',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92761] :
( c_24__type__92760___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__92761)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__92761,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_93159',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__93160] :
( c_24__type__93159___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__93160)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__93160,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_93372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__93373] :
( c_24__type__93372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__93373)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__93373,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_93585',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__93586] :
( c_24__type__93585___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__93586)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__93586,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_93780',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__93781] :
( c_24__type__93780___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__93781)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__93781,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_93993',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__93994] :
( c_24__type__93993___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__93994)
<=> ! [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__93994,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_94206',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__94207] :
( c_24__type__94206___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__94207)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__94207,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_94419',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__94420] :
( c_24__type__94419___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__94420)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__94420,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_94632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__94633] :
( c_24__type__94632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__94633)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__94633,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_94827',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__94828] :
( c_24__type__94827___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__94828)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__94828,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_95040',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__95041] :
( c_24__type__95040___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__95041)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__95041,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_95235',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__95236] :
( c_24__type__95235___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__95236)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__95236,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_95261',axiom,
! [Vvar__95262] :
( c_24__type__95261___24t(Vvar__95262)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__95262,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_95287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95288] :
( c_24__type__95287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95288)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__95288,Vv__CANONICAL__3)) ) ) ).
fof('$_type_95295',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95296] :
( c_24__type__95295___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95296)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__95296,Vv__CANONICAL__3)) ) ) ).
fof('$_type_95303',axiom,
! [Vvar__95304] :
( c_24__type__95303___24t(Vvar__95304)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__95304,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_95337',axiom,
! [Vvar__95338] :
( c_24__type__95337___24t(Vvar__95338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78559___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__95338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_95355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__95356] :
( c_24__type__95355___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__95356)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__95356,Vv__CANONICAL__2)) ) ) ).
fof('$_type_95359',axiom,
! [Vvar__95360] :
( c_24__type__95359___24t(Vvar__95360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__95360,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_95362',axiom,
! [Vv__CANONICAL__0,Vvar__95363] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vvar__95363)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__95363,Vv__CANONICAL__1)) ) ) ).
fof('$_type_95396',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95397] :
( c_24__type__95396___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95397)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__95397,Vv__CANONICAL__3)) ) ) ).
fof('$_type_95404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95405] :
( c_24__type__95404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__95405)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__95405,Vv__CANONICAL__3)) ) ) ).
fof('$_type_95412',axiom,
! [Vvar__95413] :
( c_24__type__95412___24t(Vvar__95413)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__95362___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__95413,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_98214',axiom,
! [Vvar__98215] :
( c_24__type__98214___24t(Vvar__98215)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__711___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__98215,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_98218',axiom,
! [Vvar__98219] :
( c_24__type__98218___24t(Vvar__98219)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__98219,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_98489',axiom,
! [Vvar__98490] :
( c_24__type__98489___24t(Vvar__98490)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__98490,Vv__CANONICAL__0)) ) ) ).
fof('$_type_98611',axiom,
! [Vvar__98612] :
( c_24__type__98611___24t(Vvar__98612)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__98612,Vv__CANONICAL__0)) ) ) ).
fof('$_type_98635',axiom,
! [Vvar__98636] :
( c_24__type__98635___24t(Vvar__98636)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__98636,Vv__CANONICAL__0)) ) ) ).
fof('$_type_99157',axiom,
! [Vvar__99158] :
( c_24__type__99157___24t(Vvar__99158)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__99158,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_99170',axiom,
! [Vvar__99171] :
( c_24__type__99170___24t(Vvar__99171)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__99171,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_99213',axiom,
! [Vv__CANONICAL__0,Vvar__99214] :
( c_24__type__99213___24t(Vv__CANONICAL__0,Vvar__99214)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__99214,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_99469',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__99470] :
( c_24__type__99469___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__99470)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__99470,Vv__CANONICAL__6)) ) ) ).
fof('$_type_99497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__99498] :
( c_24__type__99497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__99498)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__99498,Vv__CANONICAL__6)) ) ) ).
fof('$_type_99693',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__99694] :
( c_24__type__99693___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__99694)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__99694,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_99786',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__99787] :
( c_24__type__99786___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__99787)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__99787,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_99879',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__99880] :
( c_24__type__99879___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__99880)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__99880,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_99961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__99962] :
( c_24__type__99961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__99962)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__99962,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__81652___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__66425___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__66917___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__66425___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__66425___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__66921___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
c_24__type__66425___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.pred',axiom,
c_24__type__6___24t(cCoq_2eArith_2ePeanoNat_2eNat_2epred) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__82218___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.sub',axiom,
c_24__type__13___24t(cCoq_2eArith_2ePeanoNat_2eNat_2esub) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.t',axiom,
cType___24t(cCoq_2eArith_2ePeanoNat_2eNat_2et) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ezero) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__13___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__81086___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__104013___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__74590___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__104019___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.leb',axiom,
c_24__type__84029___24t(cCoq_2eBool_2eBool_2eleb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__99170___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__67175___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__35___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.bits_lt',axiom,
c_24__type__81758___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.eq',axiom,
c_24__type__81758___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__81906___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__81904___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__81901___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__111849___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__81904___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_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.eq',axiom,
c_24__type__81904___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__81795___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__104035___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__82745___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_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.ID',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).
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('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__66355___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__66353___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__74590___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__81984___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__66416___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__89935___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__74590___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__104028___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__104033___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.is_true',axiom,
c_24__type__104013___24t(cCoq_2eInit_2eDatatypes_2eis__true) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__74656___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__152___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__74620___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__66866___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__66411___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__152___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__74590___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__81960___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__66383___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__81972___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__66383___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__74590___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__104725___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__75966___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__25___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__35___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__25___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__76003___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__35___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.square',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esquare) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__13___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__25___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__38___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__66425___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__66425___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__66425___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__111338___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__78576___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.exist2',axiom,
c_24__type__95337___24t(cCoq_2eInit_2eSpecif_2eexist2) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__111289___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.existT2',axiom,
c_24__type__111310___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__78720___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__78725___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__78636___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__78599___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__111334___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__78641___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__78556___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__95303___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__95359___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__95412___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__78613___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__78697___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__81074___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__75794___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__75900___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__75935___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__91468___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__104603___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__123905___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__82020___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__91477___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__78521___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__78454___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__78454___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__111107___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__111107___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__8___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__104113___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
c_24__type__136247___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_',axiom,
c_24__type__104725___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__104129___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__104122___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__135730___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__81498___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__81498___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__111665___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__81498___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__81498___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__111654___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNat.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNat_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__81490___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__66902___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__66902___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__750___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__82195___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.ldiff',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__760___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__66902___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__736___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__66902___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
c_24__type__111605___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__750___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__66906___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__66921___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_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__780___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__793___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__793___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__184___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__184___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__98489___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__81758___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.iter',axiom,
c_24__type__98214___24t(cCoq_2ePArith_2eBinPos_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.iter_op',axiom,
c_24__type__81745___24t(cCoq_2ePArith_2eBinPos_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__81758___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__81758___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPos_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__111844___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPos_2ePos_2et) ).
fof('$_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__83216___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__98218___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare_cont',axiom,
c_24__type__111715___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
c_24__type__184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.divide',axiom,
c_24__type__81758___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2edivide) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__81731___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__98214___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__81745___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__81725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__81725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__81725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__81755___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__81755___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
c_24__type__184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__765___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__81725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__184___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__111762___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__104739___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__91534___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__104734___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__76169___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__66434___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('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__76180___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__76180___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__76169___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__76180___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__76180___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__66430___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__66430___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__76169___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__66430___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__104787___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__102442___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__95261___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__152___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__95261___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__152___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__66985___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_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__111341___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.N_as_DT.eq',axiom,
c_24__type__81498___24t(cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Nat_as_DT.eq',axiom,
c_24__type__66425___24t(cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Positive_as_DT.eq',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Z_as_DT.eq',axiom,
c_24__type__67173___24t(cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2eeq) ).
fof('$_typeof_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__102161___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedType.EQ',axiom,
c_24__type__184467___24t(cCoq_2eStructures_2eOrderedType_2eEQ) ).
fof('$_typeof_Coq.Structures.OrderedType.GT',axiom,
c_24__type__184498___24t(cCoq_2eStructures_2eOrderedType_2eGT) ).
fof('$_typeof_Coq.Structures.OrderedType.LT',axiom,
c_24__type__184436___24t(cCoq_2eStructures_2eOrderedType_2eLT) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__81498___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__81498___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__66425___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__66425___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
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.bits_lt',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__81758___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__111866___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__111866___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
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__67173___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__67173___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_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.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__67175___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.Vector.t',axiom,
c_24__type__78980___24t(cCoq_2eVectors_2eVector_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__79005___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__78997___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__78980___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__111906___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__111910___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lnot',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinInt_2eZ_2elnot) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinInt_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinInt_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__67173___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__84011___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__82249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__84006___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__98635___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__729___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__98635___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__98611___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__81920___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__66769___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__66773___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__84011___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__82249___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__84015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__729___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.eqm',axiom,
c_24__type__99157___24t(cCoq_2eZArith_2eZdiv_2eeqm) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__76072___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__76072___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__82716___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
c_24__type__793___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__66425___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__102442___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__111524___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__104083___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__104080___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__104099___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__104086___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__104091___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__104102___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__104102___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).
fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__104785___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
c_24__type__104781___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__104781___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
c_24__type__104785___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__104781___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
c_24__type__104776___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__104778___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__104836___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__104810___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
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('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__111385___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__111350___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__103486___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__111350___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__111368___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__66383___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__152___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.bits_lt',axiom,
c_24__type__81758___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.eq',axiom,
c_24__type__81758___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2eeq) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.t',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__81173___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.elt',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eelt) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.tree',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2etree) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
c_24__type__98635___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__81920___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__90295___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__104153___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__90298___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__104158___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__152___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__152___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__152___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__66902___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__136864___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__91337___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__91337___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__91424___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__74590___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__110306___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__110306___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__481___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__486___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__478___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__486___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__91894___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__110311___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__486___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__152___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__110304___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__110291___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__66563___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__110296___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__152___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__110329___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
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('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__78373___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__78373___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__78384___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__66902___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__77030___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__91912___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_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__104792___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__104792___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_LF.Basics.NatPlayground.nat',axiom,
cType___24t(cLF_2eBasics_2eNatPlayground_2enat) ).
fof('$_typeof_LF.Basics.NatPlayground.nat\'',axiom,
cType___24t(cLF_2eBasics_2eNatPlayground_2enat_27) ).
fof('$_typeof_LF.Basics.andb',axiom,
c_24__type__82269___24t(cLF_2eBasics_2eandb) ).
fof('$_typeof_LF.Basics.andb3',axiom,
c_24__type__82276___24t(cLF_2eBasics_2eandb3) ).
fof('$_typeof_LF.Basics.bin',axiom,
cType___24t(cLF_2eBasics_2ebin) ).
fof('$_typeof_LF.Basics.bin_to_nat',axiom,
c_24__type__104011___24t(cLF_2eBasics_2ebin__to__nat) ).
fof('$_typeof_LF.Basics.bit',axiom,
cType___24t(cLF_2eBasics_2ebit) ).
fof('$_typeof_LF.Basics.bool',axiom,
cType___24t(cLF_2eBasics_2ebool) ).
fof('$_typeof_LF.Basics.color',axiom,
cType___24t(cLF_2eBasics_2ecolor) ).
fof('$_typeof_LF.Basics.day',axiom,
cType___24t(cLF_2eBasics_2eday) ).
