TPTP Problem File: SEV660+1.p
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%------------------------------------------------------------------------------
% File : SEV660+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - monads bind eqq
% 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 : monads.bind.eqq.p [Kal26]
% Status : Theorem
% Rating : 0.74 v9.3.0
% Syntax : Number of formulae : 2690 (1082 unt; 0 def)
% Number of atoms : 8750 (2648 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6227 ( 167 ~; 652 |;1315 &)
% ( 978 <=>;3115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 515 ( 514 usr; 0 prp; 1-23 aty)
% Number of functors : 1496 (1496 usr; 964 con; 0-22 aty)
% Number of variables : 8511 (8020 !; 491 ?)
% SPC : FOF_THM_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.comparison$43278',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eEq
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__0) ) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eLt
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__1) ) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eGt
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__2) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$2348',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] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__6)
=> ( ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__7)
=> ( c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& ( ( Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242348___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__2354] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__2354)
& ? [Vvar__2___24Anonymous__2355] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__2355)
& Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2354,Vvar__2___24Anonymous__2355)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242348___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vvar__1___24Anonymous__2354),c_24__fix__2494__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vvar__2___24Anonymous__2355)) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__2370] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__2370)
& ? [Vvar__2___24Anonymous__2371] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__2371)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2370,Vvar__2___24Anonymous__2371)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242348___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2370,c_24__fix__2591__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__2371,c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$2455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__2459] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__2459)
& ? [Vvar__2___24Anonymous__2460] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__2460)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2459,Vvar__2___24Anonymous__2460)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__2459),c_24__fix__2494__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__2460)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$11640',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411640___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11641] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11641)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11641)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411640___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__11641)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$11662',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11663] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11663)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11663)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__11663)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$42495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__42508___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__42500] :
( t(Vvar__2___24Anonymous__42500,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__42501] :
( t(Vvar__3___24Anonymous__42501,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__42500,Vvar__3___24Anonymous__42501)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2442495___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__42500)),Vvar__3___24Anonymous__42501)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$11657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11658] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11658)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11658)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11658) )
| ? [Vvar__0___24Anonymous__11659] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11659)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11659)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11659) ) ) ) ).
fof('$_def_$_let_var_6_p_14614_14617',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14613] : c_24__let__var__6__p__14614__14617___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14613) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14613) ).
fof('$_def_$_let_var_6_p_14616_14618',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14615] : c_24__let__var__6__p__14616__14618___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14615) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14615) ).
fof('$_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__35826] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35826)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35826)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__35827] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35827)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35827)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__35830] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35830)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35830)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__35827,Vvar__0___24Anonymous__35830) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.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.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__28870] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28870)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28870)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
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__7361] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__7361)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__7361) ) ).
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('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__7384] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__7384)
& ? [Vvar__1___24Anonymous__7385] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__7385)
& ? [Vvar__2___24Anonymous__7386] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__7386)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__7384,Vvar__1___24Anonymous__7385,Vvar__2___24Anonymous__7386)
& ( ? [Vvar__0___24Anonymous__7399] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7399)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7399)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__7399,Vvar__2___24Anonymous__7386) )
| ? [Vvar__0___24Anonymous__7400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7400)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7400)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__7400,Vvar__0___24Anonymous__7384) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__7385 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__43468] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43468)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43468)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__43468,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__43469] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43469)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43469)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__43469,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__7362] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__7362)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__7362) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.CompSpecT',axiom,
! [V0__A,V1__eq,V2__lt,V3__x,V4__y] : cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V0__A,V1__eq,V2__lt,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(happ(happ(V1__eq,V3__x),V4__y),happ(happ(V2__lt,V3__x),V4__y),happ(happ(V2__lt,V4__y),V3__x)) ).
fof('$_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__7876] :
( t(Vvar__1___24Anonymous__7876,V0__A)
& ? [Vvar__2___24Anonymous__7877] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7877)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7876,Vvar__2___24Anonymous__7877)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7876,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__7877,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__1317] :
( t(Vvar__2___24Anonymous__1317,V0__A)
& ? [Vvar__3___24Anonymous__1318] :
( t(Vvar__3___24Anonymous__1318,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1317,Vvar__3___24Anonymous__1318)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__1317 ) ) ) ) ) ).
fof('$_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__35763] :
( t(Vvar__1___24Anonymous__35763,V0__A)
& ? [Vvar__2___24Anonymous__35764] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35764)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35763,Vvar__2___24Anonymous__35764)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__35764)) ) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__1329] :
( t(Vvar__2___24Anonymous__1329,V0__A)
& ? [Vvar__3___24Anonymous__1330] :
( t(Vvar__3___24Anonymous__1330,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__1329,Vvar__3___24Anonymous__1330)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__1330 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__3037] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3037)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3037)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__3037,V2__m)) ) ) ) ).
fof('$_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__36111] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36111)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36111)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__36112] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36112)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36112)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__36115] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36115)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36115)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__36112,Vvar__0___24Anonymous__36115) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__11278] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11278)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11278)
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__11278,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__11278)) ) ) ) ).
fof('$_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__3042] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3042)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3042)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3042)
& ( ( Vvar__0___24Anonymous__3042 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__3045] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3045)
& Vvar__0___24Anonymous__3042 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3045)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__3045)) ) ) ) ) ) ) ) ).
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__36104] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36104)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36104)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__36105] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36105)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36105)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__36108] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36108)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36108)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__36105,Vvar__0___24Anonymous__36108) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__36120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36120)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36120)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36120)
& ( ( Vvar__0___24Anonymous__36120 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__36123] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36123)
& Vvar__0___24Anonymous__36120 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36123)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__36123) ) ) ) ) ) ) ) ).
fof('$_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__36125] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36125)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36125)
& 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__36125)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36125)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__11264] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11264)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11264)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__11267] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11267)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11267)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__11264,Vvar__0___24Anonymous__11267)) ) ) ) ) ) ) ) ).
fof('$_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__11270] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11270)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11270)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__11273] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11273)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11273)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__11270,Vvar__0___24Anonymous__11273)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__2706] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2706)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2706)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__2706,V2__m)) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__11276] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11276)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11276)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__11276)) ) ) ) ).
fof('$_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__11262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11262)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11262)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__11262 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__36127,V0__a,c_24__lam__36128) ).
fof('$_def_Coq.Init.Nat.sqrt',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__31583] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31583)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31583)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__31586] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31586)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31586)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__31583,Vvar__0___24Anonymous__31586) ) ) ) ) ) ) ) ).
fof('$_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__3047] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3047)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3047)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__3047) ) ) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__14977___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__14971] :
( t(Vvar__2__x__14971,V0__A)
& p(happ(V1__P,Vvar__2__x__14971))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__14971)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__14971 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__15157___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__15151] :
( t(Vvar__2__x__15151,V0__A)
& ? [Vvar__3___24Anonymous__15152] :
( t(Vvar__3___24Anonymous__15152,happ(V1__P,Vvar__2__x__15151))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__15151,Vvar__3___24Anonymous__15152)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__15151 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__15180___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__15174] :
( t(Vvar__2__x__15174,V0__A)
& ? [Vvar__3___24Anonymous__15175] :
( t(Vvar__3___24Anonymous__15175,happ(V1__P,Vvar__2__x__15174))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__15174,Vvar__3___24Anonymous__15175)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__15175 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__3019] :
( t(Vvar__1___24Anonymous__3019,V0__A)
& ? [Vvar__2___24Anonymous__3020] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3020)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3019,Vvar__2___24Anonymous__3020)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__3019 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__3020) ) ) ) ) ) ) ) ).
fof('$_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__36023] :
( t(Vvar__1___24Anonymous__36023,V1__B)
& ? [Vvar__2___24Anonymous__36024] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__36024)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__36023,Vvar__2___24Anonymous__36024)
& 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__36024,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__36023)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__36052] :
( t(Vvar__1___24Anonymous__36052,V1__B)
& ? [Vvar__2___24Anonymous__36053] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__36053)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__36052,Vvar__2___24Anonymous__36053)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__36052),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__36053)) ) ) ) ) ) ) ).
fof('$_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__11075] :
( t(Vvar__1___24Anonymous__11075,V0__A)
& ? [Vvar__2___24Anonymous__11076] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11076)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11076)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11075,Vvar__2___24Anonymous__11076)
& ( ( Vvar__2___24Anonymous__11076 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__11075 )
| ? [Vvar__1___24Anonymous__11087] :
( t(Vvar__1___24Anonymous__11087,V0__A)
& ? [Vvar__2___24Anonymous__11088] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__11088)
& Vvar__2___24Anonymous__11076 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__11087,Vvar__2___24Anonymous__11088)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__11076,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__43] :
( t(Vvar__1___24Anonymous__43,V0__A)
& ? [Vvar__2___24Anonymous__44] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__44)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__43,Vvar__2___24Anonymous__44)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__43),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__44)) ) ) ) ) ) ) ).
fof('$_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__35998] :
( t(Vvar__1___24Anonymous__35998,V0__A)
& ? [Vvar__2___24Anonymous__35999] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35999)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35998,Vvar__2___24Anonymous__35999)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__35998 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__36001] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36001)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36001)
& ( ( 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__36008] :
( t(Vvar__1___24Anonymous__36008,V0__A)
& ? [Vvar__2___24Anonymous__36009] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__36009)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__36008,Vvar__2___24Anonymous__36009)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__36001,Vvar__2___24Anonymous__36009,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_bool',axiom,
! [V0__A,V1__eqA,V2__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V0__A,V1__eqA,V2__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11245___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cCoq_2eInit_2eDatatypes_2ebool,V1__eqA,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V2__f) ) ).
fof('$_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__35653___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__5682___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.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',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
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_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('$_def_Coq.Logic.EqdepFacts.UIP_',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V0__U)
<=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y) ) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
! [V0__U,V1__x] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__U,V1__x)
<=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ).
fof('$_def_Coq.Logic.FinFun.Bijective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eBijective___24a3(V0__A,V1__B,V2__f)
<=> ? [V3__g] :
( c_24__type__5693___24t(V0__A,V1__B,V3__g)
& ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
& ! [V4__y] :
( t(V4__y,V1__B)
=> happ(V2__f,happ(V3__g,V4__y)) = V4__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Injective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Surjective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__B)
=> ? [V4__x] :
( t(V4__x,V0__A)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bInjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__y,V0__n)
=> ( happ(V1__f,V2__x) = happ(V1__f,V3__y)
=> V2__x = V3__y ) ) ) ) ) ) ).
fof('$_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.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('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__2802] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2802)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2802)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__2805] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2805)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2805)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2802,Vvar__0___24Anonymous__2805)) ) ) ) ) ) ) ) ).
fof('$_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__29221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29221)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29221)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__29222] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29222)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29222)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__29225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29225)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29225)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__29222,Vvar__0___24Anonymous__29225) ) ) ) ) ) ) ) ).
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.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__43391] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43391)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__43391)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43391)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__29230] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29230)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29230)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__29231] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29231)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29231)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__29234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29234)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29234)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__29231,Vvar__0___24Anonymous__29234) ) ) ) ) ) ) ) ).
fof('$_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__29240] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29240)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29240)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29240)
& ( ? [Vvar__0___24Anonymous__29244] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29244)
& Vvar__0___24Anonymous__29240 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29244)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__29245] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29245)
& Vvar__0___24Anonymous__29240 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29245)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__29240 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__29260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29260)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29260)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__29263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29263)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29263)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__29260,Vvar__0___24Anonymous__29263)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.log2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29253] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29253)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29253)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29253)
& ( ? [Vvar__0___24Anonymous__29257] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29257)
& Vvar__0___24Anonymous__29253 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29257)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__29257)) )
| ? [Vvar__0___24Anonymous__29258] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29258)
& Vvar__0___24Anonymous__29253 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29258)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__29258)) )
| ( Vvar__0___24Anonymous__29253 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2680)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2680)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2683] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2683)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2683)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2680,Vvar__0___24Anonymous__2683)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.NArith.BinNatDef.N.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__29248] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29248)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29248)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29251] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29251)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29251)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__29251,Vvar__0___24Anonymous__29248)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__29220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29220)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29220)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__29220) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__43392] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43392)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__43392)
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__43392)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2807] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2807)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2807)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__2812] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2812)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2807)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2812)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2812)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__2807,Vvar__0___24Anonymous__2812) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2815)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__2807,Vvar__0___24Anonymous__2812) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__2815)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2815) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__2807,Vvar__0___24Anonymous__2812) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__29217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29217)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29217)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29217)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__43390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43390)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__43390)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43390)) ) ) ) ).
fof('$_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__29265] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29265)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29265)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__29265,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__29267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29267)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29267)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__29267) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__29410] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29410)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29410)
& ( ? [Vvar__0___24Anonymous__29414] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29414)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29414)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29409__1__add__carry___24a2(Vvar__0___24Anonymous__29410,Vvar__0___24Anonymous__29414)) )
| ? [Vvar__0___24Anonymous__29415] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29415)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29415)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29410,Vvar__0___24Anonymous__29415)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29410)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29416] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29416)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29416)
& ( ? [Vvar__0___24Anonymous__29420] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29420)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29420)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29416,Vvar__0___24Anonymous__29420)) )
| ? [Vvar__0___24Anonymous__29421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29421)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29421)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29416,Vvar__0___24Anonymous__29421)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29416) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__29422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29422)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29422)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29422)) )
| ? [Vvar__0___24Anonymous__29423] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29423)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29423)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29423) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__43412] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43412)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43412)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__43412),Vvar__0___24Anonymous__43412)) )
| ? [Vvar__0___24Anonymous__43413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43413)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43413)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__43413),Vvar__0___24Anonymous__43413) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_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__43428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43428)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43428)
& 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__43428,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__43429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43429)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43429)
& 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__43429,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('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__29452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29452)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29452)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29452,V2__y))) )
| ? [Vvar__0___24Anonymous__29453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29453)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29453)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29453,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_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__29460] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29460)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29460)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29460)
& ( ( Vvar__0___24Anonymous__29460 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__29463] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29463)
& Vvar__0___24Anonymous__29460 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29463)
& 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__29460)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__43445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43445)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43445)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__43445)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__29441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29441)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29441)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29441) )
| ? [Vvar__0___24Anonymous__29442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29442)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29442)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__29442) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__43409] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43409)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__43409)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__43409 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__29407] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29407)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29407)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29407)) )
| ? [Vvar__0___24Anonymous__29408] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29408)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29408)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29408) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_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('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__11600] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11600)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11600)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__11600) )
| ? [Vvar__0___24Anonymous__11601] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11601)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11601)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__11601)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
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('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__14778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14778)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14778)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__14778)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1449___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___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)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
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('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__7352] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__7352)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__7352) ) ).
fof('$_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__43406] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__43406)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__43406) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__43343] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__43343)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__43343) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__43474] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__43474)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__43474) ) ).
fof('$_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__30971] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__30971)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__30971) ) ).
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)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__31552] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__31552)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__31552) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Bezout',axiom,
! [V0__n,V1__m,V2__p] :
( cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p)
<=> ? [V3__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__a)
& ? [V4__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__b)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__a,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__b,V1__m)) = V2__p ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__31029] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31029)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31029)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31029) )
| ? [Vvar__0___24Anonymous__31030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31030)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31030)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31030) ) ) ) ).
fof('$_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__2827] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2827)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2827)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2831] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2831)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2831)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2827,Vvar__0___24Anonymous__2831)) )
| ? [Vvar__0___24Anonymous__2832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2832)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2832)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2827,Vvar__0___24Anonymous__2832) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2833)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2833)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2837)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2837)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2837,Vvar__0___24Anonymous__2833) )
| ? [Vvar__0___24Anonymous__2838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2838)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2838)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2833,Vvar__0___24Anonymous__2838)) ) ) ) ) ) ) ) ).
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__30993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30993)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30993)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__30994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30994)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30994)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__30995] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30995)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30995)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__30999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30999)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30999)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__30995,Vvar__0___24Anonymous__30999) )
| ? [Vvar__0___24Anonymous__31000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31000)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31000)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__31001] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31001)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31001)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__31005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31005)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31005)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__31006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31006)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31006)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__31001,Vvar__0___24Anonymous__31006)) ) ) ) ) ) ) ) ).
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__2945] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__2945)
& ? [Vvar__3___24Anonymous__2946] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__2946)
& 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__2945,Vvar__3___24Anonymous__2946)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__2945 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.eqb',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31013] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31013)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31013)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31014] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31014)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31014)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__31015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31015)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31015)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31019] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31019)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31019)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31015,Vvar__0___24Anonymous__31019) )
| ? [Vvar__0___24Anonymous__31020] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31020)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31020)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__31021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31021)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31021)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31025] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31025)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31025)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31026] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31026)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31026)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31021,Vvar__0___24Anonymous__31026) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
| ? [Vvar__0___24Anonymous__43502] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43502)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43502)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__43506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43506)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43506)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__43502,Vvar__0___24Anonymous__43506)) )
| ? [Vvar__0___24Anonymous__43507] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43507)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43507)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__43502,Vvar__0___24Anonymous__43507)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__43508] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43508)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43508)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__43512] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43512)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43512)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__43508,Vvar__0___24Anonymous__43512)) )
| ? [Vvar__0___24Anonymous__43513] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43513)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43513)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__43508,Vvar__0___24Anonymous__43513)) ) ) ) ) ) ) ) ).
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__31103] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31103)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31103)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31103)
& ( ? [Vvar__0___24Anonymous__31107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31107)
& Vvar__0___24Anonymous__31103 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31107)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31107)) )
| ? [Vvar__0___24Anonymous__31108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31108)
& Vvar__0___24Anonymous__31103 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31108)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31108)) )
| ( Vvar__0___24Anonymous__31103 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__31109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31109)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31109)
& 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('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__2953] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__2953)
& ? [Vvar__3___24Anonymous__2954] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__2954)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__2953,Vvar__3___24Anonymous__2954)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__2954 ) ) ) ) ).
fof('$_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__2846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2846)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2846)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2850] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2850)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2850)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2846,Vvar__0___24Anonymous__2850)) )
| ? [Vvar__0___24Anonymous__2851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2851)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2851)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2846,Vvar__0___24Anonymous__2851)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2852)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2852)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2856] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2856)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2856)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2852,Vvar__0___24Anonymous__2856)) )
| ? [Vvar__0___24Anonymous__2857] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2857)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2857)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2852,Vvar__0___24Anonymous__2857)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__31034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31034)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31034)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31034) ) ) ) ).
fof('$_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__31031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31031)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31031)
& 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__31031)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__2842] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2842)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2842)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2842) )
| ? [Vvar__0___24Anonymous__2843] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2843)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2843)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2843) ) ) ) ).
fof('$_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__30990] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30990)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30990)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__30990) )
| ? [Vvar__0___24Anonymous__30991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30991)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30991)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__31010] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31010)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31010)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31011] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31011)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31011)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__43500] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43500)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43500)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__43500)) )
| ? [Vvar__0___24Anonymous__43501] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43501)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43501)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_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__43496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43496)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__43496)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__43496 )
| ? [Vvar__0___24Anonymous__43497] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43497)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__43497)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b) )
| ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__8297___24a1(V0__D) ).
fof('$_def_Coq.micromega.Env.jump',axiom,
! [V0__D,V1__j,V2__e,V3__x] : cCoq_2emicromega_2eEnv_2ejump___24a4(V0__D,V1__j,V2__e,V3__x) = happ(V2__e,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V3__x,V1__j)) ).
fof('$_def_Coq.micromega.Env.nth',axiom,
! [V0__D,V1__n,V2__e] : cCoq_2emicromega_2eEnv_2enth___24a3(V0__D,V1__n,V2__e) = happ(V2__e,V1__n) ).
fof('$_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__36168] :
( t(Vvar__1___24Anonymous__36168,V1__A)
& ? [Vvar__2___24Anonymous__36169] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36169)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36169)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36168,Vvar__2___24Anonymous__36169)
& ( ( Vvar__2___24Anonymous__36169 = 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__36168)) ) )
| ? [Vvar__1___24Anonymous__36180] :
( t(Vvar__1___24Anonymous__36180,V1__A)
& ? [Vvar__2___24Anonymous__36181] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36181)
& Vvar__2___24Anonymous__36169 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36180,Vvar__2___24Anonymous__36181)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__36168))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__36169) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__11827___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__11835___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__11843___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__11851___24a2(V0__R,V3__rlt) ) ) ) ) ).