fof('$_typeof_LF.Basics.factorial',axiom,
c_24__type__6___24t(cLF_2eBasics_2efactorial) ).
fof('$_typeof_LF.Basics.false',axiom,
cLF_2eBasics_2ebool___24t(cLF_2eBasics_2efalse) ).
fof('$_typeof_LF.Basics.ltb',axiom,
c_24__type__66863___24t(cLF_2eBasics_2eltb) ).
fof('$_typeof_LF.Basics.minustwo',axiom,
c_24__type__6___24t(cLF_2eBasics_2eminustwo) ).
fof('$_typeof_LF.Basics.nandb',axiom,
c_24__type__82269___24t(cLF_2eBasics_2enandb) ).
fof('$_typeof_LF.Basics.nybble',axiom,
cType___24t(cLF_2eBasics_2enybble) ).
fof('$_typeof_LF.Basics.orb',axiom,
c_24__type__82269___24t(cLF_2eBasics_2eorb) ).
fof('$_typeof_LF.Basics.rgb',axiom,
cType___24t(cLF_2eBasics_2ergb) ).
fof('$_typeof_LF.Basics.saturday',axiom,
cLF_2eBasics_2eday___24t(cLF_2eBasics_2esaturday) ).
fof('$_typeof_LF.Basics.true',axiom,
cLF_2eBasics_2ebool___24t(cLF_2eBasics_2etrue) ).
fof('$_typeof_LF.Basics.tuesday',axiom,
cLF_2eBasics_2eday___24t(cLF_2eBasics_2etuesday) ).
fof('$_typeof_LF.Induction.nat_to_bin',axiom,
c_24__type__104571___24t(cLF_2eInduction_2enat__to__bin) ).
fof('$_typeof_LF.Lists.NatList.None',axiom,
cLF_2eLists_2eNatList_2enatoption___24t(cLF_2eLists_2eNatList_2eNone) ).
fof('$_typeof_LF.Lists.NatList.Some',axiom,
c_24__type__66752___24t(cLF_2eLists_2eNatList_2eSome) ).
fof('$_typeof_LF.Lists.NatList.add',axiom,
c_24__type__56___24t(cLF_2eLists_2eNatList_2eadd) ).
fof('$_typeof_LF.Lists.NatList.alternate',axiom,
c_24__type__66924___24t(cLF_2eLists_2eNatList_2ealternate) ).
fof('$_typeof_LF.Lists.NatList.bag',axiom,
cType___24t(cLF_2eLists_2eNatList_2ebag) ).
fof('$_typeof_LF.Lists.NatList.cons',axiom,
c_24__type__50___24t(cLF_2eLists_2eNatList_2econs) ).
fof('$_typeof_LF.Lists.NatList.count',axiom,
c_24__type__53___24t(cLF_2eLists_2eNatList_2ecount) ).
fof('$_typeof_LF.Lists.NatList.countoddmembers',axiom,
c_24__type__66745___24t(cLF_2eLists_2eNatList_2ecountoddmembers) ).
fof('$_typeof_LF.Lists.NatList.eqblist',axiom,
c_24__type__81698___24t(cLF_2eLists_2eNatList_2eeqblist) ).
fof('$_typeof_LF.Lists.NatList.fst',axiom,
c_24__type__111677___24t(cLF_2eLists_2eNatList_2efst) ).
fof('$_typeof_LF.Lists.NatList.hd',axiom,
c_24__type__81678___24t(cLF_2eLists_2eNatList_2ehd) ).
fof('$_typeof_LF.Lists.NatList.hd_error',axiom,
c_24__type__66754___24t(cLF_2eLists_2eNatList_2ehd__error) ).
fof('$_typeof_LF.Lists.NatList.member',axiom,
c_24__type__66927___24t(cLF_2eLists_2eNatList_2emember) ).
fof('$_typeof_LF.Lists.NatList.natlist',axiom,
cType___24t(cLF_2eLists_2eNatList_2enatlist) ).
fof('$_typeof_LF.Lists.NatList.natoption',axiom,
cType___24t(cLF_2eLists_2eNatList_2enatoption) ).
fof('$_typeof_LF.Lists.NatList.natprod',axiom,
cType___24t(cLF_2eLists_2eNatList_2enatprod) ).
fof('$_typeof_LF.Lists.NatList.nil',axiom,
cLF_2eLists_2eNatList_2enatlist___24t(cLF_2eLists_2eNatList_2enil) ).
fof('$_typeof_LF.Lists.NatList.nonzeros',axiom,
c_24__type__81683___24t(cLF_2eLists_2eNatList_2enonzeros) ).
fof('$_typeof_LF.Lists.NatList.oddmembers',axiom,
c_24__type__81683___24t(cLF_2eLists_2eNatList_2eoddmembers) ).
fof('$_typeof_LF.Lists.NatList.option_elim',axiom,
c_24__type__137555___24t(cLF_2eLists_2eNatList_2eoption__elim) ).
fof('$_typeof_LF.Lists.NatList.pair',axiom,
c_24__type__111672___24t(cLF_2eLists_2eNatList_2epair) ).
fof('$_typeof_LF.Lists.NatList.remove_all',axiom,
c_24__type__56___24t(cLF_2eLists_2eNatList_2eremove__all) ).
fof('$_typeof_LF.Lists.NatList.remove_one',axiom,
c_24__type__56___24t(cLF_2eLists_2eNatList_2eremove__one) ).
fof('$_typeof_LF.Lists.NatList.snd',axiom,
c_24__type__111677___24t(cLF_2eLists_2eNatList_2esnd) ).
fof('$_typeof_LF.Lists.NatList.subset',axiom,
c_24__type__81691___24t(cLF_2eLists_2eNatList_2esubset) ).
fof('$_typeof_LF.Lists.NatList.sum',axiom,
c_24__type__81687___24t(cLF_2eLists_2eNatList_2esum) ).
fof('$_typeof_LF.Lists.PartialMap.partial_map',axiom,
cType___24t(cLF_2eLists_2ePartialMap_2epartial__map) ).
fof('$_typeof_LF.Lists.baz',axiom,
cType___24t(cLF_2eLists_2ebaz) ).
fof('$_typeof_LF.Lists.id',axiom,
cType___24t(cLF_2eLists_2eid) ).
fof('$_typeof_Poly.Exercises.Church.cnat',axiom,
cType___24t(cPoly_2eExercises_2eChurch_2ecnat) ).
fof('$_typeof_Poly.Exercises.Church.one',axiom,
cPoly_2eExercises_2eChurch_2ecnat___24t(cPoly_2eExercises_2eChurch_2eone) ).
fof('$_typeof_Poly.Exercises.Church.plus',axiom,
c_24__type__192795___24t(cPoly_2eExercises_2eChurch_2eplus) ).
fof('$_typeof_Poly.Exercises.Church.succ',axiom,
c_24__type__191699___24t(cPoly_2eExercises_2eChurch_2esucc) ).
fof('$_typeof_Poly.Exercises.Church.three',axiom,
cPoly_2eExercises_2eChurch_2ecnat___24t(cPoly_2eExercises_2eChurch_2ethree) ).
fof('$_typeof_Poly.Exercises.Church.two',axiom,
cPoly_2eExercises_2eChurch_2ecnat___24t(cPoly_2eExercises_2eChurch_2etwo) ).
fof('$_typeof_Poly.Exercises.Church.zero',axiom,
cPoly_2eExercises_2eChurch_2ecnat___24t(cPoly_2eExercises_2eChurch_2ezero) ).
fof('$_typeof_Poly.MumbleGrumble.grumble',axiom,
c_24__type__152___24t(cPoly_2eMumbleGrumble_2egrumble) ).
fof('$_typeof_Poly.MumbleGrumble.mumble',axiom,
cType___24t(cPoly_2eMumbleGrumble_2emumble) ).
fof('$_typeof_Poly.OptionPlayground.option',axiom,
c_24__type__152___24t(cPoly_2eOptionPlayground_2eoption) ).
fof('$_typeof_Poly.boollist',axiom,
cType___24t(cPoly_2eboollist) ).
fof('$_typeof_Poly.cons',axiom,
c_24__type__171___24t(cPoly_2econs) ).
fof('$_typeof_Poly.constfun',axiom,
c_24__type__154264___24t(cPoly_2econstfun) ).
fof('$_typeof_Poly.doit3times',axiom,
c_24__type__152866___24t(cPoly_2edoit3times) ).
fof('$_typeof_Poly.list',axiom,
c_24__type__152___24t(cPoly_2elist) ).
fof('$_typeof_Poly.list\'',axiom,
c_24__type__152___24t(cPoly_2elist_27) ).
fof('$_typeof_Poly.nil',axiom,
c_24__type__166___24t(cPoly_2enil) ).
fof('$_typeof_Poly.pair',axiom,
c_24__type__142570___24t(cPoly_2epair) ).
fof('$_typeof_Poly.prod',axiom,
c_24__type__66383___24t(cPoly_2eprod) ).
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.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.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.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_assoc',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,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
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.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_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__37___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_lt_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_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
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__66425,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__38,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_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_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_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
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.mul_assoc',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_2emul___24a2(V0__n,cCoq_2eInit_2eNat_2emul___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
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.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.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.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_comm',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V1__b2,V0__b1) ) ) ).
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_24136210___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221___24a5(V0__A,V1__a,V2__a_27,V3__b,V4__b_27) ) ) ) ) ) ).
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_24136199___24a4(V0__A,V1__b,V2__x,V3__y) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136204___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_24136226___24a4(V0__A,V1__a,V2__a_27,V3__b) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136231___24a4(V0__A,V1__a,V2__a_27,V3__b) ) ) ) ) ).
fof('Coq.Bool.Bool.orb_comm',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V1__b2,V0__b1) ) ) ).
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.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__74643___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__38___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.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__76075___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.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__66425___24t(V0__R)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).
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_and_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(V1__B)
=> p(c_24False) ) ) ) ) ) ).
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_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__95362___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).
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__104135___24a2(V0__U,V1__P),V2__p,V4__x,V3__q,V5__y)
=> V4__x = V5__y ) ) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.f_eq_dep_non_dep',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__95362___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__104150___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.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.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.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.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.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_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.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_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__111662___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.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_trans',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_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__81498,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__82890,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_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_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.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.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__82716___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_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_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.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.iter_invariant',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__f] :
( c_24__type__711___24t(V1__A,V2__f)
=> ! [V3__Inv] :
( c_24__type__78559___24t(V1__A,V3__Inv)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> ( p(happ(V3__Inv,V4__x))
=> p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
=> ! [V5__x] :
( t(V5__x,V1__A)
=> ( p(happ(V3__Inv,V5__x))
=> p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__p))) ) ) ) ) ) ) ) ).
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.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.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_le',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)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
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.ZArith.BinInt.Z.Private_BootStrap.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.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_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.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_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.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_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.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__99129___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_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__67173,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__76072,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_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_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
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.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_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.mul_shuffle0',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(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle1',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)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V3__q)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V3__q)) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
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__98187___24a2(V0__x,V1__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.micromega.ZMicromega.Vars.Facts.MP.equal_refl',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V0__s) ) ).
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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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.ARmul_comm',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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___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__702___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__702___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__711___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.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.mk_rt',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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__702___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__711___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__75779___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> ! [V13__y] :
( t(V13__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ! [V15__z] :
( t(V15__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_srt',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__702___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__702___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__75779___24t(V0__R,V5__req)
=> ( ! [V6__n] :
( t(V6__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V1__rO),V6__n)),V6__n)) )
=> ( ! [V7__n] :
( t(V7__n,V0__R)
=> ! [V8__m] :
( t(V8__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V7__n),V8__m)),happ(happ(V3__radd,V8__m),V7__n))) ) )
=> ( ! [V8__n] :
( t(V8__n,V0__R)
=> ! [V9__m] :
( t(V9__m,V0__R)
=> ! [V10__p] :
( t(V10__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V8__n),happ(happ(V3__radd,V9__m),V10__p))),happ(happ(V3__radd,happ(happ(V3__radd,V8__n),V9__m)),V10__p))) ) ) )
=> ( ! [V9__n] :
( t(V9__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V2__rI),V9__n)),V9__n)) )
=> ( ! [V10__n] :
( t(V10__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V1__rO),V10__n)),V1__rO)) )
=> ( ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V11__n),V12__m)),happ(happ(V4__rmul,V12__m),V11__n))) ) )
=> ( ! [V12__n] :
( t(V12__n,V0__R)
=> ! [V13__m] :
( t(V13__m,V0__R)
=> ! [V14__p] :
( t(V14__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V12__n),happ(happ(V4__rmul,V13__m),V14__p))),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__n),V13__m)),V14__p))) ) ) )
=> ( ! [V13__n] :
( t(V13__n,V0__R)
=> ! [V14__m] :
( t(V14__m,V0__R)
=> ! [V15__p] :
( t(V15__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,happ(happ(V3__radd,V13__n),V14__m)),V15__p)),happ(happ(V3__radd,happ(happ(V4__rmul,V13__n),V15__p)),happ(happ(V4__rmul,V14__m),V15__p)))) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('LF.Induction.plus_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('Poly.Exercises.Church.plus_1',axiom,
cPoly_2eExercises_2eChurch_2eplus___24a2(cPoly_2eExercises_2eChurch_2ezero,cPoly_2eExercises_2eChurch_2eone) = cPoly_2eExercises_2eChurch_2eone ).
fof('Poly.Exercises.Church.succ_1',axiom,
cPoly_2eExercises_2eChurch_2esucc___24a1(cPoly_2eExercises_2eChurch_2ezero) = cPoly_2eExercises_2eChurch_2eone ).
fof('Poly.Exercises.Church.succ_2',axiom,
cPoly_2eExercises_2eChurch_2esucc___24a1(cPoly_2eExercises_2eChurch_2eone) = cPoly_2eExercises_2eChurch_2etwo ).
fof('Poly.Exercises.Church.succ_3',axiom,
cPoly_2eExercises_2eChurch_2esucc___24a1(cPoly_2eExercises_2eChurch_2etwo) = cPoly_2eExercises_2eChurch_2ethree ).
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('$adef_Coq.NArith.Ndigits.eqf_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.bool$136231_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136231,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136231___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$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('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.Init.Datatypes.BoolSpec_$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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___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('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___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('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$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('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.Tauto.Cj_$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('$adef_LF.Lists.NatList.fst_$a1',axiom,
! [V_24X1] : happ(cLF_2eLists_2eNatList_2efst,V_24X1) = cLF_2eLists_2eNatList_2efst___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPos.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
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('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Poly.Exercises.Church.plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eExercises_2eChurch_2eplus,V_24X1),V_24X2) = cPoly_2eExercises_2eChurch_2eplus___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.Env.Env_$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('$adef_Poly.nil\'_$a1',axiom,
! [V_24X1] : happ(cPoly_2enil_27,V_24X1) = cPoly_2enil_27___24a1(V_24X1) ).
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('$adef_Coq.Init.Nat.compare_$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('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$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('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
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('$adef_$_case_Coq.Init.Datatypes.bool$136204_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136204,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136204___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('$adef_$_prop_103982_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__103982,V_24X1),V_24X2),V_24X3) = c_24__prop__103982___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_LF.Basics.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eBasics_2eorb,V_24X1),V_24X2) = cLF_2eBasics_2eorb___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_103980_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__103980,V_24X1),V_24X2),V_24X3) = c_24__prop__103980___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Vectors.Vector.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVector_2enil,V_24X1) = cCoq_2eVectors_2eVector_2enil___24a1(V_24X1) ).
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('$adef_$_case_Coq.Numbers.BinNums.positive$111803_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24111803___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_111748_$a1',axiom,
! [V_24X1] : happ(c_24__lam__111748,V_24X1) = c_24__lam__111748___24a1(V_24X1) ).
fof('$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_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$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.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_Coq.PArith.BinPos.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$136221_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136221___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_37_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37,V_24X1),V_24X2) = c_24__prop__37___24a2(V_24X1,V_24X2) ).
fof('$adef_Poly.Exercises.Church.one_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2eExercises_2eChurch_2eone,V_24X1),V_24X2),V_24X3) = cPoly_2eExercises_2eChurch_2eone___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_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_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$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_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_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_Poly.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cPoly_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cPoly_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_LF.Lists.NatList.Some_$a1',axiom,
! [V_24X1] : happ(cLF_2eLists_2eNatList_2eSome,V_24X1) = cLF_2eLists_2eNatList_2eSome___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
fof('$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_Poly.list_$a1',axiom,
! [V_24X1] : happ(cPoly_2elist,V_24X1) = cPoly_2elist___24a1(V_24X1) ).
fof('$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.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_LF.Basics.bits_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cLF_2eBasics_2ebits,V_24X1),V_24X2),V_24X3),V_24X4) = cLF_2eBasics_2ebits___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esquare,V_24X1) = cCoq_2eInit_2eNat_2esquare___24a1(V_24X1) ).
fof('$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_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_LF.Basics.B_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eB,V_24X1) = cLF_2eBasics_2eB___24a1(V_24X1) ).
fof('$adef_Poly.constfun_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2econstfun,V_24X1),V_24X2),V_24X3) = cPoly_2econstfun___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.PArith.BinPosDef.Pos.compare_cont_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_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_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$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.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$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_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_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_LF.Basics.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eBasics_2eandb,V_24X1),V_24X2) = cLF_2eBasics_2eandb___24a2(V_24X1,V_24X2) ).
fof('$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_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_$_lam_82206_$a1',axiom,
! [V_24X1] : happ(c_24__lam__82206,V_24X1) = c_24__lam__82206___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Poly.cons\'_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2econs_27,V_24X1),V_24X2),V_24X3) = cPoly_2econs_27___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_LF.Basics.A_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eA,V_24X1) = cLF_2eBasics_2eA___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Poly.MumbleGrumble.grumble_$a1',axiom,
! [V_24X1] : happ(cPoly_2eMumbleGrumble_2egrumble,V_24X1) = cPoly_2eMumbleGrumble_2egrumble___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('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$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('$adef_$_lam_111642_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__111642,V_24X1),V_24X2) = c_24__lam__111642___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$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_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_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$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_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_$_lam_111748_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__111748,V_24X1),V_24X2) = c_24__lam__111748___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('$adef_Coq.Init.Logic.eq_refl_$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('$adef_Coq.Lists.List.fold_left_$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('$adef_$_prop_111571_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__111571,V_24X1),V_24X2),V_24X3) = c_24__prop__111571___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_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_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V_24X1) ).
fof('$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_$_lam_104135_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__104135,V_24X1),V_24X2),V_24X3) = c_24__lam__104135___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Strings.Ascii.Ascii_$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('$adef_$_lam_111755_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__111755,V_24X1),V_24X2) = c_24__lam__111755___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_LF.Basics.minustwo_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eminustwo,V_24X1) = cLF_2eBasics_2eminustwo___24a1(V_24X1) ).
fof('$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_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_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$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_Poly.OptionPlayground.None_$a1',axiom,
! [V_24X1] : happ(cPoly_2eOptionPlayground_2eNone,V_24X1) = cPoly_2eOptionPlayground_2eNone___24a1(V_24X1) ).
fof('$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_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_$_lam_111755_$a1',axiom,
! [V_24X1] : happ(c_24__lam__111755,V_24X1) = c_24__lam__111755___24a1(V_24X1) ).
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('$adef_Coq.Init.Nat.pow_$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('$adef_Coq.ZArith.BinIntDef.Z.even_$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('$adef_$_prop_103979_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__103979,V_24X1),V_24X2),V_24X3) = c_24__prop__103979___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_LF.Lists.Baz2_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eLists_2eBaz2,V_24X1),V_24X2) = cLF_2eLists_2eBaz2___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Vectors.Vector.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVector_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVector_2et___24a2(V_24X1,V_24X2) ).
fof('$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.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$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.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_LF.Lists.Baz1_$a1',axiom,
! [V_24X1] : happ(cLF_2eLists_2eBaz1,V_24X1) = cLF_2eLists_2eBaz1___24a1(V_24X1) ).
fof('$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.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$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_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.micromega.ZMicromega.Vars.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_case_Coq.Init.Datatypes.nat$102413_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24102413,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24102413___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_LF.Lists.PartialMap.record_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLF_2eLists_2ePartialMap_2erecord,V_24X1),V_24X2),V_24X3) = cLF_2eLists_2ePartialMap_2erecord___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Empty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty,V_24X1))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V_24X1) ) ).
fof('$adef_Poly.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2econs,V_24X1),V_24X2),V_24X3) = cPoly_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.NArith.BinNatDef.N.land_$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('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___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('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
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('$adef_Coq.Init.Peano.le_$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('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
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('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Poly.OptionPlayground.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eOptionPlayground_2eSome,V_24X1),V_24X2) = cPoly_2eOptionPlayground_2eSome___24a2(V_24X1,V_24X2) ).
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('$adef_Poly.MumbleGrumble.b_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eMumbleGrumble_2eb,V_24X1),V_24X2) = cPoly_2eMumbleGrumble_2eb___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.BinInt.Z.eqf_$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('$adef_Coq.NArith.BinNatDef.N.testbit_$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('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$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('$adef_$_prop_111572_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__111572,V_24X1),V_24X2),V_24X3) = c_24__prop__111572___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_LF.Lists.NatList.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eLists_2eNatList_2econs,V_24X1),V_24X2) = cLF_2eLists_2eNatList_2econs___24a2(V_24X1,V_24X2) ).
fof('$adef_LF.Basics.NatPlayground.S_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eNatPlayground_2eS,V_24X1) = cLF_2eBasics_2eNatPlayground_2eS___24a1(V_24X1) ).
fof('$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_LF.Lists.NatList.option_elim_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eLists_2eNatList_2eoption__elim,V_24X1),V_24X2) = cLF_2eLists_2eNatList_2eoption__elim___24a2(V_24X1,V_24X2) ).
fof('$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.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_Coq.NArith.BinNatDef.N.succ_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).
fof('$adef_Poly.MumbleGrumble.e_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eMumbleGrumble_2ee,V_24X1),V_24X2) = cPoly_2eMumbleGrumble_2ee___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$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_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Poly.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eprod,V_24X1),V_24X2) = cPoly_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Poly.list\'_$a1',axiom,
! [V_24X1] : happ(cPoly_2elist_27,V_24X1) = cPoly_2elist_27___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zdiv.eqm_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZdiv_2eeqm,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZdiv_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Coq.FSets.FSetPositive.PositiveSet.E.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_prop_103981_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__103981,V_24X1),V_24X2),V_24X3) = c_24__prop__103981___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$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('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
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_99129_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__99129,V_24X1),V_24X2) = c_24__prop__99129___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_103978_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__103978,V_24X1),V_24X2),V_24X3) = c_24__prop__103978___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___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('$adef_Coq.micromega.ZMicromega.Vars.E.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Bool.Bool.eqb_$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('$adef_Coq.NArith.BinNatDef.N.div_eucl_$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('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.micromega.ZMicromega.isZ0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eisZ0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V_24X1) ).