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.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__10514] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__10514)
& ? [Vvar__2___24Anonymous__10515] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__10515)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__10514,Vvar__2___24Anonymous__10515)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__10514),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__10515,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__9198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__9198)
& ? [Vvar__2__denum__9199] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__9199)
& ? [Vvar__3__condition__9200] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__9200)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__9198,Vvar__2__denum__9199,Vvar__3__condition__9200)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__9200 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__9189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__9189)
& ? [Vvar__2__denum__9190] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__9190)
& ? [Vvar__3__condition__9191] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__9191)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__9189,Vvar__2__denum__9190,Vvar__3__condition__9191)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__9190 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__9178] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__9178)
& ? [Vvar__2__denum__9179] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__9179)
& ? [Vvar__3__condition__9180] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__9180)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__9178,Vvar__2__denum__9179,Vvar__3__condition__9180)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__9178 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__35916] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35916)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35916)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__35916) ) ) ) ) ).
fof('$_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__11008] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11008)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11008)
& 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__11008) )
| ? [Vvar__0___24Anonymous__11009] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11009)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11009)
& 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__11009)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__5641___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_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.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__13268] :
( t(Vvar__1___24Anonymous__13268,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__13268)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__13268) )
| ? [Vvar__1___24Anonymous__13270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13270)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__13270)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__13270,V13__l) )
| ? [Vvar__1___24Anonymous__13272] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13272)
& ? [Vvar__2___24Anonymous__13273] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13273)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__13272,Vvar__2___24Anonymous__13273)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13272)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13273)) ) )
| ? [Vvar__1___24Anonymous__13276] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13276)
& ? [Vvar__2___24Anonymous__13277] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13277)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__13276,Vvar__2___24Anonymous__13277)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13276)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13277)) ) )
| ? [Vvar__1___24Anonymous__13280] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13280)
& ? [Vvar__2___24Anonymous__13281] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13281)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__13280,Vvar__2___24Anonymous__13281)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13280)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13281)) ) )
| ? [Vvar__1___24Anonymous__13284] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13284)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__13284)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13284)) )
| ? [Vvar__1___24Anonymous__13286] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13286)
& ? [Vvar__2___24Anonymous__13287] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13287)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__13286,Vvar__2___24Anonymous__13287)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13286)),happ(V10__Cp__phi,Vvar__2___24Anonymous__13287)) ) ) ) ) ) ) ) ).
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__12880] :
( t(Vvar__1___24Anonymous__12880,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__12880)
& ( ? [Vvar__1___24Anonymous__12890] :
( t(Vvar__1___24Anonymous__12890,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12890)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__12880),Vvar__1___24Anonymous__12890) )
| ? [Vvar__1___24Anonymous__12892] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12892)
& ? [Vvar__2___24Anonymous__12893] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12893)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12892,Vvar__2___24Anonymous__12893)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__12896] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12896)
& ? [Vvar__2___24Anonymous__12897] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12897)
& ? [Vvar__3___24Anonymous__12898] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12898)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12896,Vvar__2___24Anonymous__12897,Vvar__3___24Anonymous__12898)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__12903] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12903)
& ? [Vvar__2___24Anonymous__12904] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12904)
& ( 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__12903,Vvar__2___24Anonymous__12904)
& ( ? [Vvar__1___24Anonymous__12924] :
( t(Vvar__1___24Anonymous__12924,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12924)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__12926] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12926)
& ? [Vvar__2___24Anonymous__12927] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12927)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12903)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12926)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12926,Vvar__2___24Anonymous__12927)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__12903,Vvar__1___24Anonymous__12926) = 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__12904,Vvar__2___24Anonymous__12927) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__12903,Vvar__1___24Anonymous__12926) = 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__12903,Vvar__1___24Anonymous__12926) = 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__12932] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12932)
& ? [Vvar__2___24Anonymous__12933] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12933)
& ? [Vvar__3___24Anonymous__12934] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12934)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12932,Vvar__2___24Anonymous__12933,Vvar__3___24Anonymous__12934)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__12939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12939)
& ? [Vvar__2___24Anonymous__12940] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12940)
& ? [Vvar__3___24Anonymous__12941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12941)
& ( 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__12939,Vvar__2___24Anonymous__12940,Vvar__3___24Anonymous__12941)
& ( ? [Vvar__1___24Anonymous__12974] :
( t(Vvar__1___24Anonymous__12974,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__12974)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__12976] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12976)
& ? [Vvar__2___24Anonymous__12977] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__12977)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__12976,Vvar__2___24Anonymous__12977)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__12980] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12980)
& ? [Vvar__2___24Anonymous__12981] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12981)
& ? [Vvar__3___24Anonymous__12982] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__12982)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12940)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12981)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__12980,Vvar__2___24Anonymous__12981,Vvar__3___24Anonymous__12982)
& ( ( cType___24t(V0__C)
=> ( c_24__type__5641___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12939)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__12980)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__12940,Vvar__2___24Anonymous__12981) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__12939,Vvar__1___24Anonymous__12980) = 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__12941,Vvar__3___24Anonymous__12982) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__12939,Vvar__1___24Anonymous__12980) = 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__12940,Vvar__2___24Anonymous__12981) = 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__12940,Vvar__2___24Anonymous__12981) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__41519] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__41519)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__41519)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__41519) ) ) ) ) ).
fof('$_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__14613] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14613)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__14613)
& 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__14614__14617___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14613)),c_24__let__var__6__p__14614__14617___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14613))) )
| ? [Vvar__0___24Anonymous__14615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14615)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__14615)
& 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__14616__14618___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14615)),c_24__let__var__6__p__14616__14618___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__14615)) )
| ( 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('$_def_QuicksortComplexity.list_utils.count',axiom,
! [V0__X,V1__p,V3__l] :
( cType___24t(V0__X)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X)
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__43283] :
( t(Vvar__1___24Anonymous__43283,V0__X)
& ? [Vvar__2___24Anonymous__43284] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,Vvar__2___24Anonymous__43284)
& ( cType___24t(V0__X)
=> ( c_24__type__11245___24t(V0__X,V1__p)
=> ( t(Vvar__1___24Anonymous__43283,V0__X)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,Vvar__1___24Anonymous__43283,Vvar__2___24Anonymous__43284)
& ( ( happ(V1__p,Vvar__1___24Anonymous__43283) = cCoq_2eInit_2eDatatypes_2etrue
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__43284)) )
| ( happ(V1__p,Vvar__1___24Anonymous__43283) = cCoq_2eInit_2eDatatypes_2efalse
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__43284) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.list_utils.repeat',axiom,
! [V1__T,V2__n,V3__x] :
( cType___24t(V1__T)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T) )
| ? [Vvar__0___24Anonymous__65] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__65)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__65)
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V3__x,cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,Vvar__0___24Anonymous__65,V3__x)) ) ) ) ) ).
fof('$_def_QuicksortComplexity.util.ext_eq',axiom,
! [V0__A,V1__B,V2__f,V3__g] :
( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__f,V3__g)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) ) ) ).
fof('$_def_QuicksortComplexity.util.id',axiom,
! [V0__X,V1__x] : cQuicksortComplexity_2eutil_2eid___24a2(V0__X,V1__x) = V1__x ).
fof('$_def_monads.bind',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__435] :
( c_24__type__20___24t(Vvar__0__mon__435)
& ? [Vvar__1__bind__437] :
( c_24__type__594___24t(Vvar__0__mon__435,Vvar__1__bind__437)
& ? [Vvar__2__ret__448] :
( c_24__type__604___24t(Vvar__0__mon__435,Vvar__2__ret__448)
& ! [Vvar__var__3__a__454__459] :
( cType___24t(Vvar__var__3__a__454__459)
=> ! [Vvar__var__4__b__455__460] :
( cType___24t(Vvar__var__4__b__455__460)
=> ! [Vvar__var__5__x__457__462] :
( t(Vvar__var__5__x__457__462,Vvar__var__3__a__454__459)
=> ! [Vvar__var__6__f__458__463] :
( c_24__type__599___24t(Vvar__0__mon__435,Vvar__var__3__a__454__459,Vvar__var__4__b__455__460,Vvar__var__6__f__458__463)
=> happ(happ(happ(happ(Vvar__1__bind__437,Vvar__var__3__a__454__459),Vvar__var__4__b__455__460),happ(happ(Vvar__2__ret__448,Vvar__var__3__a__454__459),Vvar__var__5__x__457__462)),Vvar__var__6__f__458__463) = happ(Vvar__var__6__f__458__463,Vvar__var__5__x__457__462) ) ) ) )
& ! [Vvar__var__4__a__465__467] :
( cType___24t(Vvar__var__4__a__465__467)
=> ! [Vvar__var__5__f__466__468] :
( t(Vvar__var__5__f__466__468,happ(Vvar__0__mon__435,Vvar__var__4__a__465__467))
=> happ(happ(happ(happ(Vvar__1__bind__437,Vvar__var__4__a__465__467),Vvar__var__4__a__465__467),Vvar__var__5__f__466__468),happ(Vvar__2__ret__448,Vvar__var__4__a__465__467)) = Vvar__var__5__f__466__468 ) )
& ! [Vvar__var__5__a__470__479] :
( cType___24t(Vvar__var__5__a__470__479)
=> ! [Vvar__var__6__b__471__480] :
( cType___24t(Vvar__var__6__b__471__480)
=> ! [Vvar__var__7__c__473__482] :
( cType___24t(Vvar__var__7__c__473__482)
=> ! [Vvar__var__8__n__475__484] :
( t(Vvar__var__8__n__475__484,happ(Vvar__0__mon__435,Vvar__var__5__a__470__479))
=> ! [Vvar__var__9__f__476__485] :
( c_24__type__599___24t(Vvar__0__mon__435,Vvar__var__5__a__470__479,Vvar__var__6__b__471__480,Vvar__var__9__f__476__485)
=> ! [Vvar__var__10__g__477__486] :
( c_24__type__623___24t(Vvar__0__mon__435,Vvar__var__5__a__470__479,Vvar__var__6__b__471__480,Vvar__var__7__c__473__482,Vvar__var__10__g__477__486)
=> happ(happ(happ(happ(Vvar__1__bind__437,Vvar__var__6__b__471__480),Vvar__var__7__c__473__482),happ(happ(happ(happ(Vvar__1__bind__437,Vvar__var__5__a__470__479),Vvar__var__6__b__471__480),Vvar__var__8__n__475__484),Vvar__var__9__f__476__485)),Vvar__var__10__g__477__486) = happ(happ(happ(happ(Vvar__1__bind__437,Vvar__var__5__a__470__479),Vvar__var__7__c__473__482),Vvar__var__8__n__475__484),c_24__lam__648___24a7(Vvar__0__mon__435,Vvar__1__bind__437,Vvar__var__5__a__470__479,Vvar__var__6__b__471__480,Vvar__var__7__c__473__482,Vvar__var__9__f__476__485,Vvar__var__10__g__477__486)) ) ) ) ) ) )
& V0__m = cmonads_2eBuild__Monad___24a3(Vvar__0__mon__435,Vvar__1__bind__437,Vvar__2__ret__448)
& cmonads_2ebind___24a1(V0__m) = Vvar__1__bind__437 ) ) ) ) ).
fof('$_def_monads.extMonad',axiom,
! [V0__M] :
( cmonads_2eextMonad___24a1(V0__M)
<=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__172___24t(V0__M,V1__A,V2__B,V3__f)
=> ! [V4__g] :
( c_24__type__172___24t(V0__M,V1__A,V2__B,V4__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V1__A,cmonads_2emon___24a2(V0__M,V2__B),V3__f,V4__g)
=> ! [V6__x] :
( cmonads_2emon___24t(V0__M,V1__A,V6__x)
=> cmonads_2ebind___24a5(V0__M,V1__A,V2__B,V6__x,V3__f) = cmonads_2ebind___24a5(V0__M,V1__A,V2__B,V6__x,V4__g) ) ) ) ) ) ) ) ).
fof('$_def_monads.mon',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__677] :
( c_24__type__20___24t(Vvar__0__mon__677)
& ? [Vvar__1__bind__679] :
( c_24__type__836___24t(Vvar__0__mon__677,Vvar__1__bind__679)
& ? [Vvar__2__ret__690] :
( c_24__type__846___24t(Vvar__0__mon__677,Vvar__2__ret__690)
& ! [Vvar__var__3__a__696__701] :
( cType___24t(Vvar__var__3__a__696__701)
=> ! [Vvar__var__4__b__697__702] :
( cType___24t(Vvar__var__4__b__697__702)
=> ! [Vvar__var__5__x__699__704] :
( t(Vvar__var__5__x__699__704,Vvar__var__3__a__696__701)
=> ! [Vvar__var__6__f__700__705] :
( c_24__type__841___24t(Vvar__0__mon__677,Vvar__var__3__a__696__701,Vvar__var__4__b__697__702,Vvar__var__6__f__700__705)
=> happ(happ(happ(happ(Vvar__1__bind__679,Vvar__var__3__a__696__701),Vvar__var__4__b__697__702),happ(happ(Vvar__2__ret__690,Vvar__var__3__a__696__701),Vvar__var__5__x__699__704)),Vvar__var__6__f__700__705) = happ(Vvar__var__6__f__700__705,Vvar__var__5__x__699__704) ) ) ) )
& ! [Vvar__var__4__a__707__709] :
( cType___24t(Vvar__var__4__a__707__709)
=> ! [Vvar__var__5__f__708__710] :
( t(Vvar__var__5__f__708__710,happ(Vvar__0__mon__677,Vvar__var__4__a__707__709))
=> happ(happ(happ(happ(Vvar__1__bind__679,Vvar__var__4__a__707__709),Vvar__var__4__a__707__709),Vvar__var__5__f__708__710),happ(Vvar__2__ret__690,Vvar__var__4__a__707__709)) = Vvar__var__5__f__708__710 ) )
& ! [Vvar__var__5__a__712__721] :
( cType___24t(Vvar__var__5__a__712__721)
=> ! [Vvar__var__6__b__713__722] :
( cType___24t(Vvar__var__6__b__713__722)
=> ! [Vvar__var__7__c__715__724] :
( cType___24t(Vvar__var__7__c__715__724)
=> ! [Vvar__var__8__n__717__726] :
( t(Vvar__var__8__n__717__726,happ(Vvar__0__mon__677,Vvar__var__5__a__712__721))
=> ! [Vvar__var__9__f__718__727] :
( c_24__type__841___24t(Vvar__0__mon__677,Vvar__var__5__a__712__721,Vvar__var__6__b__713__722,Vvar__var__9__f__718__727)
=> ! [Vvar__var__10__g__719__728] :
( c_24__type__865___24t(Vvar__0__mon__677,Vvar__var__5__a__712__721,Vvar__var__6__b__713__722,Vvar__var__7__c__715__724,Vvar__var__10__g__719__728)
=> happ(happ(happ(happ(Vvar__1__bind__679,Vvar__var__6__b__713__722),Vvar__var__7__c__715__724),happ(happ(happ(happ(Vvar__1__bind__679,Vvar__var__5__a__712__721),Vvar__var__6__b__713__722),Vvar__var__8__n__717__726),Vvar__var__9__f__718__727)),Vvar__var__10__g__719__728) = happ(happ(happ(happ(Vvar__1__bind__679,Vvar__var__5__a__712__721),Vvar__var__7__c__715__724),Vvar__var__8__n__717__726),c_24__lam__890___24a7(Vvar__0__mon__677,Vvar__1__bind__679,Vvar__var__5__a__712__721,Vvar__var__6__b__713__722,Vvar__var__7__c__715__724,Vvar__var__9__f__718__727,Vvar__var__10__g__719__728)) ) ) ) ) ) )
& V0__m = cmonads_2eBuild__Monad___24a3(Vvar__0__mon__677,Vvar__1__bind__679,Vvar__2__ret__690)
& cmonads_2emon___24a1(V0__m) = Vvar__0__mon__677 ) ) ) ) ).
fof('$_def_monads.ret',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__207] :
( c_24__type__20___24t(Vvar__0__mon__207)
& ? [Vvar__1__bind__209] :
( c_24__type__366___24t(Vvar__0__mon__207,Vvar__1__bind__209)
& ? [Vvar__2__ret__220] :
( c_24__type__376___24t(Vvar__0__mon__207,Vvar__2__ret__220)
& ! [Vvar__var__3__a__226__231] :
( cType___24t(Vvar__var__3__a__226__231)
=> ! [Vvar__var__4__b__227__232] :
( cType___24t(Vvar__var__4__b__227__232)
=> ! [Vvar__var__5__x__229__234] :
( t(Vvar__var__5__x__229__234,Vvar__var__3__a__226__231)
=> ! [Vvar__var__6__f__230__235] :
( c_24__type__371___24t(Vvar__0__mon__207,Vvar__var__3__a__226__231,Vvar__var__4__b__227__232,Vvar__var__6__f__230__235)
=> happ(happ(happ(happ(Vvar__1__bind__209,Vvar__var__3__a__226__231),Vvar__var__4__b__227__232),happ(happ(Vvar__2__ret__220,Vvar__var__3__a__226__231),Vvar__var__5__x__229__234)),Vvar__var__6__f__230__235) = happ(Vvar__var__6__f__230__235,Vvar__var__5__x__229__234) ) ) ) )
& ! [Vvar__var__4__a__237__239] :
( cType___24t(Vvar__var__4__a__237__239)
=> ! [Vvar__var__5__f__238__240] :
( t(Vvar__var__5__f__238__240,happ(Vvar__0__mon__207,Vvar__var__4__a__237__239))
=> happ(happ(happ(happ(Vvar__1__bind__209,Vvar__var__4__a__237__239),Vvar__var__4__a__237__239),Vvar__var__5__f__238__240),happ(Vvar__2__ret__220,Vvar__var__4__a__237__239)) = Vvar__var__5__f__238__240 ) )
& ! [Vvar__var__5__a__242__251] :
( cType___24t(Vvar__var__5__a__242__251)
=> ! [Vvar__var__6__b__243__252] :
( cType___24t(Vvar__var__6__b__243__252)
=> ! [Vvar__var__7__c__245__254] :
( cType___24t(Vvar__var__7__c__245__254)
=> ! [Vvar__var__8__n__247__256] :
( t(Vvar__var__8__n__247__256,happ(Vvar__0__mon__207,Vvar__var__5__a__242__251))
=> ! [Vvar__var__9__f__248__257] :
( c_24__type__371___24t(Vvar__0__mon__207,Vvar__var__5__a__242__251,Vvar__var__6__b__243__252,Vvar__var__9__f__248__257)
=> ! [Vvar__var__10__g__249__258] :
( c_24__type__395___24t(Vvar__0__mon__207,Vvar__var__5__a__242__251,Vvar__var__6__b__243__252,Vvar__var__7__c__245__254,Vvar__var__10__g__249__258)
=> happ(happ(happ(happ(Vvar__1__bind__209,Vvar__var__6__b__243__252),Vvar__var__7__c__245__254),happ(happ(happ(happ(Vvar__1__bind__209,Vvar__var__5__a__242__251),Vvar__var__6__b__243__252),Vvar__var__8__n__247__256),Vvar__var__9__f__248__257)),Vvar__var__10__g__249__258) = happ(happ(happ(happ(Vvar__1__bind__209,Vvar__var__5__a__242__251),Vvar__var__7__c__245__254),Vvar__var__8__n__247__256),c_24__lam__420___24a7(Vvar__0__mon__207,Vvar__1__bind__209,Vvar__var__5__a__242__251,Vvar__var__6__b__243__252,Vvar__var__7__c__245__254,Vvar__var__9__f__248__257,Vvar__var__10__g__249__258)) ) ) ) ) ) )
& V0__m = cmonads_2eBuild__Monad___24a3(Vvar__0__mon__207,Vvar__1__bind__209,Vvar__2__ret__220)
& cmonads_2eret___24a1(V0__m) = Vvar__2__ret__220 ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__31928,Vvar__1___24Anonymous__31929,Vvar__0__P__31930,Vvar__1___24Anonymous__31931] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31928) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31930) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__43453,Vvar__1___24Anonymous__43454,Vvar__2___24Anonymous__43455] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__43453,Vvar__1___24Anonymous__43454,Vvar__2___24Anonymous__43455) ).
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__7925,Vvar__1__Plt__7926,Vvar__2__Pgt__7927,Vvar__3___24Anonymous__7928,Vvar__0__Peq__7929,Vvar__1__Plt__7930,Vvar__2__Pgt__7931,Vvar__3___24Anonymous__7932] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__7925,Vvar__1__Plt__7926,Vvar__2__Pgt__7927) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__7929,Vvar__1__Plt__7930,Vvar__2__Pgt__7931) ).
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__5] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__7806,Vvar__1___24Anonymous__7807,Vvar__0__A__7808] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7806,Vvar__1___24Anonymous__7807) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7808) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__35741,Vvar__1__B__35742,Vvar__2___24Anonymous__35743,Vvar__0__A__35744,Vvar__1__B__35745,Vvar__2___24Anonymous__35746] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__35741,Vvar__1__B__35742,Vvar__2___24Anonymous__35743) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__35744,Vvar__1__B__35745,Vvar__2___24Anonymous__35746) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__22,Vvar__0__A__23,Vvar__1___24Anonymous__24,Vvar__2___24Anonymous__25] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23,Vvar__1___24Anonymous__24,Vvar__2___24Anonymous__25) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35667,Vvar__1__B__35668,Vvar__2___24Anonymous__35669,Vvar__0__A__35670,Vvar__1__B__35671,Vvar__2___24Anonymous__35672] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35667,Vvar__1__B__35668,Vvar__2___24Anonymous__35669) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35670,Vvar__1__B__35671) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__27592,Vvar__1__B__27593,Vvar__2___24Anonymous__27594,Vvar__0__A__27595,Vvar__1__B__27596,Vvar__2___24Anonymous__27597] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__27592,Vvar__1__B__27593) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__27595,Vvar__1__B__27596) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1282] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1282) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__2693] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2693) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1274,Vvar__0___24Anonymous__1275] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1274) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1275) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__29446] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29446) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__11682,Vvar__1___24Anonymous__11683,Vvar__0__x__11684,Vvar__1__n__11685,Vvar__2___24Anonymous__11686] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__11682) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__11684,Vvar__1__n__11685) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__27623,Vvar__1___24Anonymous__27624] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__27623,Vvar__1___24Anonymous__27624) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__11424,Vvar__1__lt__11425,Vvar__2__eq__11426,Vvar__3__x__11427,Vvar__4__y__11428,Vvar__5___24Anonymous__11429,Vvar__0__X__11430,Vvar__1__lt__11431,Vvar__2__eq__11432,Vvar__3__x__11433,Vvar__4__y__11434,Vvar__5___24Anonymous__11435] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__11424,Vvar__1__lt__11425,Vvar__2__eq__11426,Vvar__3__x__11427,Vvar__4__y__11428) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__11430,Vvar__1__lt__11431,Vvar__2__eq__11432,Vvar__3__x__11433,Vvar__4__y__11434) ).
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__10695,Vvar__0__n__10696,Vvar__1___24Anonymous__10697] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__10695) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__10696,Vvar__1___24Anonymous__10697) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__27752,Vvar__0__A__27753,Vvar__1__h__27754,Vvar__2__n__27755,Vvar__3___24Anonymous__27756] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__27752) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__27753,Vvar__1__h__27754,Vvar__2__n__27755,Vvar__3___24Anonymous__27756) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__8193,Vvar__1___24Anonymous__8194,Vvar__0__C__8195,Vvar__1___24Anonymous__8196] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__8193,Vvar__1___24Anonymous__8194) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__8195,Vvar__1___24Anonymous__8196) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__31994,Vvar__1___24Anonymous__31995,Vvar__0__C__31996,Vvar__1___24Anonymous__31997,Vvar__2___24Anonymous__31998] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__31994,Vvar__1___24Anonymous__31995) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__31996,Vvar__1___24Anonymous__31997,Vvar__2___24Anonymous__31998) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__8244,Vvar__1___24Anonymous__8245] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__8244,Vvar__1___24Anonymous__8245) ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__43101,Vvar__1__TX__43102,Vvar__2__AA__43103,Vvar__3__AF__43104,Vvar__0__TA__43105,Vvar__1__TX__43106,Vvar__2__AA__43107,Vvar__3__AF__43108] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__43101,Vvar__1__TX__43102,Vvar__2__AA__43103,Vvar__3__AF__43104) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__43105,Vvar__1__TX__43106,Vvar__2__AA__43107,Vvar__3__AF__43108) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8802,Vvar__0__C__8803] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8802) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8803) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__13210,Vvar__0__C__13211] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__13210) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__13211) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12854,Vvar__1___24Anonymous__12855,Vvar__0__C__12856,Vvar__1___24Anonymous__12857,Vvar__2___24Anonymous__12858] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12854,Vvar__1___24Anonymous__12855) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12856,Vvar__1___24Anonymous__12857,Vvar__2___24Anonymous__12858) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__13020,Vvar__1___24Anonymous__13021] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__13020,Vvar__1___24Anonymous__13021) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__5735,Vvar__1__req__5736,Vvar__2__reqb__5737,Vvar__3___24Anonymous__5738] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__5735,Vvar__1__req__5736,Vvar__2__reqb__5737) ).
fof('$_fix_2494_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__fix__2494__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__2498] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__2498)
& ? [Vvar__2___24Anonymous__2499] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__2499)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2498,Vvar__2___24Anonymous__2499)
& c_24__fix__2494__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__2498),c_24__fix__2494__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__2499)) ) ) ) ) ) ).
fof('$_fix_2591_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__fix__2591__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__2595] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__2595)
& ? [Vvar__2___24Anonymous__2596] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__2596)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2595,Vvar__2___24Anonymous__2596)
& c_24__fix__2591__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__2595,c_24__fix__2591__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__2596,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_29409_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__29424] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29424)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29424)
& ( ? [Vvar__0___24Anonymous__29428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29428)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29428)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__29409__1__add__carry___24a2(Vvar__0___24Anonymous__29424,Vvar__0___24Anonymous__29428)) )
| ? [Vvar__0___24Anonymous__29429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29429)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29429)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29409__1__add__carry___24a2(Vvar__0___24Anonymous__29424,Vvar__0___24Anonymous__29429)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29424)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29430] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29430)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29430)
& ( ? [Vvar__0___24Anonymous__29434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29434)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29434)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__29409__1__add__carry___24a2(Vvar__0___24Anonymous__29430,Vvar__0___24Anonymous__29434)) )
| ? [Vvar__0___24Anonymous__29435] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29435)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29435)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29430,Vvar__0___24Anonymous__29435)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29430)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__29436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29436)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29436)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29436)) )
| ? [Vvar__0___24Anonymous__29437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29437)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29437)
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29437)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__29409__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__31936,Vvar__0__P__31937,Vvar__1___24Anonymous__31938,Vvar__1___24Anonymous__31939] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31936) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31937)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__31936 = Vvar__0__P__31937 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__31932,Vvar__0__P__31933,Vvar__1___24Anonymous__31934,Vvar__1___24Anonymous__31935] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31932) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31933)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__31932 = Vvar__0__P__31933 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__43456,Vvar__0___24Anonymous__43457,Vvar__1___24Anonymous__43458,Vvar__1___24Anonymous__43459,Vvar__2___24Anonymous__43460,Vvar__2___24Anonymous__43461] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__43456,Vvar__1___24Anonymous__43458,Vvar__2___24Anonymous__43460) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__43457,Vvar__1___24Anonymous__43459,Vvar__2___24Anonymous__43461)
=> ( Vvar__2___24Anonymous__43460 = Vvar__2___24Anonymous__43461
& Vvar__1___24Anonymous__43458 = Vvar__1___24Anonymous__43459
& Vvar__0___24Anonymous__43456 = Vvar__0___24Anonymous__43457 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__7933,Vvar__0__Peq__7934,Vvar__1__Plt__7935,Vvar__1__Plt__7936,Vvar__2__Pgt__7937,Vvar__2__Pgt__7938,Vvar__3___24Anonymous__7939,Vvar__3___24Anonymous__7940] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__7933,Vvar__1__Plt__7935,Vvar__2__Pgt__7937) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__7934,Vvar__1__Plt__7936,Vvar__2__Pgt__7938)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__7937 = Vvar__2__Pgt__7938
& Vvar__1__Plt__7935 = Vvar__1__Plt__7936
& Vvar__0__Peq__7933 = Vvar__0__Peq__7934 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__7949,Vvar__0__Peq__7950,Vvar__1__Plt__7951,Vvar__1__Plt__7952,Vvar__2__Pgt__7953,Vvar__2__Pgt__7954,Vvar__3___24Anonymous__7955,Vvar__3___24Anonymous__7956] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__7949,Vvar__1__Plt__7951,Vvar__2__Pgt__7953) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__7950,Vvar__1__Plt__7952,Vvar__2__Pgt__7954)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__7953 = Vvar__2__Pgt__7954
& Vvar__1__Plt__7951 = Vvar__1__Plt__7952
& Vvar__0__Peq__7949 = Vvar__0__Peq__7950 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__7941,Vvar__0__Peq__7942,Vvar__1__Plt__7943,Vvar__1__Plt__7944,Vvar__2__Pgt__7945,Vvar__2__Pgt__7946,Vvar__3___24Anonymous__7947,Vvar__3___24Anonymous__7948] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__7941,Vvar__1__Plt__7943,Vvar__2__Pgt__7945) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__7942,Vvar__1__Plt__7944,Vvar__2__Pgt__7946)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__7945 = Vvar__2__Pgt__7946
& Vvar__1__Plt__7943 = Vvar__1__Plt__7944
& Vvar__0__Peq__7941 = Vvar__0__Peq__7942 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__7813,Vvar__0__A__7814] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7813) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7814)
=> Vvar__0__A__7813 = Vvar__0__A__7814 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7)
=> Vvar__0___24Anonymous__6 = Vvar__0___24Anonymous__7 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__7809,Vvar__0__A__7810,Vvar__1___24Anonymous__7811,Vvar__1___24Anonymous__7812] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7809,Vvar__1___24Anonymous__7811) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7810,Vvar__1___24Anonymous__7812)
=> ( Vvar__1___24Anonymous__7811 = Vvar__1___24Anonymous__7812
& Vvar__0__A__7809 = Vvar__0__A__7810 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__28,Vvar__0__A__29,Vvar__1___24Anonymous__30,Vvar__1___24Anonymous__31,Vvar__2___24Anonymous__32,Vvar__2___24Anonymous__33] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28,Vvar__1___24Anonymous__30,Vvar__2___24Anonymous__32) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29,Vvar__1___24Anonymous__31,Vvar__2___24Anonymous__33)
=> ( Vvar__2___24Anonymous__32 = Vvar__2___24Anonymous__33
& Vvar__1___24Anonymous__30 = Vvar__1___24Anonymous__31
& Vvar__0__A__28 = Vvar__0__A__29 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__35747,Vvar__0__A__35748,Vvar__1__B__35749,Vvar__1__B__35750,Vvar__2___24Anonymous__35751,Vvar__2___24Anonymous__35752] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__35747,Vvar__1__B__35749,Vvar__2___24Anonymous__35751) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__35748,Vvar__1__B__35750,Vvar__2___24Anonymous__35752)
=> ( Vvar__2___24Anonymous__35751 = Vvar__2___24Anonymous__35752
& Vvar__1__B__35749 = Vvar__1__B__35750
& Vvar__0__A__35747 = Vvar__0__A__35748 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__35753,Vvar__0__A__35754,Vvar__1__B__35755,Vvar__1__B__35756,Vvar__2___24Anonymous__35757,Vvar__2___24Anonymous__35758] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__35753,Vvar__1__B__35755,Vvar__2___24Anonymous__35757) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__35754,Vvar__1__B__35756,Vvar__2___24Anonymous__35758)
=> ( Vvar__2___24Anonymous__35757 = Vvar__2___24Anonymous__35758
& Vvar__1__B__35755 = Vvar__1__B__35756
& Vvar__0__A__35753 = Vvar__0__A__35754 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__26,Vvar__0__A__27] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27)
=> Vvar__0__A__26 = Vvar__0__A__27 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__1297,Vvar__0__A__1298,Vvar__1__B__1299,Vvar__1__B__1300,Vvar__2___24Anonymous__1301,Vvar__2___24Anonymous__1302,Vvar__3___24Anonymous__1303,Vvar__3___24Anonymous__1304] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1297,Vvar__1__B__1299,Vvar__2___24Anonymous__1301,Vvar__3___24Anonymous__1303) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1298,Vvar__1__B__1300,Vvar__2___24Anonymous__1302,Vvar__3___24Anonymous__1304)
=> ( Vvar__3___24Anonymous__1303 = Vvar__3___24Anonymous__1304
& Vvar__2___24Anonymous__1301 = Vvar__2___24Anonymous__1302
& Vvar__1__B__1299 = Vvar__1__B__1300
& Vvar__0__A__1297 = Vvar__0__A__1298 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__1371,Vvar__0__A__1372,Vvar__1__P__1373,Vvar__1__P__1374,Vvar__2__x__1375,Vvar__2__x__1376,Vvar__3___24Anonymous__1377,Vvar__3___24Anonymous__1378] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1371,Vvar__1__P__1373,Vvar__2__x__1375) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1372,Vvar__1__P__1374,Vvar__2__x__1376)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__1375 = Vvar__2__x__1376
& Vvar__1__P__1373 = Vvar__1__P__1374
& Vvar__0__A__1371 = Vvar__0__A__1372 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__14851,Vvar__0__A__14852,Vvar__1__P__14853,Vvar__1__P__14854,Vvar__2__Q__14855,Vvar__2__Q__14856,Vvar__3__x__14857,Vvar__3__x__14858,Vvar__4___24Anonymous__14859,Vvar__4___24Anonymous__14860,Vvar__5___24Anonymous__14861,Vvar__5___24Anonymous__14862] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__14851,Vvar__1__P__14853,Vvar__2__Q__14855,Vvar__3__x__14857) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__14852,Vvar__1__P__14854,Vvar__2__Q__14856,Vvar__3__x__14858)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__14857 = Vvar__3__x__14858
& Vvar__2__Q__14855 = Vvar__2__Q__14856
& Vvar__1__P__14853 = Vvar__1__P__14854
& Vvar__0__A__14851 = Vvar__0__A__14852 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__2736,Vvar__0__A__2737,Vvar__1__P__2738,Vvar__1__P__2739,Vvar__2__x__2740,Vvar__2__x__2741,Vvar__3___24Anonymous__2742,Vvar__3___24Anonymous__2743] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2736,Vvar__1__P__2738,Vvar__2__x__2740,Vvar__3___24Anonymous__2742) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2737,Vvar__1__P__2739,Vvar__2__x__2741,Vvar__3___24Anonymous__2743)
=> ( Vvar__3___24Anonymous__2742 = Vvar__3___24Anonymous__2743
& Vvar__2__x__2740 = Vvar__2__x__2741
& Vvar__1__P__2738 = Vvar__1__P__2739
& Vvar__0__A__2736 = Vvar__0__A__2737 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__14929,Vvar__0__A__14930,Vvar__1__P__14931,Vvar__1__P__14932,Vvar__2__Q__14933,Vvar__2__Q__14934,Vvar__3__x__14935,Vvar__3__x__14936,Vvar__4___24Anonymous__14937,Vvar__4___24Anonymous__14938,Vvar__5___24Anonymous__14939,Vvar__5___24Anonymous__14940] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__14929,Vvar__1__P__14931,Vvar__2__Q__14933,Vvar__3__x__14935,Vvar__4___24Anonymous__14937,Vvar__5___24Anonymous__14939) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__14930,Vvar__1__P__14932,Vvar__2__Q__14934,Vvar__3__x__14936,Vvar__4___24Anonymous__14938,Vvar__5___24Anonymous__14940)
=> ( Vvar__5___24Anonymous__14939 = Vvar__5___24Anonymous__14940
& Vvar__4___24Anonymous__14937 = Vvar__4___24Anonymous__14938
& Vvar__3__x__14935 = Vvar__3__x__14936
& Vvar__2__Q__14933 = Vvar__2__Q__14934
& Vvar__1__P__14931 = Vvar__1__P__14932
& Vvar__0__A__14929 = Vvar__0__A__14930 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__35673,Vvar__0__A__35674,Vvar__1__B__35675,Vvar__1__B__35676,Vvar__2___24Anonymous__35677,Vvar__2___24Anonymous__35678] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35673,Vvar__1__B__35675,Vvar__2___24Anonymous__35677) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35674,Vvar__1__B__35676,Vvar__2___24Anonymous__35678)
=> ( Vvar__2___24Anonymous__35677 = Vvar__2___24Anonymous__35678
& Vvar__1__B__35675 = Vvar__1__B__35676
& Vvar__0__A__35673 = Vvar__0__A__35674 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__35679,Vvar__0__A__35680,Vvar__1__B__35681,Vvar__1__B__35682,Vvar__2___24Anonymous__35683,Vvar__2___24Anonymous__35684] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35679,Vvar__1__B__35681) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35680,Vvar__1__B__35682)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__35681 = Vvar__1__B__35682
& Vvar__0__A__35679 = Vvar__0__A__35680 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__27598,Vvar__0__A__27599,Vvar__1__B__27600,Vvar__1__B__27601,Vvar__2___24Anonymous__27602,Vvar__2___24Anonymous__27603] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__27598,Vvar__1__B__27600) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__27599,Vvar__1__B__27601)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__27600 = Vvar__1__B__27601
& Vvar__0__A__27598 = Vvar__0__A__27599 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__27604,Vvar__0__A__27605,Vvar__1__B__27606,Vvar__1__B__27607,Vvar__2___24Anonymous__27608,Vvar__2___24Anonymous__27609] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__27604,Vvar__1__B__27606) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__27605,Vvar__1__B__27607)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__27606 = Vvar__1__B__27607
& Vvar__0__A__27604 = Vvar__0__A__27605 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1283,Vvar__0___24Anonymous__1284] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1283) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1284)
=> Vvar__0___24Anonymous__1283 = Vvar__0___24Anonymous__1284 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__2696,Vvar__0___24Anonymous__2697] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2696) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2697)
=> Vvar__0___24Anonymous__2696 = Vvar__0___24Anonymous__2697 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__2694,Vvar__0___24Anonymous__2695] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2694) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2695)
=> Vvar__0___24Anonymous__2694 = Vvar__0___24Anonymous__2695 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1276,Vvar__0___24Anonymous__1277] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1276) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1277)
=> Vvar__0___24Anonymous__1276 = Vvar__0___24Anonymous__1277 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1278,Vvar__0___24Anonymous__1279] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1278) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1279)
=> Vvar__0___24Anonymous__1278 = Vvar__0___24Anonymous__1279 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__29447,Vvar__0___24Anonymous__29448] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29447) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29448)
=> Vvar__0___24Anonymous__29447 = Vvar__0___24Anonymous__29448 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__33872,Vvar__0__Qnum__33873,Vvar__1__Qden__33874,Vvar__1__Qden__33875] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__33872,Vvar__1__Qden__33874) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__33873,Vvar__1__Qden__33875)
=> ( Vvar__1__Qden__33874 = Vvar__1__Qden__33875