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('$adef_$_let_var_6_p_91898_91901_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__91898__91901,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__91898__91901___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$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_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_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_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_Poly.MumbleGrumble.d_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2eMumbleGrumble_2ed,V_24X1),V_24X2) = cPoly_2eMumbleGrumble_2ed___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_91900_91902_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__91900__91902,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__91900__91902___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Poly.doit3times_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2edoit3times,V_24X1),V_24X2),V_24X3) = cPoly_2edoit3times___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_fix_111819_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__111819__v__CANONICAL__0,V_24X1) = c_24__fix__111819__v__CANONICAL__0___24a1(V_24X1) ).
fof('$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_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_$_prop_111570_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__111570,V_24X1),V_24X2) = c_24__prop__111570___24a2(V_24X1,V_24X2) ).
fof('$adef_Poly.OptionPlayground.option_$a1',axiom,
! [V_24X1] : happ(cPoly_2eOptionPlayground_2eoption,V_24X1) = cPoly_2eOptionPlayground_2eoption___24a1(V_24X1) ).
fof('$adef_$_lam_111759_$a1',axiom,
! [V_24X1] : happ(c_24__lam__111759,V_24X1) = c_24__lam__111759___24a1(V_24X1) ).
fof('$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_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.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_prop_98187_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__98187,V_24X1),V_24X2) = c_24__prop__98187___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_111662_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__111662,V_24X1),V_24X2) = c_24__prop__111662___24a2(V_24X1,V_24X2) ).
fof('$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_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.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.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_case_Coq.Numbers.BinNums.Z$102430_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24102430___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('$adef_Coq.PArith.BinPosDef.Pos.min_$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('$adef_LF.Lists.NatList.hd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eLists_2eNatList_2ehd,V_24X1),V_24X2) = cLF_2eLists_2eNatList_2ehd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
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('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_LF.Basics.NatPlayground.tick_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eNatPlayground_2etick,V_24X1) = cLF_2eBasics_2eNatPlayground_2etick___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
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('$adef_$_lam_82206_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__82206,V_24X1),V_24X2) = c_24__lam__82206___24a2(V_24X1,V_24X2) ).
fof('$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_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_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$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_$_lam_111642_$a1',axiom,
! [V_24X1] : happ(c_24__lam__111642,V_24X1) = c_24__lam__111642___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Init.Datatypes.nat_rect_$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('$adef_$_prop_103977_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__103977,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__103977___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.Zdivide_pol_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eZdivide__pol,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V_24X1,V_24X2) ) ).
fof('$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.PArith.BinPosDef.Pos.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eldiff___24a2(V_24X1,V_24X2) ).
fof('$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.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_case_Coq.Init.Datatypes.bool$136199_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136199,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136199___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_LF.Lists.Id_$a1',axiom,
! [V_24X1] : happ(cLF_2eLists_2eId,V_24X1) = cLF_2eLists_2eId___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
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('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_Coq.ZArith.BinInt.Z.le_$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('$adef_LF.Lists.NatList.snd_$a1',axiom,
! [V_24X1] : happ(cLF_2eLists_2eNatList_2esnd,V_24X1) = cLF_2eLists_2eNatList_2esnd___24a1(V_24X1) ).
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('$adef_Coq.NArith.BinNatDef.N.ldiff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eldiff,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eldiff___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Specif.inleft_$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('$adef_Coq.Init.Datatypes.cons_$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('$adef_Coq.setoid_ring.Field_theory.field_theory_$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('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
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('$adef_Poly.nil_$a1',axiom,
! [V_24X1] : happ(cPoly_2enil,V_24X1) = cPoly_2enil___24a1(V_24X1) ).
fof('$adef_Poly.Exercises.Church.succ_$a1',axiom,
! [V_24X1] : happ(cPoly_2eExercises_2eChurch_2esucc,V_24X1) = cPoly_2eExercises_2eChurch_2esucc___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('$adef_Poly.Exercises.Church.two_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2eExercises_2eChurch_2etwo,V_24X1),V_24X2),V_24X3) = cPoly_2eExercises_2eChurch_2etwo___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
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('$adef_Coq.ZArith.BinInt.Z.lnot_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2elnot,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2elnot___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$136226_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136226,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136226___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.PArith.BinPos.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___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('$adef_Coq.setoid_ring.Field_theory.FEI_$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('$adef_$_case_Coq.Init.Datatypes.bool$136210_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136210,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24136210___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2epred,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V_24X1) ).
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('$adef_Coq.NArith.BinNatDef.N.lxor_$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('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.lxor_$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('$adef_Coq.Arith.PeanoNat.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
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('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Znat.neq_$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('$adef_LF.Lists.NatList.pair_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLF_2eLists_2eNatList_2epair,V_24X1),V_24X2) = cLF_2eLists_2eNatList_2epair___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___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('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_Poly.bool_cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cPoly_2ebool__cons,V_24X1),V_24X2) = cPoly_2ebool__cons___24a2(V_24X1,V_24X2) ).
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('$adef_Poly.Exercises.Church.zero_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPoly_2eExercises_2eChurch_2ezero,V_24X1),V_24X2),V_24X3) = cPoly_2eExercises_2eChurch_2ezero___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Lists.List.tl_$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('$adef_$_case_Coq.Init.Datatypes.nat$102435_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24102435___24a1(V_24X1) ).
fof('$adef_$_lam_104135_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__104135,V_24X1),V_24X2) = c_24__lam__104135___24a2(V_24X1,V_24X2) ).
fof('$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_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_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.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_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.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_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$110919_$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_24110919,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_24110919___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$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('$adef_LF.Basics.primary_$a1',axiom,
! [V_24X1] : happ(cLF_2eBasics_2eprimary,V_24X1) = cLF_2eBasics_2eprimary___24a1(V_24X1) ).
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('$adef_$_prop_103983_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__103983,V_24X1),V_24X2) = c_24__prop__103983___24a2(V_24X1,V_24X2) ).
fof('$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.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_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.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.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_Coq.Vectors.Vector.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVector_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVector_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_91894',axiom,
! [V_24Y] :
( c_24__type__91894___24t(V_24Y)
<=> t(V_24Y,c_24__type__91894) ) ).
fof('$tdef_$_type_99786',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__99786___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__99786___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_66902',axiom,
! [V_24Y] :
( c_24__type__66902___24t(V_24Y)
<=> t(V_24Y,c_24__type__66902) ) ).
fof('$tdef_$_type_104011',axiom,
! [V_24Y] :
( c_24__type__104011___24t(V_24Y)
<=> t(V_24Y,c_24__type__104011) ) ).
fof('$tdef_$_type_93159',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__93159___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__93159___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___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_$_type_82890',axiom,
! [V_24Y] :
( c_24__type__82890___24t(V_24Y)
<=> t(V_24Y,c_24__type__82890) ) ).
fof('$tdef_$_type_478',axiom,
! [V_24Y] :
( c_24__type__478___24t(V_24Y)
<=> t(V_24Y,c_24__type__478) ) ).
fof('$tdef_$_type_104734',axiom,
! [V_24Y] :
( c_24__type__104734___24t(V_24Y)
<=> t(V_24Y,c_24__type__104734) ) ).
fof('$tdef_$_type_95235',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__95235___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__95235___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_108798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__108798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__108798___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_101695',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__101695___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__101695___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.Vars.E.t',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et) ) ).
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_$_type_78641',axiom,
! [V_24Y] :
( c_24__type__78641___24t(V_24Y)
<=> t(V_24Y,c_24__type__78641) ) ).
fof('$tdef_$_type_184498',axiom,
! [V_24Y] :
( c_24__type__184498___24t(V_24Y)
<=> t(V_24Y,c_24__type__184498) ) ).
fof('$tdef_$_type_66921',axiom,
! [V_24Y] :
( c_24__type__66921___24t(V_24Y)
<=> t(V_24Y,c_24__type__66921) ) ).
fof('$tdef_$_type_135730',axiom,
! [V_24Y] :
( c_24__type__135730___24t(V_24Y)
<=> t(V_24Y,c_24__type__135730) ) ).
fof('$tdef_LF.Basics.day',axiom,
! [V_24Y] :
( cLF_2eBasics_2eday___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2eday) ) ).
fof('$tdef_$_type_91468',axiom,
! [V_24Y] :
( c_24__type__91468___24t(V_24Y)
<=> t(V_24Y,c_24__type__91468) ) ).
fof('$tdef_$_type_82020',axiom,
! [V_24Y] :
( c_24__type__82020___24t(V_24Y)
<=> t(V_24Y,c_24__type__82020) ) ).
fof('$tdef_$_type_76704',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76704___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76704___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.ZArith.BinInt.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinInt_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinInt_2eZ_2et) ) ).
fof('$tdef_$_type_81691',axiom,
! [V_24Y] :
( c_24__type__81691___24t(V_24Y)
<=> t(V_24Y,c_24__type__81691) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_Coq.NArith.BinNat.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNat_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNat_2eN_2et) ) ).
fof('$tdef_$_type_94419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__94419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__94419___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_66411',axiom,
! [V_24Y] :
( c_24__type__66411___24t(V_24Y)
<=> t(V_24Y,c_24__type__66411) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_74620',axiom,
! [V_24Y] :
( c_24__type__74620___24t(V_24Y)
<=> t(V_24Y,c_24__type__74620) ) ).
fof('$tdef_LF.Lists.baz',axiom,
! [V_24Y] :
( cLF_2eLists_2ebaz___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2ebaz) ) ).
fof('$tdef_$_type_111245',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__111245___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__111245___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_104725',axiom,
! [V_24Y] :
( c_24__type__104725___24t(V_24Y)
<=> t(V_24Y,c_24__type__104725) ) ).
fof('$tdef_$_type_103178',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103178___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103178___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_LF.Basics.bin',axiom,
! [V_24Y] :
( cLF_2eBasics_2ebin___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2ebin) ) ).
fof('$tdef_Poly.MumbleGrumble.grumble',axiom,
! [V_24X1,V_24Y] :
( cPoly_2eMumbleGrumble_2egrumble___24t(V_24X1,V_24Y)
<=> t(V_24Y,cPoly_2eMumbleGrumble_2egrumble___24a1(V_24X1)) ) ).
fof('$tdef_$_type_82218',axiom,
! [V_24Y] :
( c_24__type__82218___24t(V_24Y)
<=> t(V_24Y,c_24__type__82218) ) ).
fof('$tdef_$_type_103196',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103196___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103196___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_81652',axiom,
! [V_24Y] :
( c_24__type__81652___24t(V_24Y)
<=> t(V_24Y,c_24__type__81652) ) ).
fof('$tdef_$_type_75907',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75907___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75907___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_101998',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__101998___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__101998___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_104086',axiom,
! [V_24Y] :
( c_24__type__104086___24t(V_24Y)
<=> t(V_24Y,c_24__type__104086) ) ).
fof('$tdef_Poly.OptionPlayground.option',axiom,
! [V_24X1,V_24Y] :
( cPoly_2eOptionPlayground_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cPoly_2eOptionPlayground_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66866',axiom,
! [V_24Y] :
( c_24__type__66866___24t(V_24Y)
<=> t(V_24Y,c_24__type__66866) ) ).
fof('$tdef_$_type_166',axiom,
! [V_24Y] :
( c_24__type__166___24t(V_24Y)
<=> t(V_24Y,c_24__type__166) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_92346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__92346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__92346___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_100229',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__100229___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__100229___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_110764',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__110764___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__110764___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_184436',axiom,
! [V_24Y] :
( c_24__type__184436___24t(V_24Y)
<=> t(V_24Y,c_24__type__184436) ) ).
fof('$tdef_$_type_77281',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__77281___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__77281___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et) ) ).
fof('$tdef_Coq.Arith.PeanoNat.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eArith_2ePeanoNat_2eNat_2et) ) ).
fof('$tdef_$_type_82223',axiom,
! [V_24X1,V_24Y] :
( c_24__type__82223___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__82223___24a1(V_24X1)) ) ).
fof('$tdef_$_type_81984',axiom,
! [V_24Y] :
( c_24__type__81984___24t(V_24Y)
<=> t(V_24Y,c_24__type__81984) ) ).
fof('$tdef_$_type_81745',axiom,
! [V_24Y] :
( c_24__type__81745___24t(V_24Y)
<=> t(V_24Y,c_24__type__81745) ) ).
fof('$tdef_$_type_92760',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92760___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92760___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_82249',axiom,
! [V_24Y] :
( c_24__type__82249___24t(V_24Y)
<=> t(V_24Y,c_24__type__82249) ) ).
fof('$tdef_$_type_111849',axiom,
! [V_24Y] :
( c_24__type__111849___24t(V_24Y)
<=> t(V_24Y,c_24__type__111849) ) ).
fof('$tdef_$_type_100872',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__100872___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__100872___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
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_$_type_81904',axiom,
! [V_24Y] :
( c_24__type__81904___24t(V_24Y)
<=> t(V_24Y,c_24__type__81904) ) ).
fof('$tdef_$_type_75942',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75942___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75942___24a2(V_24X1,V_24X2)) ) ).
fof('$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_92409',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__92409___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__92409___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_104565',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__104565___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__104565___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_171',axiom,
! [V_24Y] :
( c_24__type__171___24t(V_24Y)
<=> t(V_24Y,c_24__type__171) ) ).
fof('$tdef_$_type_104028',axiom,
! [V_24Y] :
( c_24__type__104028___24t(V_24Y)
<=> t(V_24Y,c_24__type__104028) ) ).
fof('$tdef_$_type_103304',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__103304___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__103304___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_729',axiom,
! [V_24Y] :
( c_24__type__729___24t(V_24Y)
<=> t(V_24Y,c_24__type__729) ) ).
fof('$tdef_$_type_66863',axiom,
! [V_24Y] :
( c_24__type__66863___24t(V_24Y)
<=> t(V_24Y,c_24__type__66863) ) ).
fof('$tdef_$_type_111715',axiom,
! [V_24Y] :
( c_24__type__111715___24t(V_24Y)
<=> t(V_24Y,c_24__type__111715) ) ).
fof('$tdef_LF.Lists.NatList.natoption',axiom,
! [V_24Y] :
( cLF_2eLists_2eNatList_2enatoption___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2eNatList_2enatoption) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).
fof('$tdef_$_type_104836',axiom,
! [V_24Y] :
( c_24__type__104836___24t(V_24Y)
<=> t(V_24Y,c_24__type__104836) ) ).
fof('$tdef_$_type_104080',axiom,
! [V_24Y] :
( c_24__type__104080___24t(V_24Y)
<=> t(V_24Y,c_24__type__104080) ) ).
fof('$tdef_$_type_95295',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__95295___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__95295___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_81498',axiom,
! [V_24Y] :
( c_24__type__81498___24t(V_24Y)
<=> t(V_24Y,c_24__type__81498) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2emask) ) ).
fof('$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('$tdef_Poly.list\'',axiom,
! [V_24X1,V_24Y] :
( cPoly_2elist_27___24t(V_24X1,V_24Y)
<=> t(V_24Y,cPoly_2elist_27___24a1(V_24X1)) ) ).
fof('$tdef_$_type_110932',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__110932___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__110932___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_111677',axiom,
! [V_24Y] :
( c_24__type__111677___24t(V_24Y)
<=> t(V_24Y,c_24__type__111677) ) ).
fof('$tdef_$_type_81687',axiom,
! [V_24Y] :
( c_24__type__81687___24t(V_24Y)
<=> t(V_24Y,c_24__type__81687) ) ).
fof('$tdef_$_type_66353',axiom,
! [V_24Y] :
( c_24__type__66353___24t(V_24Y)
<=> t(V_24Y,c_24__type__66353) ) ).
fof('$tdef_$_type_53',axiom,
! [V_24Y] :
( c_24__type__53___24t(V_24Y)
<=> t(V_24Y,c_24__type__53) ) ).
fof('$tdef_LF.Basics.bit',axiom,
! [V_24Y] :
( cLF_2eBasics_2ebit___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2ebit) ) ).
fof('$tdef_$_type_94632',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__94632___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__94632___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_102122',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__102122___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__102122___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_100697',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__100697___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__100697___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_81795',axiom,
! [V_24Y] :
( c_24__type__81795___24t(V_24Y)
<=> t(V_24Y,c_24__type__81795) ) ).
fof('$tdef_$_type_110304',axiom,
! [V_24Y] :
( c_24__type__110304___24t(V_24Y)
<=> t(V_24Y,c_24__type__110304) ) ).
fof('$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_66985',axiom,
! [V_24Y] :
( c_24__type__66985___24t(V_24Y)
<=> t(V_24Y,c_24__type__66985) ) ).
fof('$tdef_$_type_77952',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__77952___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__77952___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_66383',axiom,
! [V_24Y] :
( c_24__type__66383___24t(V_24Y)
<=> t(V_24Y,c_24__type__66383) ) ).
fof('$tdef_$_type_82269',axiom,
! [V_24Y] :
( c_24__type__82269___24t(V_24Y)
<=> t(V_24Y,c_24__type__82269) ) ).
fof('$tdef_$_type_76407',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76407___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76407___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_92292',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__92292___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__92292___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_78559',axiom,
! [V_24X1,V_24Y] :
( c_24__type__78559___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__78559___24a1(V_24X1)) ) ).
fof('$tdef_$_type_100615',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__100615___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__100615___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_81960',axiom,
! [V_24Y] :
( c_24__type__81960___24t(V_24Y)
<=> t(V_24Y,c_24__type__81960) ) ).
fof('$tdef_$_type_92166',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__92166___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__92166___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_780',axiom,
! [V_24Y] :
( c_24__type__780___24t(V_24Y)
<=> t(V_24Y,c_24__type__780) ) ).
fof('$tdef_LF.Basics.color',axiom,
! [V_24Y] :
( cLF_2eBasics_2ecolor___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2ecolor) ) ).
fof('$tdef_$_type_81725',axiom,
! [V_24Y] :
( c_24__type__81725___24t(V_24Y)
<=> t(V_24Y,c_24__type__81725) ) ).
fof('$tdef_$_type_93993',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__93993___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__93993___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_104723',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__104723___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__104723___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_78556',axiom,
! [V_24Y] :
( c_24__type__78556___24t(V_24Y)
<=> t(V_24Y,c_24__type__78556) ) ).
fof('$tdef_$_type_56',axiom,
! [V_24Y] :
( c_24__type__56___24t(V_24Y)
<=> t(V_24Y,c_24__type__56) ) ).
fof('$tdef_$_type_104083',axiom,
! [V_24Y] :
( c_24__type__104083___24t(V_24Y)
<=> t(V_24Y,c_24__type__104083) ) ).
fof('$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_$_type_77030',axiom,
! [V_24Y] :
( c_24__type__77030___24t(V_24Y)
<=> t(V_24Y,c_24__type__77030) ) ).
fof('$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_66563',axiom,
! [V_24Y] :
( c_24__type__66563___24t(V_24Y)
<=> t(V_24Y,c_24__type__66563) ) ).
fof('$tdef_$_type_154264',axiom,
! [V_24Y] :
( c_24__type__154264___24t(V_24Y)
<=> t(V_24Y,c_24__type__154264) ) ).
fof('$tdef_$_type_102779',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__102779___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__102779___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_$_type_110306',axiom,
! [V_24Y] :
( c_24__type__110306___24t(V_24Y)
<=> t(V_24Y,c_24__type__110306) ) ).
fof('$tdef_$_type_104091',axiom,
! [V_24Y] :
( c_24__type__104091___24t(V_24Y)
<=> t(V_24Y,c_24__type__104091) ) ).
fof('$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_91534',axiom,
! [V_24Y] :
( c_24__type__91534___24t(V_24Y)
<=> t(V_24Y,c_24__type__91534) ) ).
fof('$tdef_$_type_111338',axiom,
! [V_24Y] :
( c_24__type__111338___24t(V_24Y)
<=> t(V_24Y,c_24__type__111338) ) ).
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_$_type_99497',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__99497___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__99497___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_95355',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__95355___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__95355___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_95303',axiom,
! [V_24Y] :
( c_24__type__95303___24t(V_24Y)
<=> t(V_24Y,c_24__type__95303) ) ).
fof('$tdef_$_type_107091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__107091___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__107091___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_110486',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__110486___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__110486___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_111469',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__111469___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__111469___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_77577',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__77577___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__77577___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_99879',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__99879___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__99879___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_184467',axiom,
! [V_24Y] :
( c_24__type__184467___24t(V_24Y)
<=> t(V_24Y,c_24__type__184467) ) ).
fof('$tdef_$_type_104129',axiom,
! [V_24Y] :
( c_24__type__104129___24t(V_24Y)
<=> t(V_24Y,c_24__type__104129) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_82716',axiom,
! [V_24Y] :
( c_24__type__82716___24t(V_24Y)
<=> t(V_24Y,c_24__type__82716) ) ).
fof('$tdef_$_type_82195',axiom,
! [V_24Y] :
( c_24__type__82195___24t(V_24Y)
<=> t(V_24Y,c_24__type__82195) ) ).
fof('$tdef_$_type_110296',axiom,
! [V_24Y] :
( c_24__type__110296___24t(V_24Y)
<=> t(V_24Y,c_24__type__110296) ) ).
fof('$tdef_Poly.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cPoly_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cPoly_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74625',axiom,
! [V_24X1,V_24Y] :
( c_24__type__74625___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__74625___24a1(V_24X1)) ) ).
fof('$tdef_$_type_111665',axiom,
! [V_24Y] :
( c_24__type__111665___24t(V_24Y)
<=> t(V_24Y,c_24__type__111665) ) ).
fof('$tdef_LF.Lists.PartialMap.partial_map',axiom,
! [V_24Y] :
( cLF_2eLists_2ePartialMap_2epartial__map___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2ePartialMap_2epartial__map) ) ).
fof('$tdef_LF.Basics.NatPlayground.nat\'',axiom,
! [V_24Y] :
( cLF_2eBasics_2eNatPlayground_2enat_27___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2eNatPlayground_2enat_27) ) ).
fof('$tdef_$_type_76003',axiom,
! [V_24Y] :
( c_24__type__76003___24t(V_24Y)
<=> t(V_24Y,c_24__type__76003) ) ).
fof('$tdef_$_type_78725',axiom,
! [V_24Y] :
( c_24__type__78725___24t(V_24Y)
<=> t(V_24Y,c_24__type__78725) ) ).
fof('$tdef_$_type_136247',axiom,
! [V_24Y] :
( c_24__type__136247___24t(V_24Y)
<=> t(V_24Y,c_24__type__136247) ) ).
fof('$tdef_$_type_66769',axiom,
! [V_24Y] :
( c_24__type__66769___24t(V_24Y)
<=> t(V_24Y,c_24__type__66769) ) ).
fof('$tdef_LF.Basics.nybble',axiom,
! [V_24Y] :
( cLF_2eBasics_2enybble___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2enybble) ) ).
fof('$tdef_$_type_102716',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__102716___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__102716___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_81683',axiom,
! [V_24Y] :
( c_24__type__81683___24t(V_24Y)
<=> t(V_24Y,c_24__type__81683) ) ).
fof('$tdef_$_type_76718',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76718___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76718___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_100965',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__100965___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__100965___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_78576',axiom,
! [V_24Y] :
( c_24__type__78576___24t(V_24Y)
<=> t(V_24Y,c_24__type__78576) ) ).
fof('$tdef_$_type_77827',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__77827___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__77827___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_92622',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92622___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92622___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et) ) ).