& Vvar__0__Qnum__33872 = Vvar__0__Qnum__33873 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__36158,Vvar__0__nonzero__36159,Vvar__1__cond__nonzero__36160,Vvar__1__cond__nonzero__36161] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__36158) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__36159)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__36158 = Vvar__0__nonzero__36159 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__11697,Vvar__0__x__11698,Vvar__1__n__11699,Vvar__1__n__11700,Vvar__2___24Anonymous__11701,Vvar__2___24Anonymous__11702] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__11697,Vvar__1__n__11699) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__11698,Vvar__1__n__11700)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__11699 = Vvar__1__n__11700
& Vvar__0__x__11697 = Vvar__0__x__11698 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__11687,Vvar__0__x__11688,Vvar__1___24Anonymous__11689,Vvar__1___24Anonymous__11690] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__11687) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__11688)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__11687 = Vvar__0__x__11688 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__11691,Vvar__0__x__11692,Vvar__1__n__11693,Vvar__1__n__11694,Vvar__2___24Anonymous__11695,Vvar__2___24Anonymous__11696] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__11691,Vvar__1__n__11693) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__11692,Vvar__1__n__11694)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__11693 = Vvar__1__n__11694
& Vvar__0__x__11691 = Vvar__0__x__11692 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__7760,Vvar__0___24Anonymous__7761,Vvar__1___24Anonymous__7762,Vvar__1___24Anonymous__7763,Vvar__2___24Anonymous__7764,Vvar__2___24Anonymous__7765,Vvar__3___24Anonymous__7766,Vvar__3___24Anonymous__7767,Vvar__4___24Anonymous__7768,Vvar__4___24Anonymous__7769,Vvar__5___24Anonymous__7770,Vvar__5___24Anonymous__7771,Vvar__6___24Anonymous__7772,Vvar__6___24Anonymous__7773,Vvar__7___24Anonymous__7774,Vvar__7___24Anonymous__7775] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__7760,Vvar__1___24Anonymous__7762,Vvar__2___24Anonymous__7764,Vvar__3___24Anonymous__7766,Vvar__4___24Anonymous__7768,Vvar__5___24Anonymous__7770,Vvar__6___24Anonymous__7772,Vvar__7___24Anonymous__7774) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__7761,Vvar__1___24Anonymous__7763,Vvar__2___24Anonymous__7765,Vvar__3___24Anonymous__7767,Vvar__4___24Anonymous__7769,Vvar__5___24Anonymous__7771,Vvar__6___24Anonymous__7773,Vvar__7___24Anonymous__7775)
=> ( Vvar__7___24Anonymous__7774 = Vvar__7___24Anonymous__7775
& Vvar__6___24Anonymous__7772 = Vvar__6___24Anonymous__7773
& Vvar__5___24Anonymous__7770 = Vvar__5___24Anonymous__7771
& Vvar__4___24Anonymous__7768 = Vvar__4___24Anonymous__7769
& Vvar__3___24Anonymous__7766 = Vvar__3___24Anonymous__7767
& Vvar__2___24Anonymous__7764 = Vvar__2___24Anonymous__7765
& Vvar__1___24Anonymous__7762 = Vvar__1___24Anonymous__7763
& Vvar__0___24Anonymous__7760 = Vvar__0___24Anonymous__7761 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__27625,Vvar__0___24Anonymous__27626,Vvar__1___24Anonymous__27627,Vvar__1___24Anonymous__27628] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__27625,Vvar__1___24Anonymous__27627) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__27626,Vvar__1___24Anonymous__27628)
=> ( Vvar__1___24Anonymous__27627 = Vvar__1___24Anonymous__27628
& Vvar__0___24Anonymous__27625 = Vvar__0___24Anonymous__27626 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__11448,Vvar__0__X__11449,Vvar__1__lt__11450,Vvar__1__lt__11451,Vvar__2__eq__11452,Vvar__2__eq__11453,Vvar__3__x__11454,Vvar__3__x__11455,Vvar__4__y__11456,Vvar__4__y__11457,Vvar__5___24Anonymous__11458,Vvar__5___24Anonymous__11459] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__11448,Vvar__1__lt__11450,Vvar__2__eq__11452,Vvar__3__x__11454,Vvar__4__y__11456) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__11449,Vvar__1__lt__11451,Vvar__2__eq__11453,Vvar__3__x__11455,Vvar__4__y__11457)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__11456 = Vvar__4__y__11457
& Vvar__3__x__11454 = Vvar__3__x__11455
& Vvar__2__eq__11452 = Vvar__2__eq__11453
& Vvar__1__lt__11450 = Vvar__1__lt__11451
& Vvar__0__X__11448 = Vvar__0__X__11449 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__11460,Vvar__0__X__11461,Vvar__1__lt__11462,Vvar__1__lt__11463,Vvar__2__eq__11464,Vvar__2__eq__11465,Vvar__3__x__11466,Vvar__3__x__11467,Vvar__4__y__11468,Vvar__4__y__11469,Vvar__5___24Anonymous__11470,Vvar__5___24Anonymous__11471] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__11460,Vvar__1__lt__11462,Vvar__2__eq__11464,Vvar__3__x__11466,Vvar__4__y__11468) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__11461,Vvar__1__lt__11463,Vvar__2__eq__11465,Vvar__3__x__11467,Vvar__4__y__11469)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__11468 = Vvar__4__y__11469
& Vvar__3__x__11466 = Vvar__3__x__11467
& Vvar__2__eq__11464 = Vvar__2__eq__11465
& Vvar__1__lt__11462 = Vvar__1__lt__11463
& Vvar__0__X__11460 = Vvar__0__X__11461 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__11436,Vvar__0__X__11437,Vvar__1__lt__11438,Vvar__1__lt__11439,Vvar__2__eq__11440,Vvar__2__eq__11441,Vvar__3__x__11442,Vvar__3__x__11443,Vvar__4__y__11444,Vvar__4__y__11445,Vvar__5___24Anonymous__11446,Vvar__5___24Anonymous__11447] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__11436,Vvar__1__lt__11438,Vvar__2__eq__11440,Vvar__3__x__11442,Vvar__4__y__11444) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__11437,Vvar__1__lt__11439,Vvar__2__eq__11441,Vvar__3__x__11443,Vvar__4__y__11445)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__11444 = Vvar__4__y__11445
& Vvar__3__x__11442 = Vvar__3__x__11443
& Vvar__2__eq__11440 = Vvar__2__eq__11441
& Vvar__1__lt__11438 = Vvar__1__lt__11439
& Vvar__0__X__11436 = Vvar__0__X__11437 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__10698,Vvar__0__n__10699] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__10698) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__10699)
=> Vvar__0__n__10698 = Vvar__0__n__10699 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__10700,Vvar__0__n__10701,Vvar__1___24Anonymous__10702,Vvar__1___24Anonymous__10703] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__10700,Vvar__1___24Anonymous__10702) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__10701,Vvar__1___24Anonymous__10703)
=> ( Vvar__1___24Anonymous__10702 = Vvar__1___24Anonymous__10703
& Vvar__0__n__10700 = Vvar__0__n__10701 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__27759,Vvar__0__A__27760,Vvar__1__h__27761,Vvar__1__h__27762,Vvar__2__n__27763,Vvar__2__n__27764,Vvar__3___24Anonymous__27765,Vvar__3___24Anonymous__27766] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__27759,Vvar__1__h__27761,Vvar__2__n__27763,Vvar__3___24Anonymous__27765) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__27760,Vvar__1__h__27762,Vvar__2__n__27764,Vvar__3___24Anonymous__27766)
=> ( Vvar__3___24Anonymous__27765 = Vvar__3___24Anonymous__27766
& Vvar__2__n__27763 = Vvar__2__n__27764
& Vvar__1__h__27761 = Vvar__1__h__27762
& Vvar__0__A__27759 = Vvar__0__A__27760 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__27757,Vvar__0__A__27758] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__27757) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__27758)
=> Vvar__0__A__27757 = Vvar__0__A__27758 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__28910,Vvar__0__a__28911,Vvar__1__b__28912,Vvar__1__b__28913,Vvar__2__u__28914,Vvar__2__u__28915,Vvar__3__v__28916,Vvar__3__v__28917,Vvar__4__d__28918,Vvar__4__d__28919,Vvar__5___24Anonymous__28920,Vvar__5___24Anonymous__28921,Vvar__6___24Anonymous__28922,Vvar__6___24Anonymous__28923] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__28910,Vvar__1__b__28912,Vvar__2__u__28914,Vvar__3__v__28916,Vvar__4__d__28918) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__28911,Vvar__1__b__28913,Vvar__2__u__28915,Vvar__3__v__28917,Vvar__4__d__28919)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__28918 = Vvar__4__d__28919
& Vvar__3__v__28916 = Vvar__3__v__28917
& Vvar__2__u__28914 = Vvar__2__u__28915
& Vvar__1__b__28912 = Vvar__1__b__28913
& Vvar__0__a__28910 = Vvar__0__a__28911 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__28980,Vvar__0__x__28981,Vvar__1__p__28982,Vvar__1__p__28983,Vvar__2__q__28984,Vvar__2__q__28985,Vvar__3__r__28986,Vvar__3__r__28987,Vvar__4___24Anonymous__28988,Vvar__4___24Anonymous__28989,Vvar__5___24Anonymous__28990,Vvar__5___24Anonymous__28991,Vvar__6___24Anonymous__28992,Vvar__6___24Anonymous__28993] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__28980,Vvar__1__p__28982,Vvar__2__q__28984,Vvar__3__r__28986) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__28981,Vvar__1__p__28983,Vvar__2__q__28985,Vvar__3__r__28987)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__28986 = Vvar__3__r__28987
& Vvar__2__q__28984 = Vvar__2__q__28985
& Vvar__1__p__28982 = Vvar__1__p__28983
& Vvar__0__x__28980 = Vvar__0__x__28981 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__8201,Vvar__0__C__8202,Vvar__1___24Anonymous__8203,Vvar__1___24Anonymous__8204] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__8201,Vvar__1___24Anonymous__8203) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__8202,Vvar__1___24Anonymous__8204)
=> ( Vvar__1___24Anonymous__8203 = Vvar__1___24Anonymous__8204
& Vvar__0__C__8201 = Vvar__0__C__8202 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__8205,Vvar__0__C__8206,Vvar__1___24Anonymous__8207,Vvar__1___24Anonymous__8208,Vvar__2___24Anonymous__8209,Vvar__2___24Anonymous__8210] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__8205,Vvar__1___24Anonymous__8207,Vvar__2___24Anonymous__8209) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__8206,Vvar__1___24Anonymous__8208,Vvar__2___24Anonymous__8210)
=> ( Vvar__2___24Anonymous__8209 = Vvar__2___24Anonymous__8210
& Vvar__1___24Anonymous__8207 = Vvar__1___24Anonymous__8208
& Vvar__0__C__8205 = Vvar__0__C__8206 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__8197,Vvar__0__C__8198,Vvar__1___24Anonymous__8199,Vvar__1___24Anonymous__8200] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__8197,Vvar__1___24Anonymous__8199) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__8198,Vvar__1___24Anonymous__8200)
=> ( Vvar__1___24Anonymous__8199 = Vvar__1___24Anonymous__8200
& Vvar__0__C__8197 = Vvar__0__C__8198 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__8217,Vvar__0__C__8218,Vvar__1___24Anonymous__8219,Vvar__1___24Anonymous__8220,Vvar__2___24Anonymous__8221,Vvar__2___24Anonymous__8222] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__8217,Vvar__1___24Anonymous__8219,Vvar__2___24Anonymous__8221) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__8218,Vvar__1___24Anonymous__8220,Vvar__2___24Anonymous__8222)
=> ( Vvar__2___24Anonymous__8221 = Vvar__2___24Anonymous__8222
& Vvar__1___24Anonymous__8219 = Vvar__1___24Anonymous__8220
& Vvar__0__C__8217 = Vvar__0__C__8218 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__8223,Vvar__0__C__8224,Vvar__1___24Anonymous__8225,Vvar__1___24Anonymous__8226] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__8223,Vvar__1___24Anonymous__8225) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__8224,Vvar__1___24Anonymous__8226)
=> ( Vvar__1___24Anonymous__8225 = Vvar__1___24Anonymous__8226
& Vvar__0__C__8223 = Vvar__0__C__8224 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__8227,Vvar__0__C__8228,Vvar__1___24Anonymous__8229,Vvar__1___24Anonymous__8230,Vvar__2___24Anonymous__8231,Vvar__2___24Anonymous__8232] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__8227,Vvar__1___24Anonymous__8229,Vvar__2___24Anonymous__8231) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__8228,Vvar__1___24Anonymous__8230,Vvar__2___24Anonymous__8232)
=> ( Vvar__2___24Anonymous__8231 = Vvar__2___24Anonymous__8232
& Vvar__1___24Anonymous__8229 = Vvar__1___24Anonymous__8230
& Vvar__0__C__8227 = Vvar__0__C__8228 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__8211,Vvar__0__C__8212,Vvar__1___24Anonymous__8213,Vvar__1___24Anonymous__8214,Vvar__2___24Anonymous__8215,Vvar__2___24Anonymous__8216] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__8211,Vvar__1___24Anonymous__8213,Vvar__2___24Anonymous__8215) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__8212,Vvar__1___24Anonymous__8214,Vvar__2___24Anonymous__8216)
=> ( Vvar__2___24Anonymous__8215 = Vvar__2___24Anonymous__8216
& Vvar__1___24Anonymous__8213 = Vvar__1___24Anonymous__8214
& Vvar__0__C__8211 = Vvar__0__C__8212 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__32009,Vvar__0__C__32010,Vvar__1___24Anonymous__32011,Vvar__1___24Anonymous__32012,Vvar__2___24Anonymous__32013,Vvar__2___24Anonymous__32014,Vvar__3___24Anonymous__32015,Vvar__3___24Anonymous__32016] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__32009,Vvar__1___24Anonymous__32011,Vvar__2___24Anonymous__32013,Vvar__3___24Anonymous__32015) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__32010,Vvar__1___24Anonymous__32012,Vvar__2___24Anonymous__32014,Vvar__3___24Anonymous__32016)
=> ( Vvar__3___24Anonymous__32015 = Vvar__3___24Anonymous__32016
& Vvar__2___24Anonymous__32013 = Vvar__2___24Anonymous__32014
& Vvar__1___24Anonymous__32011 = Vvar__1___24Anonymous__32012
& Vvar__0__C__32009 = Vvar__0__C__32010 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__31999,Vvar__0__C__32000,Vvar__1___24Anonymous__32001,Vvar__1___24Anonymous__32002] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__31999,Vvar__1___24Anonymous__32001) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__32000,Vvar__1___24Anonymous__32002)
=> ( Vvar__1___24Anonymous__32001 = Vvar__1___24Anonymous__32002
& Vvar__0__C__31999 = Vvar__0__C__32000 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__32003,Vvar__0__C__32004,Vvar__1___24Anonymous__32005,Vvar__1___24Anonymous__32006,Vvar__2___24Anonymous__32007,Vvar__2___24Anonymous__32008] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__32003,Vvar__1___24Anonymous__32005,Vvar__2___24Anonymous__32007) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__32004,Vvar__1___24Anonymous__32006,Vvar__2___24Anonymous__32008)
=> ( Vvar__2___24Anonymous__32007 = Vvar__2___24Anonymous__32008
& Vvar__1___24Anonymous__32005 = Vvar__1___24Anonymous__32006
& Vvar__0__C__32003 = Vvar__0__C__32004 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__8250,Vvar__0___24Anonymous__8251,Vvar__1___24Anonymous__8252,Vvar__1___24Anonymous__8253] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__8250,Vvar__1___24Anonymous__8252) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__8251,Vvar__1___24Anonymous__8253)
=> ( Vvar__1___24Anonymous__8252 = Vvar__1___24Anonymous__8253
& Vvar__0___24Anonymous__8250 = Vvar__0___24Anonymous__8251 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__8246,Vvar__0___24Anonymous__8247,Vvar__1___24Anonymous__8248,Vvar__1___24Anonymous__8249] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__8246,Vvar__1___24Anonymous__8248) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__8247,Vvar__1___24Anonymous__8249)
=> ( Vvar__1___24Anonymous__8248 = Vvar__1___24Anonymous__8249
& Vvar__0___24Anonymous__8246 = Vvar__0___24Anonymous__8247 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__12047,Vvar__0__T__12048,Vvar__1__Flhs__12049,Vvar__1__Flhs__12050,Vvar__2__Fop__12051,Vvar__2__Fop__12052,Vvar__3__Frhs__12053,Vvar__3__Frhs__12054] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__12047,Vvar__1__Flhs__12049,Vvar__2__Fop__12051,Vvar__3__Frhs__12053) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__12048,Vvar__1__Flhs__12050,Vvar__2__Fop__12052,Vvar__3__Frhs__12054)
=> ( Vvar__3__Frhs__12053 = Vvar__3__Frhs__12054
& Vvar__2__Fop__12051 = Vvar__2__Fop__12052
& Vvar__1__Flhs__12049 = Vvar__1__Flhs__12050
& Vvar__0__T__12047 = Vvar__0__T__12048 ) ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__43135,Vvar__0__TA__43136,Vvar__1__TX__43137,Vvar__1__TX__43138,Vvar__2__AA__43139,Vvar__2__AA__43140,Vvar__3__AF__43141,Vvar__3__AF__43142,Vvar__4___24Anonymous__43143,Vvar__4___24Anonymous__43144,Vvar__5___24Anonymous__43145,Vvar__5___24Anonymous__43146] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__43135,Vvar__1__TX__43137,Vvar__2__AA__43139,Vvar__3__AF__43141,Vvar__4___24Anonymous__43143,Vvar__5___24Anonymous__43145) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__43136,Vvar__1__TX__43138,Vvar__2__AA__43140,Vvar__3__AF__43142,Vvar__4___24Anonymous__43144,Vvar__5___24Anonymous__43146)
=> ( Vvar__5___24Anonymous__43145 = Vvar__5___24Anonymous__43146
& Vvar__4___24Anonymous__43143 = Vvar__4___24Anonymous__43144
& Vvar__3__AF__43141 = Vvar__3__AF__43142
& Vvar__2__AA__43139 = Vvar__2__AA__43140
& Vvar__1__TX__43137 = Vvar__1__TX__43138
& Vvar__0__TA__43135 = Vvar__0__TA__43136 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__43147,Vvar__0__TA__43148,Vvar__1__TX__43149,Vvar__1__TX__43150,Vvar__2__AA__43151,Vvar__2__AA__43152,Vvar__3__AF__43153,Vvar__3__AF__43154,Vvar__4___24Anonymous__43155,Vvar__4___24Anonymous__43156,Vvar__5___24Anonymous__43157,Vvar__5___24Anonymous__43158] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__43147,Vvar__1__TX__43149,Vvar__2__AA__43151,Vvar__3__AF__43153,Vvar__4___24Anonymous__43155,Vvar__5___24Anonymous__43157) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__43148,Vvar__1__TX__43150,Vvar__2__AA__43152,Vvar__3__AF__43154,Vvar__4___24Anonymous__43156,Vvar__5___24Anonymous__43158)
=> ( Vvar__5___24Anonymous__43157 = Vvar__5___24Anonymous__43158
& Vvar__4___24Anonymous__43155 = Vvar__4___24Anonymous__43156
& Vvar__3__AF__43153 = Vvar__3__AF__43154
& Vvar__2__AA__43151 = Vvar__2__AA__43152
& Vvar__1__TX__43149 = Vvar__1__TX__43150
& Vvar__0__TA__43147 = Vvar__0__TA__43148 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__43159,Vvar__0__TA__43160,Vvar__1__TX__43161,Vvar__1__TX__43162,Vvar__2__AA__43163,Vvar__2__AA__43164,Vvar__3__AF__43165,Vvar__3__AF__43166,Vvar__4___24Anonymous__43167,Vvar__4___24Anonymous__43168,Vvar__5___24Anonymous__43169,Vvar__5___24Anonymous__43170] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__43159,Vvar__1__TX__43161,Vvar__2__AA__43163,Vvar__3__AF__43165,Vvar__4___24Anonymous__43167,Vvar__5___24Anonymous__43169) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__43160,Vvar__1__TX__43162,Vvar__2__AA__43164,Vvar__3__AF__43166,Vvar__4___24Anonymous__43168,Vvar__5___24Anonymous__43170)
=> ( Vvar__5___24Anonymous__43169 = Vvar__5___24Anonymous__43170
& Vvar__4___24Anonymous__43167 = Vvar__4___24Anonymous__43168
& Vvar__3__AF__43165 = Vvar__3__AF__43166
& Vvar__2__AA__43163 = Vvar__2__AA__43164
& Vvar__1__TX__43161 = Vvar__1__TX__43162
& Vvar__0__TA__43159 = Vvar__0__TA__43160 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__43117,Vvar__0__TA__43118,Vvar__1__TX__43119,Vvar__1__TX__43120,Vvar__2__AA__43121,Vvar__2__AA__43122,Vvar__3__AF__43123,Vvar__3__AF__43124] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__43117,Vvar__1__TX__43119,Vvar__2__AA__43121,Vvar__3__AF__43123) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__43118,Vvar__1__TX__43120,Vvar__2__AA__43122,Vvar__3__AF__43124)
=> ( Vvar__3__AF__43123 = Vvar__3__AF__43124
& Vvar__2__AA__43121 = Vvar__2__AA__43122
& Vvar__1__TX__43119 = Vvar__1__TX__43120
& Vvar__0__TA__43117 = Vvar__0__TA__43118 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__43181,Vvar__0__TA__43182,Vvar__1__TX__43183,Vvar__1__TX__43184,Vvar__2__AA__43185,Vvar__2__AA__43186,Vvar__3__AF__43187,Vvar__3__AF__43188,Vvar__4___24Anonymous__43189,Vvar__4___24Anonymous__43190,Vvar__5___24Anonymous__43191,Vvar__5___24Anonymous__43192,Vvar__6___24Anonymous__43193,Vvar__6___24Anonymous__43194] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__43181,Vvar__1__TX__43183,Vvar__2__AA__43185,Vvar__3__AF__43187,Vvar__4___24Anonymous__43189,Vvar__5___24Anonymous__43191,Vvar__6___24Anonymous__43193) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__43182,Vvar__1__TX__43184,Vvar__2__AA__43186,Vvar__3__AF__43188,Vvar__4___24Anonymous__43190,Vvar__5___24Anonymous__43192,Vvar__6___24Anonymous__43194)