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_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_66425',axiom,
! [V_24Y] :
( c_24__type__66425___24t(V_24Y)
<=> t(V_24Y,c_24__type__66425) ) ).
fof('$tdef_$_type_92568',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92568___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92568___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_83216',axiom,
! [V_24Y] :
( c_24__type__83216___24t(V_24Y)
<=> t(V_24Y,c_24__type__83216) ) ).
fof('$tdef_$_type_104019',axiom,
! [V_24Y] :
( c_24__type__104019___24t(V_24Y)
<=> t(V_24Y,c_24__type__104019) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_78202',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__78202___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__78202___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('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_104739',axiom,
! [V_24Y] :
( c_24__type__104739___24t(V_24Y)
<=> t(V_24Y,c_24__type__104739) ) ).
fof('$tdef_$_type_104150',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__104150___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__104150___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_67146',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__67146___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__67146___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_136864',axiom,
! [V_24Y] :
( c_24__type__136864___24t(V_24Y)
<=> t(V_24Y,c_24__type__136864) ) ).
fof('$tdef_$_type_104013',axiom,
! [V_24Y] :
( c_24__type__104013___24t(V_24Y)
<=> t(V_24Y,c_24__type__104013) ) ).
fof('$tdef_$_type_104641',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__104641___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__104641___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_81755',axiom,
! [V_24Y] :
( c_24__type__81755___24t(V_24Y)
<=> t(V_24Y,c_24__type__81755) ) ).
fof('$tdef_$_type_99170',axiom,
! [V_24Y] :
( c_24__type__99170___24t(V_24Y)
<=> t(V_24Y,c_24__type__99170) ) ).
fof('$tdef_$_type_77702',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__77702___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__77702___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('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_81074',axiom,
! [V_24Y] :
( c_24__type__81074___24t(V_24Y)
<=> t(V_24Y,c_24__type__81074) ) ).
fof('$tdef_LF.Lists.NatList.natlist',axiom,
! [V_24Y] :
( cLF_2eLists_2eNatList_2enatlist___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2eNatList_2enatlist) ) ).
fof('$tdef_$_type_67175',axiom,
! [V_24Y] :
( c_24__type__67175___24t(V_24Y)
<=> t(V_24Y,c_24__type__67175) ) ).
fof('$tdef_$_type_486',axiom,
! [V_24Y] :
( c_24__type__486___24t(V_24Y)
<=> t(V_24Y,c_24__type__486) ) ).
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_$_type_50',axiom,
! [V_24Y] :
( c_24__type__50___24t(V_24Y)
<=> t(V_24Y,c_24__type__50) ) ).
fof('$tdef_$_type_81920',axiom,
! [V_24Y] :
( c_24__type__81920___24t(V_24Y)
<=> t(V_24Y,c_24__type__81920) ) ).
fof('$tdef_$_type_78454',axiom,
! [V_24Y] :
( c_24__type__78454___24t(V_24Y)
<=> t(V_24Y,c_24__type__78454) ) ).
fof('$tdef_$_type_78464',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78464___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78464___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.Vars.elt',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2eelt) ) ).
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_$_type_104158',axiom,
! [V_24Y] :
( c_24__type__104158___24t(V_24Y)
<=> t(V_24Y,c_24__type__104158) ) ).
fof('$tdef_$_type_104385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__104385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__104385___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_98635',axiom,
! [V_24Y] :
( c_24__type__98635___24t(V_24Y)
<=> t(V_24Y,c_24__type__98635) ) ).
fof('$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('$tdef_LF.Lists.NatList.bag',axiom,
! [V_24Y] :
( cLF_2eLists_2eNatList_2ebag___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2eNatList_2ebag) ) ).
fof('$tdef_$_type_111524',axiom,
! [V_24Y] :
( c_24__type__111524___24t(V_24Y)
<=> t(V_24Y,c_24__type__111524) ) ).
fof('$tdef_$_type_106745',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__106745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__106745___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_75935',axiom,
! [V_24Y] :
( c_24__type__75935___24t(V_24Y)
<=> t(V_24Y,c_24__type__75935) ) ).
fof('$tdef_$_type_111368',axiom,
! [V_24Y] :
( c_24__type__111368___24t(V_24Y)
<=> t(V_24Y,c_24__type__111368) ) ).
fof('$tdef_$_type_76725',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76725___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76725___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_78552',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78552___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78552___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Poly.Exercises.Church.cnat',axiom,
! [V_24Y] :
( cPoly_2eExercises_2eChurch_2ecnat___24t(V_24Y)
<=> t(V_24Y,cPoly_2eExercises_2eChurch_2ecnat) ) ).
fof('$tdef_$_type_104776',axiom,
! [V_24Y] :
( c_24__type__104776___24t(V_24Y)
<=> t(V_24Y,c_24__type__104776) ) ).
fof('$tdef_$_type_89942',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__89942___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__89942___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_81490',axiom,
! [V_24Y] :
( c_24__type__81490___24t(V_24Y)
<=> t(V_24Y,c_24__type__81490) ) ).
fof('$tdef_$_type_750',axiom,
! [V_24Y] :
( c_24__type__750___24t(V_24Y)
<=> t(V_24Y,c_24__type__750) ) ).
fof('$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_100054',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__100054___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__100054___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_75794',axiom,
! [V_24Y] :
( c_24__type__75794___24t(V_24Y)
<=> t(V_24Y,c_24__type__75794) ) ).
fof('$tdef_$_type_104102',axiom,
! [V_24Y] :
( c_24__type__104102___24t(V_24Y)
<=> t(V_24Y,c_24__type__104102) ) ).
fof('$tdef_$_type_110519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__110519___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__110519___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_78521',axiom,
! [V_24Y] :
( c_24__type__78521___24t(V_24Y)
<=> t(V_24Y,c_24__type__78521) ) ).
fof('$tdef_$_type_104603',axiom,
! [V_24Y] :
( c_24__type__104603___24t(V_24Y)
<=> t(V_24Y,c_24__type__104603) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_74656',axiom,
! [V_24Y] :
( c_24__type__74656___24t(V_24Y)
<=> t(V_24Y,c_24__type__74656) ) ).
fof('$tdef_$_type_101403',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__101403___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__101403___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_481',axiom,
! [V_24Y] :
( c_24__type__481___24t(V_24Y)
<=> t(V_24Y,c_24__type__481) ) ).
fof('$tdef_$_type_82745',axiom,
! [V_24Y] :
( c_24__type__82745___24t(V_24Y)
<=> t(V_24Y,c_24__type__82745) ) ).
fof('$tdef_$_type_102141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__102141___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__102141___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_110999',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__110999___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__110999___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et) ) ).
fof('$tdef_$_type_105730',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__105730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__105730___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_191699',axiom,
! [V_24Y] :
( c_24__type__191699___24t(V_24Y)
<=> t(V_24Y,c_24__type__191699) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_95040',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__95040___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__95040___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('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_102959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__102959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__102959___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_102896',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__102896___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__102896___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_81173',axiom,
! [V_24Y] :
( c_24__type__81173___24t(V_24Y)
<=> t(V_24Y,c_24__type__81173) ) ).
fof('$tdef_$_type_184',axiom,
! [V_24Y] :
( c_24__type__184___24t(V_24Y)
<=> t(V_24Y,c_24__type__184) ) ).
fof('$tdef_$_type_142570',axiom,
! [V_24Y] :
( c_24__type__142570___24t(V_24Y)
<=> t(V_24Y,c_24__type__142570) ) ).
fof('$tdef_$_type_111334',axiom,
! [V_24Y] :
( c_24__type__111334___24t(V_24Y)
<=> t(V_24Y,c_24__type__111334) ) ).
fof('$tdef_$_type_82276',axiom,
! [V_24Y] :
( c_24__type__82276___24t(V_24Y)
<=> t(V_24Y,c_24__type__82276) ) ).
fof('$tdef_$_type_111310',axiom,
! [V_24Y] :
( c_24__type__111310___24t(V_24Y)
<=> t(V_24Y,c_24__type__111310) ) ).
fof('$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_74590',axiom,
! [V_24Y] :
( c_24__type__74590___24t(V_24Y)
<=> t(V_24Y,c_24__type__74590) ) ).
fof('$tdef_$_type_104322',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__104322___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__104322___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_90295',axiom,
! [V_24Y] :
( c_24__type__90295___24t(V_24Y)
<=> t(V_24Y,c_24__type__90295) ) ).
fof('$tdef_$_type_104781',axiom,
! [V_24Y] :
( c_24__type__104781___24t(V_24Y)
<=> t(V_24Y,c_24__type__104781) ) ).
fof('$tdef_$_type_111866',axiom,
! [V_24Y] :
( c_24__type__111866___24t(V_24Y)
<=> t(V_24Y,c_24__type__111866) ) ).
fof('$tdef_$_type_110664',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__110664___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__110664___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_103088',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103088___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103088___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_76075',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76075___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76075___24a1(V_24X1)) ) ).
fof('$tdef_$_type_104502',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__104502___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__104502___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Vectors.Vector.t',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eVectors_2eVector_2et___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eVector_2et___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Poly.MumbleGrumble.mumble',axiom,
! [V_24Y] :
( cPoly_2eMumbleGrumble_2emumble___24t(V_24Y)
<=> t(V_24Y,cPoly_2eMumbleGrumble_2emumble) ) ).
fof('$tdef_$_type_98489',axiom,
! [V_24Y] :
( c_24__type__98489___24t(V_24Y)
<=> t(V_24Y,c_24__type__98489) ) ).
fof('$tdef_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et) ) ).
fof('$tdef_$_type_81089',axiom,
! [V_24X1,V_24Y] :
( c_24__type__81089___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__81089___24a1(V_24X1)) ) ).
fof('$tdef_$_type_104153',axiom,
! [V_24Y] :
( c_24__type__104153___24t(V_24Y)
<=> t(V_24Y,c_24__type__104153) ) ).
fof('$tdef_$_type_108452',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__108452___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__108452___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_81086',axiom,
! [V_24Y] :
( c_24__type__81086___24t(V_24Y)
<=> t(V_24Y,c_24__type__81086) ) ).
fof('$tdef_$_type_94827',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__94827___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__94827___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_78980',axiom,
! [V_24Y] :
( c_24__type__78980___24t(V_24Y)
<=> t(V_24Y,c_24__type__78980) ) ).