=> ( Vvar__6___24Anonymous__43193 = Vvar__6___24Anonymous__43194
& Vvar__5___24Anonymous__43191 = Vvar__5___24Anonymous__43192
& Vvar__4___24Anonymous__43189 = Vvar__4___24Anonymous__43190
& Vvar__3__AF__43187 = Vvar__3__AF__43188
& Vvar__2__AA__43185 = Vvar__2__AA__43186
& Vvar__1__TX__43183 = Vvar__1__TX__43184
& Vvar__0__TA__43181 = Vvar__0__TA__43182 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__43171,Vvar__0__TA__43172,Vvar__1__TX__43173,Vvar__1__TX__43174,Vvar__2__AA__43175,Vvar__2__AA__43176,Vvar__3__AF__43177,Vvar__3__AF__43178,Vvar__4___24Anonymous__43179,Vvar__4___24Anonymous__43180] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__43171,Vvar__1__TX__43173,Vvar__2__AA__43175,Vvar__3__AF__43177,Vvar__4___24Anonymous__43179) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__43172,Vvar__1__TX__43174,Vvar__2__AA__43176,Vvar__3__AF__43178,Vvar__4___24Anonymous__43180)
=> ( Vvar__4___24Anonymous__43179 = Vvar__4___24Anonymous__43180
& Vvar__3__AF__43177 = Vvar__3__AF__43178
& Vvar__2__AA__43175 = Vvar__2__AA__43176
& Vvar__1__TX__43173 = Vvar__1__TX__43174
& Vvar__0__TA__43171 = Vvar__0__TA__43172 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__43109,Vvar__0__TA__43110,Vvar__1__TX__43111,Vvar__1__TX__43112,Vvar__2__AA__43113,Vvar__2__AA__43114,Vvar__3__AF__43115,Vvar__3__AF__43116] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__43109,Vvar__1__TX__43111,Vvar__2__AA__43113,Vvar__3__AF__43115) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__43110,Vvar__1__TX__43112,Vvar__2__AA__43114,Vvar__3__AF__43116)
=> ( Vvar__3__AF__43115 = Vvar__3__AF__43116
& Vvar__2__AA__43113 = Vvar__2__AA__43114
& Vvar__1__TX__43111 = Vvar__1__TX__43112
& Vvar__0__TA__43109 = Vvar__0__TA__43110 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__43125,Vvar__0__TA__43126,Vvar__1__TX__43127,Vvar__1__TX__43128,Vvar__2__AA__43129,Vvar__2__AA__43130,Vvar__3__AF__43131,Vvar__3__AF__43132,Vvar__4___24Anonymous__43133,Vvar__4___24Anonymous__43134] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__43125,Vvar__1__TX__43127,Vvar__2__AA__43129,Vvar__3__AF__43131,Vvar__4___24Anonymous__43133) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__43126,Vvar__1__TX__43128,Vvar__2__AA__43130,Vvar__3__AF__43132,Vvar__4___24Anonymous__43134)
=> ( Vvar__4___24Anonymous__43133 = Vvar__4___24Anonymous__43134
& Vvar__3__AF__43131 = Vvar__3__AF__43132
& Vvar__2__AA__43129 = Vvar__2__AA__43130
& Vvar__1__TX__43127 = Vvar__1__TX__43128
& Vvar__0__TA__43125 = Vvar__0__TA__43126 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8806,Vvar__0__C__8807] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8806) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8807)
=> Vvar__0__C__8806 = Vvar__0__C__8807 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__8804,Vvar__0__C__8805] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8804) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8805)
=> Vvar__0__C__8804 = Vvar__0__C__8805 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__8812,Vvar__0__C__8813,Vvar__1___24Anonymous__8814,Vvar__1___24Anonymous__8815] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8812,Vvar__1___24Anonymous__8814) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8813,Vvar__1___24Anonymous__8815)
=> ( Vvar__1___24Anonymous__8814 = Vvar__1___24Anonymous__8815
& Vvar__0__C__8812 = Vvar__0__C__8813 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__8816,Vvar__0__C__8817,Vvar__1___24Anonymous__8818,Vvar__1___24Anonymous__8819,Vvar__2___24Anonymous__8820,Vvar__2___24Anonymous__8821] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8816,Vvar__1___24Anonymous__8818,Vvar__2___24Anonymous__8820) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8817,Vvar__1___24Anonymous__8819,Vvar__2___24Anonymous__8821)
=> ( Vvar__2___24Anonymous__8820 = Vvar__2___24Anonymous__8821
& Vvar__1___24Anonymous__8818 = Vvar__1___24Anonymous__8819
& Vvar__0__C__8816 = Vvar__0__C__8817 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__8808,Vvar__0__C__8809,Vvar__1___24Anonymous__8810,Vvar__1___24Anonymous__8811] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8808,Vvar__1___24Anonymous__8810) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8809,Vvar__1___24Anonymous__8811)
=> ( Vvar__1___24Anonymous__8810 = Vvar__1___24Anonymous__8811
& Vvar__0__C__8808 = Vvar__0__C__8809 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__8842,Vvar__0__C__8843,Vvar__1___24Anonymous__8844,Vvar__1___24Anonymous__8845,Vvar__2___24Anonymous__8846,Vvar__2___24Anonymous__8847] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8842,Vvar__1___24Anonymous__8844,Vvar__2___24Anonymous__8846) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8843,Vvar__1___24Anonymous__8845,Vvar__2___24Anonymous__8847)
=> ( Vvar__2___24Anonymous__8846 = Vvar__2___24Anonymous__8847
& Vvar__1___24Anonymous__8844 = Vvar__1___24Anonymous__8845
& Vvar__0__C__8842 = Vvar__0__C__8843 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__8838,Vvar__0__C__8839,Vvar__1___24Anonymous__8840,Vvar__1___24Anonymous__8841] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8838,Vvar__1___24Anonymous__8840) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8839,Vvar__1___24Anonymous__8841)
=> ( Vvar__1___24Anonymous__8840 = Vvar__1___24Anonymous__8841
& Vvar__0__C__8838 = Vvar__0__C__8839 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__8828,Vvar__0__C__8829,Vvar__1___24Anonymous__8830,Vvar__1___24Anonymous__8831,Vvar__2___24Anonymous__8832,Vvar__2___24Anonymous__8833] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8828,Vvar__1___24Anonymous__8830,Vvar__2___24Anonymous__8832) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8829,Vvar__1___24Anonymous__8831,Vvar__2___24Anonymous__8833)
=> ( Vvar__2___24Anonymous__8832 = Vvar__2___24Anonymous__8833
& Vvar__1___24Anonymous__8830 = Vvar__1___24Anonymous__8831
& Vvar__0__C__8828 = Vvar__0__C__8829 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__8834,Vvar__0__C__8835,Vvar__1___24Anonymous__8836,Vvar__1___24Anonymous__8837] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8834,Vvar__1___24Anonymous__8836) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8835,Vvar__1___24Anonymous__8837)
=> ( Vvar__1___24Anonymous__8836 = Vvar__1___24Anonymous__8837
& Vvar__0__C__8834 = Vvar__0__C__8835 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__8848,Vvar__0__C__8849,Vvar__1___24Anonymous__8850,Vvar__1___24Anonymous__8851,Vvar__2___24Anonymous__8852,Vvar__2___24Anonymous__8853] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8848,Vvar__1___24Anonymous__8850,Vvar__2___24Anonymous__8852) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8849,Vvar__1___24Anonymous__8851,Vvar__2___24Anonymous__8853)
=> ( Vvar__2___24Anonymous__8852 = Vvar__2___24Anonymous__8853
& Vvar__1___24Anonymous__8850 = Vvar__1___24Anonymous__8851
& Vvar__0__C__8848 = Vvar__0__C__8849 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__8822,Vvar__0__C__8823,Vvar__1___24Anonymous__8824,Vvar__1___24Anonymous__8825,Vvar__2___24Anonymous__8826,Vvar__2___24Anonymous__8827] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8822,Vvar__1___24Anonymous__8824,Vvar__2___24Anonymous__8826) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8823,Vvar__1___24Anonymous__8825,Vvar__2___24Anonymous__8827)
=> ( Vvar__2___24Anonymous__8826 = Vvar__2___24Anonymous__8827
& Vvar__1___24Anonymous__8824 = Vvar__1___24Anonymous__8825
& Vvar__0__C__8822 = Vvar__0__C__8823 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__9160,Vvar__0__C__9161,Vvar__1__num__9162,Vvar__1__num__9163,Vvar__2__denum__9164,Vvar__2__denum__9165,Vvar__3__condition__9166,Vvar__3__condition__9167] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__9160,Vvar__1__num__9162,Vvar__2__denum__9164,Vvar__3__condition__9166) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__9161,Vvar__1__num__9163,Vvar__2__denum__9165,Vvar__3__condition__9167)
=> ( Vvar__3__condition__9166 = Vvar__3__condition__9167
& Vvar__2__denum__9164 = Vvar__2__denum__9165
& Vvar__1__num__9162 = Vvar__1__num__9163
& Vvar__0__C__9160 = Vvar__0__C__9161 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__32783,Vvar__0__C__32784,Vvar__1__rsplit__left__32785,Vvar__1__rsplit__left__32786,Vvar__2__rsplit__common__32787,Vvar__2__rsplit__common__32788,Vvar__3__rsplit__right__32789,Vvar__3__rsplit__right__32790] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__32783,Vvar__1__rsplit__left__32785,Vvar__2__rsplit__common__32787,Vvar__3__rsplit__right__32789) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__32784,Vvar__1__rsplit__left__32786,Vvar__2__rsplit__common__32788,Vvar__3__rsplit__right__32790)
=> ( Vvar__3__rsplit__right__32789 = Vvar__3__rsplit__right__32790
& Vvar__2__rsplit__common__32787 = Vvar__2__rsplit__common__32788
& Vvar__1__rsplit__left__32785 = Vvar__1__rsplit__left__32786
& Vvar__0__C__32783 = Vvar__0__C__32784 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__13214,Vvar__0__C__13215] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__13214) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__13215)
=> Vvar__0__C__13214 = Vvar__0__C__13215 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__13212,Vvar__0__C__13213] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__13212) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__13213)
=> Vvar__0__C__13212 = Vvar__0__C__13213 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__13220,Vvar__0__C__13221,Vvar__1___24Anonymous__13222,Vvar__1___24Anonymous__13223] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__13220,Vvar__1___24Anonymous__13222) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__13221,Vvar__1___24Anonymous__13223)
=> ( Vvar__1___24Anonymous__13222 = Vvar__1___24Anonymous__13223
& Vvar__0__C__13220 = Vvar__0__C__13221 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__13224,Vvar__0__C__13225,Vvar__1___24Anonymous__13226,Vvar__1___24Anonymous__13227,Vvar__2___24Anonymous__13228,Vvar__2___24Anonymous__13229] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__13224,Vvar__1___24Anonymous__13226,Vvar__2___24Anonymous__13228) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__13225,Vvar__1___24Anonymous__13227,Vvar__2___24Anonymous__13229)
=> ( Vvar__2___24Anonymous__13228 = Vvar__2___24Anonymous__13229
& Vvar__1___24Anonymous__13226 = Vvar__1___24Anonymous__13227
& Vvar__0__C__13224 = Vvar__0__C__13225 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__13216,Vvar__0__C__13217,Vvar__1___24Anonymous__13218,Vvar__1___24Anonymous__13219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__13216,Vvar__1___24Anonymous__13218) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__13217,Vvar__1___24Anonymous__13219)
=> ( Vvar__1___24Anonymous__13218 = Vvar__1___24Anonymous__13219
& Vvar__0__C__13216 = Vvar__0__C__13217 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__13236,Vvar__0__C__13237,Vvar__1___24Anonymous__13238,Vvar__1___24Anonymous__13239,Vvar__2___24Anonymous__13240,Vvar__2___24Anonymous__13241] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__13236,Vvar__1___24Anonymous__13238,Vvar__2___24Anonymous__13240) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__13237,Vvar__1___24Anonymous__13239,Vvar__2___24Anonymous__13241)
=> ( Vvar__2___24Anonymous__13240 = Vvar__2___24Anonymous__13241
& Vvar__1___24Anonymous__13238 = Vvar__1___24Anonymous__13239
& Vvar__0__C__13236 = Vvar__0__C__13237 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__13242,Vvar__0__C__13243,Vvar__1___24Anonymous__13244,Vvar__1___24Anonymous__13245] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__13242,Vvar__1___24Anonymous__13244) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__13243,Vvar__1___24Anonymous__13245)
=> ( Vvar__1___24Anonymous__13244 = Vvar__1___24Anonymous__13245
& Vvar__0__C__13242 = Vvar__0__C__13243 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__13246,Vvar__0__C__13247,Vvar__1___24Anonymous__13248,Vvar__1___24Anonymous__13249,Vvar__2___24Anonymous__13250,Vvar__2___24Anonymous__13251] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__13246,Vvar__1___24Anonymous__13248,Vvar__2___24Anonymous__13250) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__13247,Vvar__1___24Anonymous__13249,Vvar__2___24Anonymous__13251)
=> ( Vvar__2___24Anonymous__13250 = Vvar__2___24Anonymous__13251
& Vvar__1___24Anonymous__13248 = Vvar__1___24Anonymous__13249
& Vvar__0__C__13246 = Vvar__0__C__13247 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__13230,Vvar__0__C__13231,Vvar__1___24Anonymous__13232,Vvar__1___24Anonymous__13233,Vvar__2___24Anonymous__13234,Vvar__2___24Anonymous__13235] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__13230,Vvar__1___24Anonymous__13232,Vvar__2___24Anonymous__13234) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__13231,Vvar__1___24Anonymous__13233,Vvar__2___24Anonymous__13235)
=> ( Vvar__2___24Anonymous__13234 = Vvar__2___24Anonymous__13235
& Vvar__1___24Anonymous__13232 = Vvar__1___24Anonymous__13233
& Vvar__0__C__13230 = Vvar__0__C__13231 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__12869,Vvar__0__C__12870,Vvar__1___24Anonymous__12871,Vvar__1___24Anonymous__12872,Vvar__2___24Anonymous__12873,Vvar__2___24Anonymous__12874,Vvar__3___24Anonymous__12875,Vvar__3___24Anonymous__12876] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12869,Vvar__1___24Anonymous__12871,Vvar__2___24Anonymous__12873,Vvar__3___24Anonymous__12875) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12870,Vvar__1___24Anonymous__12872,Vvar__2___24Anonymous__12874,Vvar__3___24Anonymous__12876)
=> ( Vvar__3___24Anonymous__12875 = Vvar__3___24Anonymous__12876
& Vvar__2___24Anonymous__12873 = Vvar__2___24Anonymous__12874
& Vvar__1___24Anonymous__12871 = Vvar__1___24Anonymous__12872
& Vvar__0__C__12869 = Vvar__0__C__12870 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__12859,Vvar__0__C__12860,Vvar__1___24Anonymous__12861,Vvar__1___24Anonymous__12862] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12859,Vvar__1___24Anonymous__12861) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12860,Vvar__1___24Anonymous__12862)
=> ( Vvar__1___24Anonymous__12861 = Vvar__1___24Anonymous__12862
& Vvar__0__C__12859 = Vvar__0__C__12860 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12863,Vvar__0__C__12864,Vvar__1___24Anonymous__12865,Vvar__1___24Anonymous__12866,Vvar__2___24Anonymous__12867,Vvar__2___24Anonymous__12868] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12863,Vvar__1___24Anonymous__12865,Vvar__2___24Anonymous__12867) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12864,Vvar__1___24Anonymous__12866,Vvar__2___24Anonymous__12868)
=> ( Vvar__2___24Anonymous__12867 = Vvar__2___24Anonymous__12868
& Vvar__1___24Anonymous__12865 = Vvar__1___24Anonymous__12866
& Vvar__0__C__12863 = Vvar__0__C__12864 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__13026,Vvar__0___24Anonymous__13027,Vvar__1___24Anonymous__13028,Vvar__1___24Anonymous__13029] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__13026,Vvar__1___24Anonymous__13028) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__13027,Vvar__1___24Anonymous__13029)
=> ( Vvar__1___24Anonymous__13028 = Vvar__1___24Anonymous__13029
& Vvar__0___24Anonymous__13026 = Vvar__0___24Anonymous__13027 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__13022,Vvar__0___24Anonymous__13023,Vvar__1___24Anonymous__13024,Vvar__1___24Anonymous__13025] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__13022,Vvar__1___24Anonymous__13024) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__13023,Vvar__1___24Anonymous__13025)
=> ( Vvar__1___24Anonymous__13024 = Vvar__1___24Anonymous__13025
& Vvar__0___24Anonymous__13022 = Vvar__0___24Anonymous__13023 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__5739,Vvar__0__R__5740,Vvar__1__req__5741,Vvar__1__req__5742,Vvar__2__reqb__5743,Vvar__2__reqb__5744,Vvar__3___24Anonymous__5745,Vvar__3___24Anonymous__5746] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__5739,Vvar__1__req__5741,Vvar__2__reqb__5743) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__5740,Vvar__1__req__5742,Vvar__2__reqb__5744)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__5743 = Vvar__2__reqb__5744
& Vvar__1__req__5741 = Vvar__1__req__5742
& Vvar__0__R__5739 = Vvar__0__R__5740 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__5747,Vvar__0__R__5748,Vvar__1__rO__5749,Vvar__1__rO__5750,Vvar__2__rI__5751,Vvar__2__rI__5752,Vvar__3__radd__5753,Vvar__3__radd__5754,Vvar__4__rmul__5755,Vvar__4__rmul__5756,Vvar__5__rsub__5757,Vvar__5__rsub__5758,Vvar__6__ropp__5759,Vvar__6__ropp__5760,Vvar__7__req__5761,Vvar__7__req__5762,Vvar__8__C__5763,Vvar__8__C__5764,Vvar__9__cO__5765,Vvar__9__cO__5766,Vvar__10__cI__5767,Vvar__10__cI__5768,Vvar__11__cadd__5769,Vvar__11__cadd__5770,Vvar__12__cmul__5771,Vvar__12__cmul__5772,Vvar__13__csub__5773,Vvar__13__csub__5774,Vvar__14__copp__5775,Vvar__14__copp__5776,Vvar__15__ceqb__5777,Vvar__15__ceqb__5778,Vvar__16__phi__5779,Vvar__16__phi__5780,Vvar__17___24Anonymous__5781,Vvar__17___24Anonymous__5782] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__5747,Vvar__1__rO__5749,Vvar__2__rI__5751,Vvar__3__radd__5753,Vvar__4__rmul__5755,Vvar__5__rsub__5757,Vvar__6__ropp__5759,Vvar__7__req__5761,Vvar__8__C__5763,Vvar__9__cO__5765,Vvar__10__cI__5767,Vvar__11__cadd__5769,Vvar__12__cmul__5771,Vvar__13__csub__5773,Vvar__14__copp__5775,Vvar__15__ceqb__5777,Vvar__16__phi__5779) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__5748,Vvar__1__rO__5750,Vvar__2__rI__5752,Vvar__3__radd__5754,Vvar__4__rmul__5756,Vvar__5__rsub__5758,Vvar__6__ropp__5760,Vvar__7__req__5762,Vvar__8__C__5764,Vvar__9__cO__5766,Vvar__10__cI__5768,Vvar__11__cadd__5770,Vvar__12__cmul__5772,Vvar__13__csub__5774,Vvar__14__copp__5776,Vvar__15__ceqb__5778,Vvar__16__phi__5780)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__5779 = Vvar__16__phi__5780
& Vvar__15__ceqb__5777 = Vvar__15__ceqb__5778
& Vvar__14__copp__5775 = Vvar__14__copp__5776
& Vvar__13__csub__5773 = Vvar__13__csub__5774
& Vvar__12__cmul__5771 = Vvar__12__cmul__5772
& Vvar__11__cadd__5769 = Vvar__11__cadd__5770
& Vvar__10__cI__5767 = Vvar__10__cI__5768
& Vvar__9__cO__5765 = Vvar__9__cO__5766
& Vvar__8__C__5763 = Vvar__8__C__5764
& Vvar__7__req__5761 = Vvar__7__req__5762
& Vvar__6__ropp__5759 = Vvar__6__ropp__5760
& Vvar__5__rsub__5757 = Vvar__5__rsub__5758
& Vvar__4__rmul__5755 = Vvar__4__rmul__5756
& Vvar__3__radd__5753 = Vvar__3__radd__5754
& Vvar__2__rI__5751 = Vvar__2__rI__5752
& Vvar__1__rO__5749 = Vvar__1__rO__5750
& Vvar__0__R__5747 = Vvar__0__R__5748 ) ) ).
fof('$_inj_monads.Build_Functor',axiom,
! [Vvar__0__func__43615,Vvar__0__func__43616,Vvar__1__func__map__43617,Vvar__1__func__map__43618,Vvar__2__func__id__43619,Vvar__2__func__id__43620,Vvar__3__func__assoc__43621,Vvar__3__func__assoc__43622] :
( cmonads_2eBuild__Functor___24a2(Vvar__0__func__43615,Vvar__1__func__map__43617) = cmonads_2eBuild__Functor___24a2(Vvar__0__func__43616,Vvar__1__func__map__43618)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__func__map__43617 = Vvar__1__func__map__43618
& Vvar__0__func__43615 = Vvar__0__func__43616 ) ) ).
fof('$_inj_monads.Build_Monad',axiom,
! [Vvar__0__mon__1035,Vvar__0__mon__1036,Vvar__1__bind__1037,Vvar__1__bind__1038,Vvar__2__ret__1039,Vvar__2__ret__1040,Vvar__3__mon__lunit__1041,Vvar__3__mon__lunit__1042,Vvar__4__mon__runit__1043,Vvar__4__mon__runit__1044,Vvar__5__mon__assoc__1045,Vvar__5__mon__assoc__1046] :
( cmonads_2eBuild__Monad___24a3(Vvar__0__mon__1035,Vvar__1__bind__1037,Vvar__2__ret__1039) = cmonads_2eBuild__Monad___24a3(Vvar__0__mon__1036,Vvar__1__bind__1038,Vvar__2__ret__1040)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__ret__1039 = Vvar__2__ret__1040
& Vvar__1__bind__1037 = Vvar__1__bind__1038
& Vvar__0__mon__1035 = Vvar__0__mon__1036 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__35703,Vvar__1__k__35705,Vvar__2___24Anonymous__35706] :
( c_24__type__35720___24t(Vvar__0__P__35703,Vvar__1__k__35705,Vvar__2___24Anonymous__35706,Vvar__0__P__35703)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__35705)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__35706)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__35703,Vvar__1__k__35705,Vvar__2___24Anonymous__35706)
=> ( Vvar__2___24Anonymous__35706 = Vvar__1__k__35705
| ? [Vvar__2__l__35714] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__35714)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__35703,Vvar__1__k__35705,Vvar__2__l__35714)
& p(happ(Vvar__0__P__35703,Vvar__2__l__35714))
& Vvar__2___24Anonymous__35706 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__35714) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__32033] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32033)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__32033)
=> ( Vvar__0___24Anonymous__32033 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__32035] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32035)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__32035)
& Vvar__0___24Anonymous__32033 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__32035) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__32037] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32037)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__32037)
=> ? [Vvar__0__n__32039] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32039)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__32039)
& Vvar__0___24Anonymous__32037 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__32039) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__31918,Vvar__1___24Anonymous__31919,VX31920] :
( cProp___24t(Vvar__0__P__31918)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__31919)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__31918,Vvar__1___24Anonymous__31919,VX31920)
=> ( ( p(Vvar__0__P__31918)
& Vvar__1___24Anonymous__31919 = cCoq_2eInit_2eDatatypes_2etrue
& VX31920 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31918) )
| ( ~ p(Vvar__0__P__31918)
& Vvar__1___24Anonymous__31919 = cCoq_2eInit_2eDatatypes_2efalse
& VX31920 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31918) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX43449] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX43449)
=> ( VX43449 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__43450] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__43450)
& ? [Vvar__1___24Anonymous__43451] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__43451)
& ? [Vvar__2___24Anonymous__43452] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__43452)
& VX43449 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__43450,Vvar__1___24Anonymous__43451,Vvar__2___24Anonymous__43452) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX31940] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX31940)
=> ( VX31940 = cCoq_2eInit_2eByte_2ex00
| VX31940 = cCoq_2eInit_2eByte_2ex01
| VX31940 = cCoq_2eInit_2eByte_2ex02
| VX31940 = cCoq_2eInit_2eByte_2ex03
| VX31940 = cCoq_2eInit_2eByte_2ex04
| VX31940 = cCoq_2eInit_2eByte_2ex05
| VX31940 = cCoq_2eInit_2eByte_2ex06
| VX31940 = cCoq_2eInit_2eByte_2ex07
| VX31940 = cCoq_2eInit_2eByte_2ex08
| VX31940 = cCoq_2eInit_2eByte_2ex09
| VX31940 = cCoq_2eInit_2eByte_2ex0a
| VX31940 = cCoq_2eInit_2eByte_2ex0b
| VX31940 = cCoq_2eInit_2eByte_2ex0c
| VX31940 = cCoq_2eInit_2eByte_2ex0d
| VX31940 = cCoq_2eInit_2eByte_2ex0e
| VX31940 = cCoq_2eInit_2eByte_2ex0f
| VX31940 = cCoq_2eInit_2eByte_2ex10
| VX31940 = cCoq_2eInit_2eByte_2ex11
| VX31940 = cCoq_2eInit_2eByte_2ex12
| VX31940 = cCoq_2eInit_2eByte_2ex13
| VX31940 = cCoq_2eInit_2eByte_2ex14
| VX31940 = cCoq_2eInit_2eByte_2ex15
| VX31940 = cCoq_2eInit_2eByte_2ex16
| VX31940 = cCoq_2eInit_2eByte_2ex17
| VX31940 = cCoq_2eInit_2eByte_2ex18
| VX31940 = cCoq_2eInit_2eByte_2ex19
| VX31940 = cCoq_2eInit_2eByte_2ex1a
| VX31940 = cCoq_2eInit_2eByte_2ex1b
| VX31940 = cCoq_2eInit_2eByte_2ex1c
| VX31940 = cCoq_2eInit_2eByte_2ex1d
| VX31940 = cCoq_2eInit_2eByte_2ex1e
| VX31940 = cCoq_2eInit_2eByte_2ex1f
| VX31940 = cCoq_2eInit_2eByte_2ex20
| VX31940 = cCoq_2eInit_2eByte_2ex21
| VX31940 = cCoq_2eInit_2eByte_2ex22
| VX31940 = cCoq_2eInit_2eByte_2ex23
| VX31940 = cCoq_2eInit_2eByte_2ex24
| VX31940 = cCoq_2eInit_2eByte_2ex25
| VX31940 = cCoq_2eInit_2eByte_2ex26
| VX31940 = cCoq_2eInit_2eByte_2ex27
| VX31940 = cCoq_2eInit_2eByte_2ex28
| VX31940 = cCoq_2eInit_2eByte_2ex29
| VX31940 = cCoq_2eInit_2eByte_2ex2a
| VX31940 = cCoq_2eInit_2eByte_2ex2b
| VX31940 = cCoq_2eInit_2eByte_2ex2c
| VX31940 = cCoq_2eInit_2eByte_2ex2d
| VX31940 = cCoq_2eInit_2eByte_2ex2e
| VX31940 = cCoq_2eInit_2eByte_2ex2f
| VX31940 = cCoq_2eInit_2eByte_2ex30
| VX31940 = cCoq_2eInit_2eByte_2ex31
| VX31940 = cCoq_2eInit_2eByte_2ex32
| VX31940 = cCoq_2eInit_2eByte_2ex33
| VX31940 = cCoq_2eInit_2eByte_2ex34
| VX31940 = cCoq_2eInit_2eByte_2ex35
| VX31940 = cCoq_2eInit_2eByte_2ex36
| VX31940 = cCoq_2eInit_2eByte_2ex37
| VX31940 = cCoq_2eInit_2eByte_2ex38
| VX31940 = cCoq_2eInit_2eByte_2ex39
| VX31940 = cCoq_2eInit_2eByte_2ex3a
| VX31940 = cCoq_2eInit_2eByte_2ex3b
| VX31940 = cCoq_2eInit_2eByte_2ex3c
| VX31940 = cCoq_2eInit_2eByte_2ex3d
| VX31940 = cCoq_2eInit_2eByte_2ex3e
| VX31940 = cCoq_2eInit_2eByte_2ex3f
| VX31940 = cCoq_2eInit_2eByte_2ex40
| VX31940 = cCoq_2eInit_2eByte_2ex41
| VX31940 = cCoq_2eInit_2eByte_2ex42
| VX31940 = cCoq_2eInit_2eByte_2ex43
| VX31940 = cCoq_2eInit_2eByte_2ex44
| VX31940 = cCoq_2eInit_2eByte_2ex45
| VX31940 = cCoq_2eInit_2eByte_2ex46
| VX31940 = cCoq_2eInit_2eByte_2ex47
| VX31940 = cCoq_2eInit_2eByte_2ex48
| VX31940 = cCoq_2eInit_2eByte_2ex49
| VX31940 = cCoq_2eInit_2eByte_2ex4a
| VX31940 = cCoq_2eInit_2eByte_2ex4b
| VX31940 = cCoq_2eInit_2eByte_2ex4c
| VX31940 = cCoq_2eInit_2eByte_2ex4d
| VX31940 = cCoq_2eInit_2eByte_2ex4e
| VX31940 = cCoq_2eInit_2eByte_2ex4f
| VX31940 = cCoq_2eInit_2eByte_2ex50
| VX31940 = cCoq_2eInit_2eByte_2ex51
| VX31940 = cCoq_2eInit_2eByte_2ex52
| VX31940 = cCoq_2eInit_2eByte_2ex53
| VX31940 = cCoq_2eInit_2eByte_2ex54
| VX31940 = cCoq_2eInit_2eByte_2ex55
| VX31940 = cCoq_2eInit_2eByte_2ex56
| VX31940 = cCoq_2eInit_2eByte_2ex57
| VX31940 = cCoq_2eInit_2eByte_2ex58
| VX31940 = cCoq_2eInit_2eByte_2ex59
| VX31940 = cCoq_2eInit_2eByte_2ex5a
| VX31940 = cCoq_2eInit_2eByte_2ex5b
| VX31940 = cCoq_2eInit_2eByte_2ex5c
| VX31940 = cCoq_2eInit_2eByte_2ex5d
| VX31940 = cCoq_2eInit_2eByte_2ex5e
| VX31940 = cCoq_2eInit_2eByte_2ex5f
| VX31940 = cCoq_2eInit_2eByte_2ex60
| VX31940 = cCoq_2eInit_2eByte_2ex61
| VX31940 = cCoq_2eInit_2eByte_2ex62
| VX31940 = cCoq_2eInit_2eByte_2ex63
| VX31940 = cCoq_2eInit_2eByte_2ex64
| VX31940 = cCoq_2eInit_2eByte_2ex65
| VX31940 = cCoq_2eInit_2eByte_2ex66
| VX31940 = cCoq_2eInit_2eByte_2ex67
| VX31940 = cCoq_2eInit_2eByte_2ex68
| VX31940 = cCoq_2eInit_2eByte_2ex69
| VX31940 = cCoq_2eInit_2eByte_2ex6a
| VX31940 = cCoq_2eInit_2eByte_2ex6b
| VX31940 = cCoq_2eInit_2eByte_2ex6c
| VX31940 = cCoq_2eInit_2eByte_2ex6d
| VX31940 = cCoq_2eInit_2eByte_2ex6e
| VX31940 = cCoq_2eInit_2eByte_2ex6f
| VX31940 = cCoq_2eInit_2eByte_2ex70
| VX31940 = cCoq_2eInit_2eByte_2ex71
| VX31940 = cCoq_2eInit_2eByte_2ex72
| VX31940 = cCoq_2eInit_2eByte_2ex73
| VX31940 = cCoq_2eInit_2eByte_2ex74
| VX31940 = cCoq_2eInit_2eByte_2ex75
| VX31940 = cCoq_2eInit_2eByte_2ex76
| VX31940 = cCoq_2eInit_2eByte_2ex77
| VX31940 = cCoq_2eInit_2eByte_2ex78
| VX31940 = cCoq_2eInit_2eByte_2ex79
| VX31940 = cCoq_2eInit_2eByte_2ex7a
| VX31940 = cCoq_2eInit_2eByte_2ex7b
| VX31940 = cCoq_2eInit_2eByte_2ex7c
| VX31940 = cCoq_2eInit_2eByte_2ex7d
| VX31940 = cCoq_2eInit_2eByte_2ex7e
| VX31940 = cCoq_2eInit_2eByte_2ex7f
| VX31940 = cCoq_2eInit_2eByte_2ex80
| VX31940 = cCoq_2eInit_2eByte_2ex81
| VX31940 = cCoq_2eInit_2eByte_2ex82
| VX31940 = cCoq_2eInit_2eByte_2ex83
| VX31940 = cCoq_2eInit_2eByte_2ex84
| VX31940 = cCoq_2eInit_2eByte_2ex85
| VX31940 = cCoq_2eInit_2eByte_2ex86
| VX31940 = cCoq_2eInit_2eByte_2ex87
| VX31940 = cCoq_2eInit_2eByte_2ex88
| VX31940 = cCoq_2eInit_2eByte_2ex89
| VX31940 = cCoq_2eInit_2eByte_2ex8a
| VX31940 = cCoq_2eInit_2eByte_2ex8b
| VX31940 = cCoq_2eInit_2eByte_2ex8c
| VX31940 = cCoq_2eInit_2eByte_2ex8d
| VX31940 = cCoq_2eInit_2eByte_2ex8e
| VX31940 = cCoq_2eInit_2eByte_2ex8f
| VX31940 = cCoq_2eInit_2eByte_2ex90
| VX31940 = cCoq_2eInit_2eByte_2ex91
| VX31940 = cCoq_2eInit_2eByte_2ex92
| VX31940 = cCoq_2eInit_2eByte_2ex93
| VX31940 = cCoq_2eInit_2eByte_2ex94
| VX31940 = cCoq_2eInit_2eByte_2ex95
| VX31940 = cCoq_2eInit_2eByte_2ex96
| VX31940 = cCoq_2eInit_2eByte_2ex97
| VX31940 = cCoq_2eInit_2eByte_2ex98
| VX31940 = cCoq_2eInit_2eByte_2ex99
| VX31940 = cCoq_2eInit_2eByte_2ex9a
| VX31940 = cCoq_2eInit_2eByte_2ex9b
| VX31940 = cCoq_2eInit_2eByte_2ex9c
| VX31940 = cCoq_2eInit_2eByte_2ex9d
| VX31940 = cCoq_2eInit_2eByte_2ex9e
| VX31940 = cCoq_2eInit_2eByte_2ex9f
| VX31940 = cCoq_2eInit_2eByte_2exa0
| VX31940 = cCoq_2eInit_2eByte_2exa1
| VX31940 = cCoq_2eInit_2eByte_2exa2
| VX31940 = cCoq_2eInit_2eByte_2exa3
| VX31940 = cCoq_2eInit_2eByte_2exa4
| VX31940 = cCoq_2eInit_2eByte_2exa5
| VX31940 = cCoq_2eInit_2eByte_2exa6
| VX31940 = cCoq_2eInit_2eByte_2exa7
| VX31940 = cCoq_2eInit_2eByte_2exa8
| VX31940 = cCoq_2eInit_2eByte_2exa9
| VX31940 = cCoq_2eInit_2eByte_2exaa
| VX31940 = cCoq_2eInit_2eByte_2exab
| VX31940 = cCoq_2eInit_2eByte_2exac
| VX31940 = cCoq_2eInit_2eByte_2exad
| VX31940 = cCoq_2eInit_2eByte_2exae
| VX31940 = cCoq_2eInit_2eByte_2exaf
| VX31940 = cCoq_2eInit_2eByte_2exb0
| VX31940 = cCoq_2eInit_2eByte_2exb1
| VX31940 = cCoq_2eInit_2eByte_2exb2
| VX31940 = cCoq_2eInit_2eByte_2exb3
| VX31940 = cCoq_2eInit_2eByte_2exb4
| VX31940 = cCoq_2eInit_2eByte_2exb5
| VX31940 = cCoq_2eInit_2eByte_2exb6
| VX31940 = cCoq_2eInit_2eByte_2exb7
| VX31940 = cCoq_2eInit_2eByte_2exb8
| VX31940 = cCoq_2eInit_2eByte_2exb9
| VX31940 = cCoq_2eInit_2eByte_2exba
| VX31940 = cCoq_2eInit_2eByte_2exbb
| VX31940 = cCoq_2eInit_2eByte_2exbc
| VX31940 = cCoq_2eInit_2eByte_2exbd
| VX31940 = cCoq_2eInit_2eByte_2exbe
| VX31940 = cCoq_2eInit_2eByte_2exbf
| VX31940 = cCoq_2eInit_2eByte_2exc0
| VX31940 = cCoq_2eInit_2eByte_2exc1
| VX31940 = cCoq_2eInit_2eByte_2exc2
| VX31940 = cCoq_2eInit_2eByte_2exc3
| VX31940 = cCoq_2eInit_2eByte_2exc4
| VX31940 = cCoq_2eInit_2eByte_2exc5
| VX31940 = cCoq_2eInit_2eByte_2exc6
| VX31940 = cCoq_2eInit_2eByte_2exc7
| VX31940 = cCoq_2eInit_2eByte_2exc8
| VX31940 = cCoq_2eInit_2eByte_2exc9
| VX31940 = cCoq_2eInit_2eByte_2exca
| VX31940 = cCoq_2eInit_2eByte_2excb
| VX31940 = cCoq_2eInit_2eByte_2excc
| VX31940 = cCoq_2eInit_2eByte_2excd
| VX31940 = cCoq_2eInit_2eByte_2exce
| VX31940 = cCoq_2eInit_2eByte_2excf
| VX31940 = cCoq_2eInit_2eByte_2exd0
| VX31940 = cCoq_2eInit_2eByte_2exd1
| VX31940 = cCoq_2eInit_2eByte_2exd2
| VX31940 = cCoq_2eInit_2eByte_2exd3
| VX31940 = cCoq_2eInit_2eByte_2exd4
| VX31940 = cCoq_2eInit_2eByte_2exd5
| VX31940 = cCoq_2eInit_2eByte_2exd6
| VX31940 = cCoq_2eInit_2eByte_2exd7
| VX31940 = cCoq_2eInit_2eByte_2exd8
| VX31940 = cCoq_2eInit_2eByte_2exd9
| VX31940 = cCoq_2eInit_2eByte_2exda
| VX31940 = cCoq_2eInit_2eByte_2exdb
| VX31940 = cCoq_2eInit_2eByte_2exdc
| VX31940 = cCoq_2eInit_2eByte_2exdd
| VX31940 = cCoq_2eInit_2eByte_2exde
| VX31940 = cCoq_2eInit_2eByte_2exdf
| VX31940 = cCoq_2eInit_2eByte_2exe0
| VX31940 = cCoq_2eInit_2eByte_2exe1
| VX31940 = cCoq_2eInit_2eByte_2exe2
| VX31940 = cCoq_2eInit_2eByte_2exe3
| VX31940 = cCoq_2eInit_2eByte_2exe4
| VX31940 = cCoq_2eInit_2eByte_2exe5
| VX31940 = cCoq_2eInit_2eByte_2exe6
| VX31940 = cCoq_2eInit_2eByte_2exe7
| VX31940 = cCoq_2eInit_2eByte_2exe8
| VX31940 = cCoq_2eInit_2eByte_2exe9
| VX31940 = cCoq_2eInit_2eByte_2exea
| VX31940 = cCoq_2eInit_2eByte_2exeb
| VX31940 = cCoq_2eInit_2eByte_2exec
| VX31940 = cCoq_2eInit_2eByte_2exed
| VX31940 = cCoq_2eInit_2eByte_2exee
| VX31940 = cCoq_2eInit_2eByte_2exef
| VX31940 = cCoq_2eInit_2eByte_2exf0
| VX31940 = cCoq_2eInit_2eByte_2exf1
| VX31940 = cCoq_2eInit_2eByte_2exf2
| VX31940 = cCoq_2eInit_2eByte_2exf3
| VX31940 = cCoq_2eInit_2eByte_2exf4
| VX31940 = cCoq_2eInit_2eByte_2exf5
| VX31940 = cCoq_2eInit_2eByte_2exf6
| VX31940 = cCoq_2eInit_2eByte_2exf7
| VX31940 = cCoq_2eInit_2eByte_2exf8
| VX31940 = cCoq_2eInit_2eByte_2exf9
| VX31940 = cCoq_2eInit_2eByte_2exfa
| VX31940 = cCoq_2eInit_2eByte_2exfb
| VX31940 = cCoq_2eInit_2eByte_2exfc
| VX31940 = cCoq_2eInit_2eByte_2exfd
| VX31940 = cCoq_2eInit_2eByte_2exfe
| VX31940 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__31941,Vvar__1__Q__31942,Vvar__2___24Anonymous__31943] :
( cProp___24t(Vvar__0__P__31941)
=> ( cProp___24t(Vvar__1__Q__31942)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__31943)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__31941,Vvar__1__Q__31942,Vvar__2___24Anonymous__31943)
=> ( ( p(Vvar__0__P__31941)
& Vvar__2___24Anonymous__31943 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__31942)
& Vvar__2___24Anonymous__31943 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__31951,Vvar__1__Plt__31952,Vvar__2__Pgt__31953,Vvar__3___24Anonymous__31954] :
( cProp___24t(Vvar__0__Peq__31951)
=> ( cProp___24t(Vvar__1__Plt__31952)
=> ( cProp___24t(Vvar__2__Pgt__31953)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__31954)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__31951,Vvar__1__Plt__31952,Vvar__2__Pgt__31953,Vvar__3___24Anonymous__31954)
=> ( ( p(Vvar__0__Peq__31951)
& Vvar__3___24Anonymous__31954 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__31952)
& Vvar__3___24Anonymous__31954 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__31953)
& Vvar__3___24Anonymous__31954 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__7884,Vvar__1__Plt__7885,Vvar__2__Pgt__7886,Vvar__3___24Anonymous__7887,VX7888] :
( cProp___24t(Vvar__0__Peq__7884)
=> ( cProp___24t(Vvar__1__Plt__7885)
=> ( cProp___24t(Vvar__2__Pgt__7886)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__7887)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__7884,Vvar__1__Plt__7885,Vvar__2__Pgt__7886,Vvar__3___24Anonymous__7887,VX7888)
=> ( ( p(Vvar__0__Peq__7884)
& Vvar__3___24Anonymous__7887 = cCoq_2eInit_2eDatatypes_2eEq
& VX7888 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__7884,Vvar__1__Plt__7885,Vvar__2__Pgt__7886) )
| ( p(Vvar__1__Plt__7885)
& Vvar__3___24Anonymous__7887 = cCoq_2eInit_2eDatatypes_2eLt
& VX7888 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__7884,Vvar__1__Plt__7885,Vvar__2__Pgt__7886) )
| ( p(Vvar__2__Pgt__7886)
& Vvar__3___24Anonymous__7887 = cCoq_2eInit_2eDatatypes_2eGt
& VX7888 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__7884,Vvar__1__Plt__7885,Vvar__2__Pgt__7886) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX2979] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX2979)
=> ( VX2979 = cCoq_2eInit_2eDatatypes_2etrue
| VX2979 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX2700] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX2700)
=> ( VX2700 = cCoq_2eInit_2eDatatypes_2eEq
| VX2700 = cCoq_2eInit_2eDatatypes_2eLt
| VX2700 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__14,VX15] :
( cType___24t(Vvar__0__A__14)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14,VX15)
=> ( VX15 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14)
| ? [Vvar__1___24Anonymous__18] :
( t(Vvar__1___24Anonymous__18,Vvar__0__A__14)
& ? [Vvar__2___24Anonymous__19] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14,Vvar__2___24Anonymous__19)
& VX15 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14,Vvar__1___24Anonymous__18,Vvar__2___24Anonymous__19) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX3)
=> ( VX3 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4)
& VX3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__7801,VX7802] :
( cType___24t(Vvar__0__A__7801)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__7801,VX7802)
=> ( ? [Vvar__1___24Anonymous__7804] :
( t(Vvar__1___24Anonymous__7804,Vvar__0__A__7801)
& VX7802 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7801,Vvar__1___24Anonymous__7804) )
| VX7802 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7801) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__1287,Vvar__1__B__1288,VX1289] :
( cType___24t(Vvar__0__A__1287)
=> ( cType___24t(Vvar__1__B__1288)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1287,Vvar__1__B__1288,VX1289)
=> ? [Vvar__2___24Anonymous__1292] :
( t(Vvar__2___24Anonymous__1292,Vvar__0__A__1287)
& ? [Vvar__3___24Anonymous__1293] :
( t(Vvar__3___24Anonymous__1293,Vvar__1__B__1288)
& VX1289 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1287,Vvar__1__B__1288,Vvar__2___24Anonymous__1292,Vvar__3___24Anonymous__1293) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__35731,Vvar__1__B__35732,VX35733] :
( cType___24t(Vvar__0__A__35731)
=> ( cType___24t(Vvar__1__B__35732)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__35731,Vvar__1__B__35732,VX35733)
=> ( ? [Vvar__2___24Anonymous__35736] :
( t(Vvar__2___24Anonymous__35736,Vvar__0__A__35731)
& VX35733 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__35731,Vvar__1__B__35732,Vvar__2___24Anonymous__35736) )
| ? [Vvar__2___24Anonymous__35739] :
( t(Vvar__2___24Anonymous__35739,Vvar__1__B__35732)
& VX35733 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__35731,Vvar__1__B__35732,Vvar__2___24Anonymous__35739) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2978] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2978)
=> VX2978 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__3069,Vvar__1___24Anonymous__3070] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__3069)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__3070)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__3069,Vvar__1___24Anonymous__3070)
=> ( Vvar__1___24Anonymous__3070 = Vvar__0__n__3069
| ? [Vvar__1__m__3074] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__3074)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__3069,Vvar__1__m__3074)
& Vvar__1___24Anonymous__3070 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__3074) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__1348,Vvar__1__P__1349,VX1352] :
( cType___24t(Vvar__0__A__1348)
=> ( c_24__type__1362___24t(Vvar__0__A__1348,Vvar__1__P__1349,Vvar__1__P__1349)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__1348,Vvar__1__P__1349,VX1352)
=> ? [Vvar__2__x__1357] :
( t(Vvar__2__x__1357,Vvar__0__A__1348)
& p(happ(Vvar__1__P__1349,Vvar__2__x__1357))
& VX1352 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__1348,Vvar__1__P__1349,Vvar__2__x__1357) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__14807,Vvar__1__P__14808,Vvar__2__Q__14811,VX14814] :
( cType___24t(Vvar__0__A__14807)
=> ( c_24__type__14831___24t(Vvar__0__A__14807,Vvar__1__P__14808,Vvar__2__Q__14811,Vvar__1__P__14808)
=> ( c_24__type__14839___24t(Vvar__0__A__14807,Vvar__1__P__14808,Vvar__2__Q__14811,Vvar__2__Q__14811)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__14807,Vvar__1__P__14808,Vvar__2__Q__14811,VX14814)
=> ? [Vvar__3__x__14822] :
( t(Vvar__3__x__14822,Vvar__0__A__14807)
& p(happ(Vvar__1__P__14808,Vvar__3__x__14822))
& p(happ(Vvar__2__Q__14811,Vvar__3__x__14822))
& VX14814 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__14807,Vvar__1__P__14808,Vvar__2__Q__14811,Vvar__3__x__14822) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__2715,Vvar__1__P__2716,VX2719] :
( cType___24t(Vvar__0__A__2715)
=> ( c_24__type__2729___24t(Vvar__0__A__2715,Vvar__1__P__2716,Vvar__1__P__2716)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__2715,Vvar__1__P__2716,VX2719)
=> ? [Vvar__2__x__2724] :
( t(Vvar__2__x__2724,Vvar__0__A__2715)
& ? [Vvar__3___24Anonymous__2725] :
( t(Vvar__3___24Anonymous__2725,happ(Vvar__1__P__2716,Vvar__2__x__2724))
& VX2719 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__2715,Vvar__1__P__2716,Vvar__2__x__2724,Vvar__3___24Anonymous__2725) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__14885,Vvar__1__P__14886,Vvar__2__Q__14889,VX14892] :
( cType___24t(Vvar__0__A__14885)
=> ( c_24__type__14909___24t(Vvar__0__A__14885,Vvar__1__P__14886,Vvar__2__Q__14889,Vvar__1__P__14886)
=> ( c_24__type__14917___24t(Vvar__0__A__14885,Vvar__1__P__14886,Vvar__2__Q__14889,Vvar__2__Q__14889)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__14885,Vvar__1__P__14886,Vvar__2__Q__14889,VX14892)
=> ? [Vvar__3__x__14900] :
( t(Vvar__3__x__14900,Vvar__0__A__14885)
& ? [Vvar__4___24Anonymous__14901] :
( t(Vvar__4___24Anonymous__14901,happ(Vvar__1__P__14886,Vvar__3__x__14900))
& ? [Vvar__5___24Anonymous__14902] :
( t(Vvar__5___24Anonymous__14902,happ(Vvar__2__Q__14889,Vvar__3__x__14900))
& VX14892 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__14885,Vvar__1__P__14886,Vvar__2__Q__14889,Vvar__3__x__14900,Vvar__4___24Anonymous__14901,Vvar__5___24Anonymous__14902) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__27580,Vvar__1__B__27581,VX27582] :
( cProp___24t(Vvar__0__A__27580)
=> ( cProp___24t(Vvar__1__B__27581)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__27580,Vvar__1__B__27581,VX27582)
=> ( ( p(Vvar__0__A__27580)
& VX27582 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__27580,Vvar__1__B__27581) )
| ( p(Vvar__1__B__27581)
& VX27582 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__27580,Vvar__1__B__27581) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__35655,Vvar__1__B__35656,VX35657] :
( cType___24t(Vvar__0__A__35655)
=> ( cProp___24t(Vvar__1__B__35656)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__35655,Vvar__1__B__35656,VX35657)
=> ( ? [Vvar__2___24Anonymous__35660] :
( t(Vvar__2___24Anonymous__35660,Vvar__0__A__35655)
& VX35657 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__35655,Vvar__1__B__35656,Vvar__2___24Anonymous__35660) )
| ( p(Vvar__1__B__35656)
& VX35657 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__35655,Vvar__1__B__35656) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__43195,Vvar__1__R__43196,Vvar__2__x__43201] :