fof('$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_$_type_716',axiom,
! [V_24X1,V_24Y] :
( c_24__type__716___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__716___24a1(V_24X1)) ) ).
fof('$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_108129',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__108129___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__108129___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_78720',axiom,
! [V_24Y] :
( c_24__type__78720___24t(V_24Y)
<=> t(V_24Y,c_24__type__78720) ) ).
fof('$tdef_$_type_110856',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__110856___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__110856___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_100429',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__100429___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__100429___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_111280',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__111280___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__111280___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_95396',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__95396___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__95396___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_760',axiom,
! [V_24Y] :
( c_24__type__760___24t(V_24Y)
<=> t(V_24Y,c_24__type__760) ) ).
fof('$tdef_$_type_66430',axiom,
! [V_24Y] :
( c_24__type__66430___24t(V_24Y)
<=> t(V_24Y,c_24__type__66430) ) ).
fof('$tdef_$_type_75779',axiom,
! [V_24X1,V_24Y] :
( c_24__type__75779___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__75779___24a1(V_24X1)) ) ).
fof('$tdef_$_type_81901',axiom,
! [V_24Y] :
( c_24__type__81901___24t(V_24Y)
<=> t(V_24Y,c_24__type__81901) ) ).
fof('$tdef_$_type_75966',axiom,
! [V_24Y] :
( c_24__type__75966___24t(V_24Y)
<=> t(V_24Y,c_24__type__75966) ) ).
fof('$tdef_$_type_99693',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__99693___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__99693___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_95412',axiom,
! [V_24Y] :
( c_24__type__95412___24t(V_24Y)
<=> t(V_24Y,c_24__type__95412) ) ).
fof('$tdef_$_type_104122',axiom,
! [V_24Y] :
( c_24__type__104122___24t(V_24Y)
<=> t(V_24Y,c_24__type__104122) ) ).
fof('$tdef_$_type_711',axiom,
! [V_24X1,V_24Y] :
( c_24__type__711___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__711___24a1(V_24X1)) ) ).
fof('$tdef_$_type_76180',axiom,
! [V_24Y] :
( c_24__type__76180___24t(V_24Y)
<=> t(V_24Y,c_24__type__76180) ) ).
fof('$tdef_$_type_76169',axiom,
! [V_24Y] :
( c_24__type__76169___24t(V_24Y)
<=> t(V_24Y,c_24__type__76169) ) ).
fof('$tdef_$_type_98611',axiom,
! [V_24Y] :
( c_24__type__98611___24t(V_24Y)
<=> t(V_24Y,c_24__type__98611) ) ).
fof('$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_66754',axiom,
! [V_24Y] :
( c_24__type__66754___24t(V_24Y)
<=> t(V_24Y,c_24__type__66754) ) ).
fof('$tdef_$_type_100790',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__100790___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__100790___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_66745',axiom,
! [V_24Y] :
( c_24__type__66745___24t(V_24Y)
<=> t(V_24Y,c_24__type__66745) ) ).
fof('$tdef_LF.Lists.id',axiom,
! [V_24Y] :
( cLF_2eLists_2eid___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2eid) ) ).
fof('$tdef_$_type_111117',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__111117___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__111117___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_111844',axiom,
! [V_24Y] :
( c_24__type__111844___24t(V_24Y)
<=> t(V_24Y,c_24__type__111844) ) ).
fof('$tdef_$_type_93585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__93585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__93585___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_92538',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92538___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92538___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_793',axiom,
! [V_24Y] :
( c_24__type__793___24t(V_24Y)
<=> t(V_24Y,c_24__type__793) ) ).
fof('$tdef_$_type_152',axiom,
! [V_24Y] :
( c_24__type__152___24t(V_24Y)
<=> t(V_24Y,c_24__type__152) ) ).
fof('$tdef_$_type_111762',axiom,
! [V_24Y] :
( c_24__type__111762___24t(V_24Y)
<=> t(V_24Y,c_24__type__111762) ) ).
fof('$tdef_$_type_66924',axiom,
! [V_24Y] :
( c_24__type__66924___24t(V_24Y)
<=> t(V_24Y,c_24__type__66924) ) ).
fof('$tdef_$_type_765',axiom,
! [V_24Y] :
( c_24__type__765___24t(V_24Y)
<=> t(V_24Y,c_24__type__765) ) ).
fof('$tdef_$_type_95362',axiom,
! [V_24X1,V_24Y] :
( c_24__type__95362___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__95362___24a1(V_24X1)) ) ).
fof('$tdef_$_type_103428',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__103428___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__103428___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_109790',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__109790___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__109790___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_75900',axiom,
! [V_24Y] :
( c_24__type__75900___24t(V_24Y)
<=> t(V_24Y,c_24__type__75900) ) ).
fof('$tdef_$_type_110311',axiom,
! [V_24Y] :
( c_24__type__110311___24t(V_24Y)
<=> t(V_24Y,c_24__type__110311) ) ).
fof('$tdef_$_type_106076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__106076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__106076___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.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_$_type_98218',axiom,
! [V_24Y] :
( c_24__type__98218___24t(V_24Y)
<=> t(V_24Y,c_24__type__98218) ) ).
fof('$tdef_$_type_736',axiom,
! [V_24Y] :
( c_24__type__736___24t(V_24Y)
<=> t(V_24Y,c_24__type__736) ) ).
fof('$tdef_LF.Basics.NatPlayground.nat',axiom,
! [V_24Y] :
( cLF_2eBasics_2eNatPlayground_2enat___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2eNatPlayground_2enat) ) ).
fof('$tdef_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et) ) ).
fof('$tdef_$_type_78531',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78531___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78531___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_104099',axiom,
! [V_24Y] :
( c_24__type__104099___24t(V_24Y)
<=> t(V_24Y,c_24__type__104099) ) ).
fof('$tdef_$_type_66917',axiom,
! [V_24Y] :
( c_24__type__66917___24t(V_24Y)
<=> t(V_24Y,c_24__type__66917) ) ).
fof('$tdef_$_type_103348',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__103348___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__103348___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_152866',axiom,
! [V_24Y] :
( c_24__type__152866___24t(V_24Y)
<=> t(V_24Y,c_24__type__152866) ) ).
fof('$tdef_$_type_110505',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__110505___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__110505___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_111107',axiom,
! [V_24Y] :
( c_24__type__111107___24t(V_24Y)
<=> t(V_24Y,c_24__type__111107) ) ).
fof('$tdef_$_type_81678',axiom,
! [V_24Y] :
( c_24__type__81678___24t(V_24Y)
<=> t(V_24Y,c_24__type__81678) ) ).
fof('$tdef_$_type_84015',axiom,
! [V_24Y] :
( c_24__type__84015___24t(V_24Y)
<=> t(V_24Y,c_24__type__84015) ) ).
fof('$tdef_$_type_81698',axiom,
! [V_24Y] :
( c_24__type__81698___24t(V_24Y)
<=> t(V_24Y,c_24__type__81698) ) ).
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.PArith.BinPos.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2et) ) ).
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_$_type_6',axiom,
! [V_24Y] :
( c_24__type__6___24t(V_24Y)
<=> t(V_24Y,c_24__type__6) ) ).
fof('$tdef_$_type_103111',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103111___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103111___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_100136',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__100136___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__100136___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_104113',axiom,
! [V_24Y] :
( c_24__type__104113___24t(V_24Y)
<=> t(V_24Y,c_24__type__104113) ) ).
fof('$tdef_$_type_104035',axiom,
! [V_24Y] :
( c_24__type__104035___24t(V_24Y)
<=> t(V_24Y,c_24__type__104035) ) ).
fof('$tdef_$_type_94206',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__94206___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__94206___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_67111',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__67111___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__67111___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_89935',axiom,
! [V_24Y] :
( c_24__type__89935___24t(V_24Y)
<=> t(V_24Y,c_24__type__89935) ) ).
fof('$tdef_$_type_78313',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__78313___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__78313___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_84029',axiom,
! [V_24Y] :
( c_24__type__84029___24t(V_24Y)
<=> t(V_24Y,c_24__type__84029) ) ).
fof('$tdef_$_type_104571',axiom,
! [V_24Y] :
( c_24__type__104571___24t(V_24Y)
<=> t(V_24Y,c_24__type__104571) ) ).
fof('$tdef_LF.Basics.rgb',axiom,
! [V_24Y] :
( cLF_2eBasics_2ergb___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2ergb) ) ).
fof('$tdef_LF.Basics.bool',axiom,
! [V_24Y] :
( cLF_2eBasics_2ebool___24t(V_24Y)
<=> t(V_24Y,cLF_2eBasics_2ebool) ) ).
fof('$tdef_$_type_92709',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92709___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92709___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_102442',axiom,
! [V_24Y] :
( c_24__type__102442___24t(V_24Y)
<=> t(V_24Y,c_24__type__102442) ) ).
fof('$tdef_$_type_104448',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__104448___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__104448___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_109144',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__109144___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__109144___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_99469',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__99469___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__99469___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_38',axiom,
! [V_24Y] :
( c_24__type__38___24t(V_24Y)
<=> t(V_24Y,c_24__type__38) ) ).
fof('$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_99213',axiom,
! [V_24X1,V_24Y] :
( c_24__type__99213___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__99213___24a1(V_24X1)) ) ).
fof('$tdef_$_type_137555',axiom,
! [V_24Y] :
( c_24__type__137555___24t(V_24Y)
<=> t(V_24Y,c_24__type__137555) ) ).
fof('$tdef_$_type_103134',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103134___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103134___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_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_$_type_92733',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92733___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92733___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_66434',axiom,
! [V_24Y] :
( c_24__type__66434___24t(V_24Y)
<=> t(V_24Y,c_24__type__66434) ) ).
fof('$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_78373',axiom,
! [V_24Y] :
( c_24__type__78373___24t(V_24Y)
<=> t(V_24Y,c_24__type__78373) ) ).
fof('$tdef_$_type_111659',axiom,
! [V_24X1,V_24Y] :
( c_24__type__111659___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__111659___24a1(V_24X1)) ) ).
fof('$tdef_$_type_103152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103152___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103152___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_110136',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__110136___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__110136___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_84006',axiom,
! [V_24Y] :
( c_24__type__84006___24t(V_24Y)
<=> t(V_24Y,c_24__type__84006) ) ).
fof('$tdef_$_type_66752',axiom,
! [V_24Y] :
( c_24__type__66752___24t(V_24Y)
<=> t(V_24Y,c_24__type__66752) ) ).
fof('$tdef_$_type_104792',axiom,
! [V_24Y] :
( c_24__type__104792___24t(V_24Y)
<=> t(V_24Y,c_24__type__104792) ) ).
fof('$tdef_$_type_105384',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__105384___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__105384___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_101504',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__101504___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__101504___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_104785',axiom,
! [V_24Y] :
( c_24__type__104785___24t(V_24Y)
<=> t(V_24Y,c_24__type__104785) ) ).
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_$_type_66773',axiom,
! [V_24Y] :
( c_24__type__66773___24t(V_24Y)
<=> t(V_24Y,c_24__type__66773) ) ).
fof('$tdef_$_type_104810',axiom,
! [V_24Y] :
( c_24__type__104810___24t(V_24Y)
<=> t(V_24Y,c_24__type__104810) ) ).
fof('$tdef_$_type_111478',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__111478___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__111478___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_78593',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78593___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78593___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_78636',axiom,
! [V_24Y] :
( c_24__type__78636___24t(V_24Y)
<=> t(V_24Y,c_24__type__78636) ) ).
fof('$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_111385',axiom,
! [V_24Y] :
( c_24__type__111385___24t(V_24Y)
<=> t(V_24Y,c_24__type__111385) ) ).
fof('$tdef_$_type_702',axiom,
! [V_24X1,V_24Y] :
( c_24__type__702___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__702___24a1(V_24X1)) ) ).
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_$_type_95287',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__95287___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__95287___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_102842',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__102842___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__102842___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_111654',axiom,
! [V_24Y] :
( c_24__type__111654___24t(V_24Y)
<=> t(V_24Y,c_24__type__111654) ) ).
fof('$tdef_$_type_77203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__77203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__77203___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_74607',axiom,
! [V_24X1,V_24Y] :
( c_24__type__74607___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__74607___24a1(V_24X1)) ) ).
fof('$tdef_$_type_98214',axiom,
! [V_24Y] :
( c_24__type__98214___24t(V_24Y)
<=> t(V_24Y,c_24__type__98214) ) ).
fof('$tdef_$_type_78077',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__78077___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__78077___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_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('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_81972',axiom,
! [V_24Y] :
( c_24__type__81972___24t(V_24Y)
<=> t(V_24Y,c_24__type__81972) ) ).
fof('$tdef_$_type_81731',axiom,
! [V_24Y] :
( c_24__type__81731___24t(V_24Y)
<=> t(V_24Y,c_24__type__81731) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_66927',axiom,
! [V_24Y] :
( c_24__type__66927___24t(V_24Y)
<=> t(V_24Y,c_24__type__66927) ) ).
fof('$tdef_$_type_95404',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__95404___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__95404___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_123905',axiom,
! [V_24Y] :
( c_24__type__123905___24t(V_24Y)
<=> t(V_24Y,c_24__type__123905) ) ).
fof('$tdef_$_type_111210',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__111210___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__111210___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_91337',axiom,
! [V_24Y] :
( c_24__type__91337___24t(V_24Y)
<=> t(V_24Y,c_24__type__91337) ) ).
fof('$tdef_$_type_92676',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92676___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92676___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_78697',axiom,
! [V_24Y] :
( c_24__type__78697___24t(V_24Y)
<=> t(V_24Y,c_24__type__78697) ) ).
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_$_type_81906',axiom,
! [V_24Y] :
( c_24__type__81906___24t(V_24Y)
<=> t(V_24Y,c_24__type__81906) ) ).
fof('$tdef_$_type_101796',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__101796___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__101796___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_101605',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__101605___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__101605___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_99961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__99961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__99961___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_99157',axiom,
! [V_24Y] :
( c_24__type__99157___24t(V_24Y)
<=> t(V_24Y,c_24__type__99157) ) ).
fof('$tdef_$_type_111289',axiom,
! [V_24Y] :
( c_24__type__111289___24t(V_24Y)
<=> t(V_24Y,c_24__type__111289) ) ).
fof('$tdef_Poly.boollist',axiom,
! [V_24Y] :
( cPoly_2eboollist___24t(V_24Y)
<=> t(V_24Y,cPoly_2eboollist) ) ).
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_$_type_66416',axiom,
! [V_24Y] :
( c_24__type__66416___24t(V_24Y)
<=> t(V_24Y,c_24__type__66416) ) ).
fof('$tdef_$_type_111350',axiom,
! [V_24Y] :
( c_24__type__111350___24t(V_24Y)
<=> t(V_24Y,c_24__type__111350) ) ).
fof('$tdef_$_type_13',axiom,
! [V_24Y] :
( c_24__type__13___24t(V_24Y)
<=> t(V_24Y,c_24__type__13) ) ).
fof('$tdef_$_type_104787',axiom,
! [V_24Y] :
( c_24__type__104787___24t(V_24Y)
<=> t(V_24Y,c_24__type__104787) ) ).
fof('$tdef_$_type_92229',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__92229___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__92229___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_111074',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__111074___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__111074___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_111910',axiom,
! [V_24Y] :
( c_24__type__111910___24t(V_24Y)
<=> t(V_24Y,c_24__type__111910) ) ).
fof('$tdef_$_type_111341',axiom,
! [V_24Y] :
( c_24__type__111341___24t(V_24Y)
<=> t(V_24Y,c_24__type__111341) ) ).
fof('$tdef_$_type_109467',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__109467___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__109467___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_81949',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__81949___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__81949___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_95337',axiom,
! [V_24Y] :
( c_24__type__95337___24t(V_24Y)
<=> t(V_24Y,c_24__type__95337) ) ).
fof('$tdef_$_type_91912',axiom,
! [V_24Y] :
( c_24__type__91912___24t(V_24Y)
<=> t(V_24Y,c_24__type__91912) ) ).
fof('$tdef_$_type_74643',axiom,
! [V_24X1,V_24Y] :
( c_24__type__74643___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__74643___24a1(V_24X1)) ) ).
fof('$tdef_$_type_93372',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__93372___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__93372___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_91477',axiom,
! [V_24Y] :
( c_24__type__91477___24t(V_24Y)
<=> t(V_24Y,c_24__type__91477) ) ).
fof('$tdef_$_type_81758',axiom,
! [V_24Y] :
( c_24__type__81758___24t(V_24Y)
<=> t(V_24Y,c_24__type__81758) ) ).
fof('$tdef_$_type_78613',axiom,
! [V_24Y] :
( c_24__type__78613___24t(V_24Y)
<=> t(V_24Y,c_24__type__78613) ) ).
fof('$tdef_$_type_110329',axiom,
! [V_24Y] :
( c_24__type__110329___24t(V_24Y)
<=> t(V_24Y,c_24__type__110329) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_84011',axiom,
! [V_24Y] :
( c_24__type__84011___24t(V_24Y)
<=> t(V_24Y,c_24__type__84011) ) ).
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_$_type_78997',axiom,
! [V_24Y] :
( c_24__type__78997___24t(V_24Y)
<=> t(V_24Y,c_24__type__78997) ) ).
fof('$tdef_$_type_92592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92592___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_90298',axiom,
! [V_24Y] :
( c_24__type__90298___24t(V_24Y)
<=> t(V_24Y,c_24__type__90298) ) ).
fof('$tdef_$_type_67173',axiom,
! [V_24Y] :
( c_24__type__67173___24t(V_24Y)
<=> t(V_24Y,c_24__type__67173) ) ).
fof('$tdef_$_type_110714',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__110714___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__110714___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_103486',axiom,
! [V_24Y] :
( c_24__type__103486___24t(V_24Y)
<=> t(V_24Y,c_24__type__103486) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24Y] :
( c_24__type__8___24t(V_24Y)
<=> t(V_24Y,c_24__type__8) ) ).
fof('$tdef_$_type_102161',axiom,
! [V_24Y] :
( c_24__type__102161___24t(V_24Y)
<=> t(V_24Y,c_24__type__102161) ) ).
fof('$tdef_$_type_192795',axiom,
! [V_24Y] :
( c_24__type__192795___24t(V_24Y)
<=> t(V_24Y,c_24__type__192795) ) ).
fof('$tdef_$_type_104778',axiom,
! [V_24Y] :
( c_24__type__104778___24t(V_24Y)
<=> t(V_24Y,c_24__type__104778) ) ).
fof('$tdef_$_type_104033',axiom,
! [V_24Y] :
( c_24__type__104033___24t(V_24Y)
<=> t(V_24Y,c_24__type__104033) ) ).
fof('$tdef_$_type_103065',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__103065___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__103065___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.Vars.tree',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2etree) ) ).
fof('$tdef_$_type_67154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__67154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__67154___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_111328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__111328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__111328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_92652',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__92652___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__92652___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_93780',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__93780___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__93780___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('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$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_111672',axiom,
! [V_24Y] :
( c_24__type__111672___24t(V_24Y)
<=> t(V_24Y,c_24__type__111672) ) ).
fof('$tdef_$_type_104688',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__104688___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__104688___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_111034',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__111034___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__111034___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25',axiom,
! [V_24Y] :
( c_24__type__25___24t(V_24Y)
<=> t(V_24Y,c_24__type__25) ) ).
fof('$tdef_$_type_79005',axiom,
! [V_24Y] :
( c_24__type__79005___24t(V_24Y)
<=> t(V_24Y,c_24__type__79005) ) ).
fof('$tdef_$_type_78384',axiom,
! [V_24Y] :
( c_24__type__78384___24t(V_24Y)
<=> t(V_24Y,c_24__type__78384) ) ).
fof('$tdef_$_type_103384',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__103384___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__103384___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_100522',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__100522___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__100522___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_78599',axiom,
! [V_24Y] :
( c_24__type__78599___24t(V_24Y)
<=> t(V_24Y,c_24__type__78599) ) ).
fof('$tdef_$_type_77242',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__77242___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__77242___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_107783',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__107783___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__107783___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_107437',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__107437___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__107437___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('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_91424',axiom,
! [V_24Y] :
( c_24__type__91424___24t(V_24Y)
<=> t(V_24Y,c_24__type__91424) ) ).
fof('$tdef_$_type_66355',axiom,
! [V_24Y] :
( c_24__type__66355___24t(V_24Y)
<=> t(V_24Y,c_24__type__66355) ) ).
fof('$tdef_$_type_66373',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__66373___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__66373___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_101897',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__101897___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__101897___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_95359',axiom,
! [V_24Y] :
( c_24__type__95359___24t(V_24Y)
<=> t(V_24Y,c_24__type__95359) ) ).
fof('$tdef_$_type_106399',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__106399___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__106399___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_81061',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__81061___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__81061___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_111605',axiom,
! [V_24Y] :
( c_24__type__111605___24t(V_24Y)
<=> t(V_24Y,c_24__type__111605) ) ).
fof('$tdef_$_type_110291',axiom,
! [V_24Y] :
( c_24__type__110291___24t(V_24Y)
<=> t(V_24Y,c_24__type__110291) ) ).
fof('$tdef_$_type_66906',axiom,
! [V_24Y] :
( c_24__type__66906___24t(V_24Y)
<=> t(V_24Y,c_24__type__66906) ) ).
fof('$tdef_Poly.list',axiom,
! [V_24X1,V_24Y] :
( cPoly_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cPoly_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_110806',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__110806___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__110806___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_LF.Lists.NatList.natprod',axiom,
! [V_24Y] :
( cLF_2eLists_2eNatList_2enatprod___24t(V_24Y)
<=> t(V_24Y,cLF_2eLists_2eNatList_2enatprod) ) ).
fof('$tdef_$_type_111906',axiom,
! [V_24Y] :
( c_24__type__111906___24t(V_24Y)
<=> t(V_24Y,c_24__type__111906) ) ).
fof('$tdef_$_type_95261',axiom,
! [V_24Y] :
( c_24__type__95261___24t(V_24Y)
<=> t(V_24Y,c_24__type__95261) ) ).
fof('$tdef_$_type_76072',axiom,
! [V_24Y] :
( c_24__type__76072___24t(V_24Y)
<=> t(V_24Y,c_24__type__76072) ) ).
fof('_HAMMER_GOAL',conjecture,
cPoly_2eExercises_2eChurch_2eplus___24a2(cPoly_2eExercises_2eChurch_2etwo,cPoly_2eExercises_2eChurch_2ethree) = cPoly_2eExercises_2eChurch_2eplus___24a2(cPoly_2eExercises_2eChurch_2ethree,cPoly_2eExercises_2eChurch_2etwo) ).
%------------------------------------------------------------------------------