( cType___24t(Vvar__0__A__43195)
=> ( c_24__type__43230___24t(Vvar__0__A__43195,Vvar__1__R__43196,Vvar__2__x__43201,Vvar__1__R__43196)
=> ( t(Vvar__2__x__43201,Vvar__0__A__43195)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__43195,Vvar__1__R__43196,Vvar__2__x__43201)
=> ( ! [Vvar__var__var__var__var__3__y__43211__43213__43215__43217__43219] :
( t(Vvar__var__var__var__var__3__y__43211__43213__43215__43217__43219,Vvar__0__A__43195)
=> ( p(happ(happ(Vvar__1__R__43196,Vvar__var__var__var__var__3__y__43211__43213__43215__43217__43219),Vvar__2__x__43201))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__43195,Vvar__1__R__43196,Vvar__var__var__var__var__3__y__43211__43213__43215__43217__43219) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__36079,Vvar__1__P__36080,Vvar__2___24Anonymous__36083] :
( cType___24t(Vvar__0__A__36079)
=> ( c_24__type__36101___24t(Vvar__0__A__36079,Vvar__1__P__36080,Vvar__2___24Anonymous__36083,Vvar__1__P__36080)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36079,Vvar__2___24Anonymous__36083)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__36079,Vvar__1__P__36080,Vvar__2___24Anonymous__36083)
=> ( Vvar__2___24Anonymous__36083 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36079)
| ? [Vvar__2__x__36093] :
( t(Vvar__2__x__36093,Vvar__0__A__36079)
& ? [Vvar__3__l__36094] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36079,Vvar__3__l__36094)
& p(happ(Vvar__1__P__36080,Vvar__2__x__36093))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__36079,Vvar__1__P__36080,Vvar__3__l__36094)
& Vvar__2___24Anonymous__36083 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36079,Vvar__2__x__36093,Vvar__3__l__36094) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__3027,Vvar__1___24Anonymous__3028] :
( cType___24t(Vvar__0__A__3027)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3027,Vvar__1___24Anonymous__3028)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__3027,Vvar__1___24Anonymous__3028)
=> ( Vvar__1___24Anonymous__3028 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3027)
| ? [Vvar__1__x__3032] :
( t(Vvar__1__x__3032,Vvar__0__A__3027)
& ? [Vvar__2__l__3033] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3027,Vvar__2__l__3033)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__3027,Vvar__1__x__3032,Vvar__2__l__3033)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__3027,Vvar__2__l__3033)
& Vvar__1___24Anonymous__3028 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3027,Vvar__1__x__3032,Vvar__2__l__3033) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__42575,Vvar__1__eqA__42576,Vvar__2__x__42581,Vvar__3___24Anonymous__42582] :
( cType___24t(Vvar__0__A__42575)
=> ( c_24__type__42615___24t(Vvar__0__A__42575,Vvar__1__eqA__42576,Vvar__2__x__42581,Vvar__3___24Anonymous__42582,Vvar__1__eqA__42576)
=> ( t(Vvar__2__x__42581,Vvar__0__A__42575)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42575,Vvar__3___24Anonymous__42582)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__42575,Vvar__1__eqA__42576,Vvar__2__x__42581,Vvar__3___24Anonymous__42582)
=> ( ? [Vvar__3__y__42591] :
( t(Vvar__3__y__42591,Vvar__0__A__42575)
& ? [Vvar__4__l__42592] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42575,Vvar__4__l__42592)
& p(happ(happ(Vvar__1__eqA__42576,Vvar__2__x__42581),Vvar__3__y__42591))
& Vvar__3___24Anonymous__42582 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42575,Vvar__3__y__42591,Vvar__4__l__42592) ) )
| ? [Vvar__3__y__42601] :
( t(Vvar__3__y__42601,Vvar__0__A__42575)
& ? [Vvar__4__l__42602] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42575,Vvar__4__l__42602)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__42575,Vvar__1__eqA__42576,Vvar__2__x__42581,Vvar__4__l__42602)
& Vvar__3___24Anonymous__42582 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42575,Vvar__3__y__42601,Vvar__4__l__42602) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__42617,Vvar__1__eqA__42618,Vvar__2___24Anonymous__42623] :
( cType___24t(Vvar__0__A__42617)
=> ( c_24__type__42650___24t(Vvar__0__A__42617,Vvar__1__eqA__42618,Vvar__2___24Anonymous__42623,Vvar__1__eqA__42618)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42617,Vvar__2___24Anonymous__42623)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__42617,Vvar__1__eqA__42618,Vvar__2___24Anonymous__42623)
=> ( Vvar__2___24Anonymous__42623 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42617)
| ? [Vvar__2__x__42637] :
( t(Vvar__2__x__42637,Vvar__0__A__42617)
& ? [Vvar__3__l__42638] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42617,Vvar__3__l__42638)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__42617,Vvar__1__eqA__42618,Vvar__2__x__42637,Vvar__3__l__42638)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__42617,Vvar__1__eqA__42618,Vvar__3__l__42638)
& Vvar__2___24Anonymous__42623 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42617,Vvar__2__x__42637,Vvar__3__l__42638) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__8301,Vvar__1__P__8302,Vvar__2__p__8305,Vvar__3__x__8306,Vvar__4__q__8307,Vvar__5___24Anonymous__8308] :
( cType___24t(Vvar__0__U__8301)
=> ( c_24__type__8323___24t(Vvar__0__U__8301,Vvar__1__P__8302,Vvar__2__p__8305,Vvar__3__x__8306,Vvar__4__q__8307,Vvar__5___24Anonymous__8308,Vvar__1__P__8302)
=> ( t(Vvar__2__p__8305,Vvar__0__U__8301)
=> ( t(Vvar__3__x__8306,happ(Vvar__1__P__8302,Vvar__2__p__8305))
=> ( t(Vvar__4__q__8307,Vvar__0__U__8301)
=> ( t(Vvar__5___24Anonymous__8308,happ(Vvar__1__P__8302,Vvar__4__q__8307))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__8301,Vvar__1__P__8302,Vvar__2__p__8305,Vvar__3__x__8306,Vvar__4__q__8307,Vvar__5___24Anonymous__8308)
=> ( Vvar__5___24Anonymous__8308 = Vvar__3__x__8306
& Vvar__4__q__8307 = Vvar__2__p__8305 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__8325,Vvar__1__P__8326,Vvar__2__p__8329,Vvar__3__x__8330,Vvar__4__q__8331,Vvar__5__y__8332] :
( cType___24t(Vvar__0__U__8325)
=> ( c_24__type__8351___24t(Vvar__0__U__8325,Vvar__1__P__8326,Vvar__2__p__8329,Vvar__3__x__8330,Vvar__4__q__8331,Vvar__5__y__8332,Vvar__1__P__8326)
=> ( t(Vvar__2__p__8329,Vvar__0__U__8325)
=> ( t(Vvar__3__x__8330,happ(Vvar__1__P__8326,Vvar__2__p__8329))
=> ( t(Vvar__4__q__8331,Vvar__0__U__8325)
=> ( t(Vvar__5__y__8332,happ(Vvar__1__P__8326,Vvar__4__q__8331))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__8325,Vvar__1__P__8326,Vvar__2__p__8329,Vvar__3__x__8330,Vvar__4__q__8331,Vvar__5__y__8332)
=> ( Vvar__4__q__8331 = Vvar__2__p__8329
& Vvar__3__x__8330 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__8325,Vvar__4__q__8331,Vvar__1__P__8326,Vvar__5__y__8332,Vvar__2__p__8329)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.JMeq.JMeq',axiom,
! [Vvar__0__A__35986,Vvar__1__x__35987,Vvar__2__B__35988,Vvar__3___24Anonymous__35989] :
( cType___24t(Vvar__0__A__35986)
=> ( t(Vvar__1__x__35987,Vvar__0__A__35986)
=> ( cType___24t(Vvar__2__B__35988)
=> ( t(Vvar__3___24Anonymous__35989,Vvar__2__B__35988)
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(Vvar__0__A__35986,Vvar__1__x__35987,Vvar__2__B__35988,Vvar__3___24Anonymous__35989)
=> ( Vvar__3___24Anonymous__35989 = Vvar__1__x__35987
& Vvar__2__B__35988 = Vvar__0__A__35986 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1280] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1280)
=> ( VX1280 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1281)
& VX1280 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1281) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX2687] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX2687)
=> ( VX2687 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__2688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2688)
& VX2687 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2688) )
| ? [Vvar__0___24Anonymous__2689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2689)
& VX2687 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2689) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1269)
=> ( ? [Vvar__0___24Anonymous__1270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1270)
& VX1269 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1270) )
| ? [Vvar__0___24Anonymous__1271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1271)
& VX1269 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1271) )
| VX1269 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__29470,Vvar__1__q__29471,Vvar__2___24Anonymous__29472] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__29470)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__29471)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__29472)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__29470,Vvar__1__q__29471,Vvar__2___24Anonymous__29472)
=> ( ( Vvar__0__p__29470 = Vvar__1__q__29471
& Vvar__2___24Anonymous__29472 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__29479] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__29479)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__29471,Vvar__2__r__29479) = Vvar__0__p__29470
& Vvar__2___24Anonymous__29472 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__29479) )
| ? [Vvar__2__r__29483] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__29483)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__29470,Vvar__2__r__29483) = Vvar__1__q__29471
& Vvar__2___24Anonymous__29472 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX29443] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX29443)
=> ( VX29443 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__29444] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29444)
& VX29443 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29444) )
| VX29443 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX33869] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX33869)
=> ? [Vvar__0__Qnum__33870] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__33870)
& ? [Vvar__1__Qden__33871] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__33871)
& VX33869 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__33870,Vvar__1__Qden__33871) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX36155] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX36155)
=> ? [Vvar__0__nonzero__36156] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__36156)
& Vvar__0__nonzero__36156 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX36155 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__36156) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__11614,Vvar__1___24Anonymous__11615,VX11616] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__11614)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__11615)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__11614,Vvar__1___24Anonymous__11615,VX11616)
=> ( ( Vvar__0__x__11614 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__11615 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX11616 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__11614) )
| ? [Vvar__1__n__11620] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__11620)
& Vvar__0__x__11614 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__11620)
& Vvar__1___24Anonymous__11615 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2411640___24a3(Vvar__0__x__11614,Vvar__1___24Anonymous__11615,Vvar__1__n__11620)
& VX11616 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__11614,Vvar__1__n__11620) )
| ? [Vvar__1__n__11625] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__11625)
& Vvar__0__x__11614 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__11625))
& Vvar__1___24Anonymous__11615 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657___24a3(Vvar__0__x__11614,Vvar__1___24Anonymous__11615,Vvar__1__n__11625)
& VX11616 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__11614,Vvar__1__n__11625) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__36135,Vvar__1___24Anonymous__36136,Vvar__2___24Anonymous__36137] :
( cType___24t(Vvar__0__A__36135)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__1___24Anonymous__36136)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__2___24Anonymous__36137)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__36135,Vvar__1___24Anonymous__36136,Vvar__2___24Anonymous__36137)
=> ( ( Vvar__2___24Anonymous__36137 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36135)
& Vvar__1___24Anonymous__36136 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36135) )
| ? [Vvar__1__x__36141] :
( t(Vvar__1__x__36141,Vvar__0__A__36135)
& ? [Vvar__2__l__36142] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__2__l__36142)
& ? [Vvar__3__l_27__36143] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__3__l_27__36143)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__36135,Vvar__2__l__36142,Vvar__3__l_27__36143)
& Vvar__2___24Anonymous__36137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__1__x__36141,Vvar__3__l_27__36143)
& Vvar__1___24Anonymous__36136 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__1__x__36141,Vvar__2__l__36142) ) ) )
| ? [Vvar__1__x__36146] :
( t(Vvar__1__x__36146,Vvar__0__A__36135)
& ? [Vvar__2__y__36147] :
( t(Vvar__2__y__36147,Vvar__0__A__36135)
& ? [Vvar__3__l__36148] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__3__l__36148)
& Vvar__2___24Anonymous__36137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__1__x__36146,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__2__y__36147,Vvar__3__l__36148))
& Vvar__1___24Anonymous__36136 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__2__y__36147,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36135,Vvar__1__x__36146,Vvar__3__l__36148)) ) ) )
| ? [Vvar__1__l__36150] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__1__l__36150)
& ? [Vvar__2__l_27__36151] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__2__l_27__36151)
& ? [Vvar__3__l_27_27__36152] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36135,Vvar__3__l_27_27__36152)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__36135,Vvar__1__l__36150,Vvar__2__l_27__36151)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__36135,Vvar__2__l_27__36151,Vvar__3__l_27_27__36152)
& Vvar__2___24Anonymous__36137 = Vvar__3__l_27_27__36152
& Vvar__1___24Anonymous__36136 = Vvar__1__l__36150 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__42707,Vvar__1__R__42708,Vvar__2___24Anonymous__42713] :
( cType___24t(Vvar__0__A__42707)
=> ( c_24__type__42740___24t(Vvar__0__A__42707,Vvar__1__R__42708,Vvar__2___24Anonymous__42713,Vvar__1__R__42708)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42707,Vvar__2___24Anonymous__42713)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__42707,Vvar__1__R__42708,Vvar__2___24Anonymous__42713)
=> ( Vvar__2___24Anonymous__42713 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42707)
| ? [Vvar__2__a__42727] :
( t(Vvar__2__a__42727,Vvar__0__A__42707)
& ? [Vvar__3__l__42728] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42707,Vvar__3__l__42728)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__42707,Vvar__1__R__42708,Vvar__3__l__42728)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__42707,happ(Vvar__1__R__42708,Vvar__2__a__42727),Vvar__3__l__42728)
& Vvar__2___24Anonymous__42713 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42707,Vvar__2__a__42727,Vvar__3__l__42728) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX7751] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX7751)
=> ? [Vvar__0___24Anonymous__7752] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__7752)
& ? [Vvar__1___24Anonymous__7753] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__7753)
& ? [Vvar__2___24Anonymous__7754] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__7754)
& ? [Vvar__3___24Anonymous__7755] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__7755)
& ? [Vvar__4___24Anonymous__7756] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__7756)
& ? [Vvar__5___24Anonymous__7757] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__7757)
& ? [Vvar__6___24Anonymous__7758] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__7758)
& ? [Vvar__7___24Anonymous__7759] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__7759)
& VX7751 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__7752,Vvar__1___24Anonymous__7753,Vvar__2___24Anonymous__7754,Vvar__3___24Anonymous__7755,Vvar__4___24Anonymous__7756,Vvar__5___24Anonymous__7757,Vvar__6___24Anonymous__7758,Vvar__7___24Anonymous__7759) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX27620] :
( cCoq_2eStrings_2eString_2estring___24t(VX27620)
=> ( VX27620 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__27621] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__27621)
& ? [Vvar__1___24Anonymous__27622] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__27622)
& VX27620 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__27621,Vvar__1___24Anonymous__27622) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292,VX11293] :
( cType___24t(Vvar__0__X__11280)
=> ( c_24__type__11353___24t(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292,Vvar__1__lt__11281)
=> ( c_24__type__11372___24t(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292,Vvar__2__eq__11286)
=> ( t(Vvar__3__x__11291,Vvar__0__X__11280)
=> ( t(Vvar__4__y__11292,Vvar__0__X__11280)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292,VX11293)
=> ( ( p(happ(happ(Vvar__1__lt__11281,Vvar__3__x__11291),Vvar__4__y__11292))
& VX11293 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292) )
| ( p(happ(happ(Vvar__2__eq__11286,Vvar__3__x__11291),Vvar__4__y__11292))
& VX11293 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292) )
| ( p(happ(happ(Vvar__1__lt__11281,Vvar__4__y__11292),Vvar__3__x__11291))
& VX11293 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__11280,Vvar__1__lt__11281,Vvar__2__eq__11286,Vvar__3__x__11291,Vvar__4__y__11292) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__43480,Vvar__1___24Anonymous__43481] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__43480)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__43481)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__43480,Vvar__1___24Anonymous__43481)
=> ( ? [Vvar__0__a__43483] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__43483)
& ? [Vvar__1__s__43484] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__43484)
& Vvar__1___24Anonymous__43481 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__43483,Vvar__1__s__43484)
& Vvar__0___24Anonymous__43480 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__43485] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__43485)
& ? [Vvar__1__s1__43486] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__43486)
& ? [Vvar__2__s2__43487] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__43487)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__43486,Vvar__2__s2__43487)
& Vvar__1___24Anonymous__43481 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__43485,Vvar__2__s2__43487)
& Vvar__0___24Anonymous__43480 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__43485,Vvar__1__s1__43486) ) ) )
| ? [Vvar__0__a__43489] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__43489)
& ? [Vvar__1__b__43490] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__43490)
& ? [Vvar__2__s1__43491] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__43491)
& ? [Vvar__3__s2__43492] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__43492)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__43489),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__43490))
& Vvar__1___24Anonymous__43481 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__43490,Vvar__3__s2__43492)
& Vvar__0___24Anonymous__43480 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__43489,Vvar__2__s1__43491) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX11565] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX11565)
=> ( VX11565 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX11565 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX11565 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__10690,VX10691] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10690)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__10690,VX10691)
=> ( ? [Vvar__0__n__10692] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__10692)
& Vvar__0___24Anonymous__10690 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__10692)
& VX10691 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__10692) )
| ? [Vvar__0__n__10693] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__10693)
& ? [Vvar__1___24Anonymous__10694] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__10693,Vvar__1___24Anonymous__10694)
& Vvar__0___24Anonymous__10690 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__10693)
& VX10691 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__10693,Vvar__1___24Anonymous__10694) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__27741,Vvar__1___24Anonymous__27742,VX27743] :
( cType___24t(Vvar__0__A__27741)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__27742)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__27741,Vvar__1___24Anonymous__27742,VX27743)
=> ( ( Vvar__1___24Anonymous__27742 = cCoq_2eInit_2eDatatypes_2eO
& VX27743 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__27741) )
| ? [Vvar__1__h__27746] :
( t(Vvar__1__h__27746,Vvar__0__A__27741)
& ? [Vvar__2__n__27747] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__27747)
& ? [Vvar__3___24Anonymous__27748] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__27741,Vvar__2__n__27747,Vvar__3___24Anonymous__27748)
& Vvar__1___24Anonymous__27742 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__27747)
& VX27743 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__27741,Vvar__1__h__27746,Vvar__2__n__27747,Vvar__3___24Anonymous__27748) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__2784,Vvar__1__b__2785,Vvar__2__d__2786] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__2784)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__2785)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__2786)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__2784,Vvar__1__b__2785,Vvar__2__d__2786)
=> ? [Vvar__3__u__2791] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__2791)
& ? [Vvar__4__v__2792] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__2792)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__2791,Vvar__0__a__2784),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__2792,Vvar__1__b__2785)) = Vvar__2__d__2786
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__28899,Vvar__1__b__28900,VX28901] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__28899)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__28900)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__28899,Vvar__1__b__28900,VX28901)
=> ? [Vvar__2__u__28904] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__28904)
& ? [Vvar__3__v__28905] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__28905)
& ? [Vvar__4__d__28906] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__28906)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__28904,Vvar__0__a__28899),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__28905,Vvar__1__b__28900)) = Vvar__4__d__28906
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__28899,Vvar__1__b__28900,Vvar__4__d__28906)
& VX28901 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__28899,Vvar__1__b__28900,Vvar__2__u__28904,Vvar__3__v__28905,Vvar__4__d__28906) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__28871,Vvar__1__b__28872,Vvar__2__g__28873] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__28871)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__28872)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__28873)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__28871,Vvar__1__b__28872,Vvar__2__g__28873)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__28873,Vvar__0__a__28871)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__28873,Vvar__1__b__28872)
& ! [Vvar__var__var__var__var__5__x__28881__28884__28887__28890__28893] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__28881__28884__28887__28890__28893)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__28881__28884__28887__28890__28893,Vvar__0__a__28871)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__28881__28884__28887__28890__28893,Vvar__1__b__28872)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__28881__28884__28887__28890__28893,Vvar__2__g__28873) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__28956,Vvar__1__p__28957,VX28958] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__28956)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__28957)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__28956,Vvar__1__p__28957,VX28958)
=> ? [Vvar__2__q__28961] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__28961)
& ? [Vvar__3__r__28962] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__28962)
& Vvar__0__x__28956 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__28961,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__28957)),Vvar__3__r__28962)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__28962))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__28962,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__28957))
& VX28958 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__28956,Vvar__1__p__28957,Vvar__2__q__28961,Vvar__3__r__28962) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX8233] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX8233)
=> ( VX8233 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__8234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8234)
& ? [Vvar__1___24Anonymous__8235] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__8235)
& VX8233 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__8234,Vvar__1___24Anonymous__8235) ) )
| ? [Vvar__0___24Anonymous__8236] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8236)
& ? [Vvar__1___24Anonymous__8237] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__8237)
& VX8233 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__8236,Vvar__1___24Anonymous__8237) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__8069,VX8070] :
( cType___24t(Vvar__0__C__8069)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,VX8070)
=> ( ? [Vvar__1___24Anonymous__8072] :
( t(Vvar__1___24Anonymous__8072,Vvar__0__C__8069)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__8069,Vvar__1___24Anonymous__8072) )
| ? [Vvar__1___24Anonymous__8074] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8074)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__8069,Vvar__1___24Anonymous__8074) )
| ? [Vvar__1___24Anonymous__8076] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__1___24Anonymous__8076)
& ? [Vvar__2___24Anonymous__8077] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__2___24Anonymous__8077)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__8069,Vvar__1___24Anonymous__8076,Vvar__2___24Anonymous__8077) ) )
| ? [Vvar__1___24Anonymous__8079] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__1___24Anonymous__8079)
& ? [Vvar__2___24Anonymous__8080] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__2___24Anonymous__8080)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__8069,Vvar__1___24Anonymous__8079,Vvar__2___24Anonymous__8080) ) )
| ? [Vvar__1___24Anonymous__8082] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__1___24Anonymous__8082)
& ? [Vvar__2___24Anonymous__8083] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__2___24Anonymous__8083)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__8069,Vvar__1___24Anonymous__8082,Vvar__2___24Anonymous__8083) ) )
| ? [Vvar__1___24Anonymous__8085] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__1___24Anonymous__8085)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__8069,Vvar__1___24Anonymous__8085) )
| ? [Vvar__1___24Anonymous__8087] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__8069,Vvar__1___24Anonymous__8087)
& ? [Vvar__2___24Anonymous__8088] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8088)
& VX8070 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__8069,Vvar__1___24Anonymous__8087,Vvar__2___24Anonymous__8088) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__31970,VX31971] :
( cType___24t(Vvar__0__C__31970)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__31970,VX31971)
=> ( ? [Vvar__1___24Anonymous__31973] :
( t(Vvar__1___24Anonymous__31973,Vvar__0__C__31970)
& VX31971 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__31970,Vvar__1___24Anonymous__31973) )
| ? [Vvar__1___24Anonymous__31975] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__31975)
& ? [Vvar__2___24Anonymous__31976] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__31970,Vvar__2___24Anonymous__31976)
& VX31971 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__31970,Vvar__1___24Anonymous__31975,Vvar__2___24Anonymous__31976) ) )
| ? [Vvar__1___24Anonymous__31978] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__31970,Vvar__1___24Anonymous__31978)
& ? [Vvar__2___24Anonymous__31979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__31979)
& ? [Vvar__3___24Anonymous__31980] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__31970,Vvar__3___24Anonymous__31980)
& VX31971 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__31970,Vvar__1___24Anonymous__31978,Vvar__2___24Anonymous__31979,Vvar__3___24Anonymous__31980) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822] :
( cType___24t(Vvar__0__R__32791)
=> ( t(Vvar__1__rO__32792,Vvar__0__R__32791)
=> ( t(Vvar__2__rI__32793,Vvar__0__R__32791)
=> ( c_24__type__33223___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__3__rplus__32794)
=> ( c_24__type__33324___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__4__rtimes__32799)
=> ( c_24__type__33425___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__5__rminus__32804)
=> ( c_24__type__33515___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__6__ropp__32809)
=> ( c_24__type__33616___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__7__req__32812)
=> ( c_24__type__33717___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__8__rle__32817)
=> ( c_24__type__33818___24t(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822,Vvar__9__rlt__32822)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812,Vvar__8__rle__32817,Vvar__9__rlt__32822)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__32791,Vvar__7__req__32812)
& ! [Vvar__var__var__var__var__11__x1__32866__32872__32977__32983__32989] :
( t(Vvar__var__var__var__var__11__x1__32866__32872__32977__32983__32989,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__12__x2__32867__32873__32978__32984__32990] :
( t(Vvar__var__var__var__var__12__x2__32867__32873__32978__32984__32990,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__11__x1__32866__32872__32977__32983__32989),Vvar__var__var__var__var__12__x2__32867__32873__32978__32984__32990))
=> ! [Vvar__var__var__var__var__14__y1__32868__32874__32979__32985__32991] :
( t(Vvar__var__var__var__var__14__y1__32868__32874__32979__32985__32991,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__15__y2__32869__32875__32980__32986__32992] :
( t(Vvar__var__var__var__var__15__y2__32869__32875__32980__32986__32992,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__14__y1__32868__32874__32979__32985__32991),Vvar__var__var__var__var__15__y2__32869__32875__32980__32986__32992))
=> p(happ(happ(Vvar__7__req__32812,happ(happ(Vvar__3__rplus__32794,Vvar__var__var__var__var__11__x1__32866__32872__32977__32983__32989),Vvar__var__var__var__var__14__y1__32868__32874__32979__32985__32991)),happ(happ(Vvar__3__rplus__32794,Vvar__var__var__var__var__12__x2__32867__32873__32978__32984__32990),Vvar__var__var__var__var__15__y2__32869__32875__32980__32986__32992))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__32879__32885__32995__33001__33007] :
( t(Vvar__var__var__var__var__12__x1__32879__32885__32995__33001__33007,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__13__x2__32880__32886__32996__33002__33008] :
( t(Vvar__var__var__var__var__13__x2__32880__32886__32996__33002__33008,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__12__x1__32879__32885__32995__33001__33007),Vvar__var__var__var__var__13__x2__32880__32886__32996__33002__33008))
=> ! [Vvar__var__var__var__var__15__y1__32881__32887__32997__33003__33009] :
( t(Vvar__var__var__var__var__15__y1__32881__32887__32997__33003__33009,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__16__y2__32882__32888__32998__33004__33010] :
( t(Vvar__var__var__var__var__16__y2__32882__32888__32998__33004__33010,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__15__y1__32881__32887__32997__33003__33009),Vvar__var__var__var__var__16__y2__32882__32888__32998__33004__33010))
=> p(happ(happ(Vvar__7__req__32812,happ(happ(Vvar__4__rtimes__32799,Vvar__var__var__var__var__12__x1__32879__32885__32995__33001__33007),Vvar__var__var__var__var__15__y1__32881__32887__32997__33003__33009)),happ(happ(Vvar__4__rtimes__32799,Vvar__var__var__var__var__13__x2__32880__32886__32996__33002__33008),Vvar__var__var__var__var__16__y2__32882__32888__32998__33004__33010))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__32892__32895__33013__33016__33019] :
( t(Vvar__var__var__var__var__13__x1__32892__32895__33013__33016__33019,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__14__x2__32893__32896__33014__33017__33020] :
( t(Vvar__var__var__var__var__14__x2__32893__32896__33014__33017__33020,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__13__x1__32892__32895__33013__33016__33019),Vvar__var__var__var__var__14__x2__32893__32896__33014__33017__33020))
=> p(happ(happ(Vvar__7__req__32812,happ(Vvar__6__ropp__32809,Vvar__var__var__var__var__13__x1__32892__32895__33013__33016__33019)),happ(Vvar__6__ropp__32809,Vvar__var__var__var__var__14__x2__32893__32896__33014__33017__33020))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__32899__32905__33022__33028__33034] :
( t(Vvar__var__var__var__var__14__x1__32899__32905__33022__33028__33034,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__15__x2__32900__32906__33023__33029__33035] :
( t(Vvar__var__var__var__var__15__x2__32900__32906__33023__33029__33035,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__14__x1__32899__32905__33022__33028__33034),Vvar__var__var__var__var__15__x2__32900__32906__33023__33029__33035))
=> ! [Vvar__var__var__var__var__17__y1__32901__32907__33024__33030__33036] :
( t(Vvar__var__var__var__var__17__y1__32901__32907__33024__33030__33036,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__18__y2__32902__32908__33025__33031__33037] :
( t(Vvar__var__var__var__var__18__y2__32902__32908__33025__33031__33037,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__17__y1__32901__32907__33024__33030__33036),Vvar__var__var__var__var__18__y2__32902__32908__33025__33031__33037))
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__14__x1__32899__32905__33022__33028__33034),Vvar__var__var__var__var__17__y1__32901__32907__33024__33030__33036))
<=> p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__15__x2__32900__32906__33023__33029__33035),Vvar__var__var__var__var__18__y2__32902__32908__33025__33031__33037)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__32912__32918__33040__33046__33052] :
( t(Vvar__var__var__var__var__15__x1__32912__32918__33040__33046__33052,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__16__x2__32913__32919__33041__33047__33053] :
( t(Vvar__var__var__var__var__16__x2__32913__32919__33041__33047__33053,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__15__x1__32912__32918__33040__33046__33052),Vvar__var__var__var__var__16__x2__32913__32919__33041__33047__33053))
=> ! [Vvar__var__var__var__var__18__y1__32914__32920__33042__33048__33054] :
( t(Vvar__var__var__var__var__18__y1__32914__32920__33042__33048__33054,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__19__y2__32915__32921__33043__33049__33055] :
( t(Vvar__var__var__var__var__19__y2__32915__32921__33043__33049__33055,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__18__y1__32914__32920__33042__33048__33054),Vvar__var__var__var__var__19__y2__32915__32921__33043__33049__33055))
=> ( p(happ(happ(Vvar__9__rlt__32822,Vvar__var__var__var__var__15__x1__32912__32918__33040__33046__33052),Vvar__var__var__var__var__18__y1__32914__32920__33042__33048__33054))
<=> p(happ(happ(Vvar__9__rlt__32822,Vvar__var__var__var__var__16__x2__32913__32919__33041__33047__33053),Vvar__var__var__var__var__19__y2__32915__32921__33043__33049__33055)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__32791,Vvar__1__rO__32792,Vvar__2__rI__32793,Vvar__3__rplus__32794,Vvar__4__rtimes__32799,Vvar__5__rminus__32804,Vvar__6__ropp__32809,Vvar__7__req__32812)
& ! [Vvar__var__var__var__17__n__32926__32927__33058__33059] :
( t(Vvar__var__var__var__17__n__32926__32927__33058__33059,Vvar__0__R__32791)
=> p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__17__n__32926__32927__33058__33059),Vvar__var__var__var__17__n__32926__32927__33058__33059)) )
& ! [Vvar__var__var__var__var__18__n__32929__32933__33060__33064__33068] :
( t(Vvar__var__var__var__var__18__n__32929__32933__33060__33064__33068,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__19__m__32930__32934__33061__33065__33069] :
( t(Vvar__var__var__var__var__19__m__32930__32934__33061__33065__33069,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__18__n__32929__32933__33060__33064__33068),Vvar__var__var__var__var__19__m__32930__32934__33061__33065__33069))
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__19__m__32930__32934__33061__33065__33069),Vvar__var__var__var__var__18__n__32929__32933__33060__33064__33068))
=> p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__18__n__32929__32933__33060__33064__33068),Vvar__var__var__var__var__19__m__32930__32934__33061__33065__33069)) ) ) ) )
& ! [Vvar__var__var__var__19__n__32938__32943__33072__33077] :
( t(Vvar__var__var__var__19__n__32938__32943__33072__33077,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__20__m__32939__32944__33073__33078] :
( t(Vvar__var__var__var__20__m__32939__32944__33073__33078,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__21__p__32940__32945__33074__33079] :
( t(Vvar__var__var__var__21__p__32940__32945__33074__33079,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__19__n__32938__32943__33072__33077),Vvar__var__var__var__20__m__32939__32944__33073__33078))
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__20__m__32939__32944__33073__33078),Vvar__var__var__var__21__p__32940__32945__33074__33079))
=> p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__19__n__32938__32943__33072__33077),Vvar__var__var__var__21__p__32940__32945__33074__33079)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__32949__32951__33082__33084__33086__33088] :
( t(Vvar__var__var__var__var__var__20__n__32949__32951__33082__33084__33086__33088,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__var__21__m__32950__32952__33083__33085__33087__33089] :
( t(Vvar__var__var__var__var__var__21__m__32950__32952__33083__33085__33087__33089,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__9__rlt__32822,Vvar__var__var__var__var__var__20__n__32949__32951__33082__33084__33086__33088),Vvar__var__var__var__var__var__21__m__32950__32952__33083__33085__33087__33089))
<=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__var__20__n__32949__32951__33082__33084__33086__33088),Vvar__var__var__var__var__var__21__m__32950__32952__33083__33085__33087__33089))
& ~ p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__var__20__n__32949__32951__33082__33084__33086__33088),Vvar__var__var__var__var__var__21__m__32950__32952__33083__33085__33087__33089)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__32954__32956__33090__33092__33094] :
( t(Vvar__var__var__var__var__21__n__32954__32956__33090__33092__33094,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__22__m__32955__32957__33091__33093__33095] :
( t(Vvar__var__var__var__var__22__m__32955__32957__33091__33093__33095,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__9__rlt__32822,Vvar__var__var__var__var__21__n__32954__32956__33090__33092__33094),Vvar__var__var__var__var__22__m__32955__32957__33091__33093__33095))
| p(happ(happ(Vvar__7__req__32812,Vvar__var__var__var__var__21__n__32954__32956__33090__33092__33094),Vvar__var__var__var__var__22__m__32955__32957__33091__33093__33095))
| p(happ(happ(Vvar__9__rlt__32822,Vvar__var__var__var__var__22__m__32955__32957__33091__33093__33095),Vvar__var__var__var__var__21__n__32954__32956__33090__33092__33094)) ) ) )
& ! [Vvar__var__var__var__var__22__n__32959__32963__33096__33100__33104] :
( t(Vvar__var__var__var__var__22__n__32959__32963__33096__33100__33104,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__23__m__32960__32964__33097__33101__33105] :
( t(Vvar__var__var__var__var__23__m__32960__32964__33097__33101__33105,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__24__p__32961__32965__33098__33102__33106] :
( t(Vvar__var__var__var__var__24__p__32961__32965__33098__33102__33106,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__8__rle__32817,Vvar__var__var__var__var__22__n__32959__32963__33096__33100__33104),Vvar__var__var__var__var__23__m__32960__32964__33097__33101__33105))
=> p(happ(happ(Vvar__8__rle__32817,happ(happ(Vvar__3__rplus__32794,Vvar__var__var__var__var__24__p__32961__32965__33098__33102__33106),Vvar__var__var__var__var__22__n__32959__32963__33096__33100__33104)),happ(happ(Vvar__3__rplus__32794,Vvar__var__var__var__var__24__p__32961__32965__33098__33102__33106),Vvar__var__var__var__var__23__m__32960__32964__33097__33101__33105))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__32968__32972__33108__33112__33116__33120] :
( t(Vvar__var__var__var__var__var__23__n__32968__32972__33108__33112__33116__33120,Vvar__0__R__32791)
=> ! [Vvar__var__var__var__var__var__24__m__32969__32973__33109__33113__33117__33121] :
( t(Vvar__var__var__var__var__var__24__m__32969__32973__33109__33113__33117__33121,Vvar__0__R__32791)
=> ( p(happ(happ(Vvar__9__rlt__32822,Vvar__1__rO__32792),Vvar__var__var__var__var__var__23__n__32968__32972__33108__33112__33116__33120))
=> ( p(happ(happ(Vvar__9__rlt__32822,Vvar__1__rO__32792),Vvar__var__var__var__var__var__24__m__32969__32973__33109__33113__33117__33121))
=> p(happ(happ(Vvar__9__rlt__32822,Vvar__1__rO__32792),happ(happ(Vvar__4__rtimes__32799,Vvar__var__var__var__var__var__23__n__32968__32972__33108__33112__33116__33120),Vvar__var__var__var__var__var__24__m__32969__32973__33109__33113__33117__33121))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__32812,Vvar__1__rO__32792),Vvar__2__rI__32793))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__12041,VX12042] :
( cType___24t(Vvar__0__T__12041)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__12041,VX12042)
=> ? [Vvar__1__Flhs__12044] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__12041,Vvar__1__Flhs__12044)
& ? [Vvar__2__Fop__12045] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__12045)
& ? [Vvar__3__Frhs__12046] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__12041,Vvar__3__Frhs__12046)
& VX12042 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__12041,Vvar__1__Flhs__12044,Vvar__2__Fop__12045,Vvar__3__Frhs__12046) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX41486] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX41486)
=> ( VX41486 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX41486 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX41486 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX41486 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX11819] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX11819)
=> ( VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX11819 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262] :
( cType___24t(Vvar__0__R__36193)
=> ( t(Vvar__1__rO__36194,Vvar__0__R__36193)
=> ( t(Vvar__2__rI__36195,Vvar__0__R__36193)
=> ( c_24__type__36726___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__3__rplus__36196)
=> ( c_24__type__37072___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__4__rtimes__36201)
=> ( c_24__type__37418___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__5__rminus__36206)
=> ( c_24__type__37741___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__6__ropp__36211)
=> ( c_24__type__38087___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__7__req__36214)
=> ( c_24__type__38433___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__8__rle__36219)
=> ( cType___24t(Vvar__9__C__36224)
=> ( t(Vvar__10__cO__36225,Vvar__9__C__36224)
=> ( t(Vvar__11__cI__36226,Vvar__9__C__36224)
=> ( c_24__type__38779___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__12__cplus__36227)
=> ( c_24__type__39125___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__13__ctimes__36232)
=> ( c_24__type__39471___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__14__cminus__36237)
=> ( c_24__type__39794___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__15__copp__36242)
=> ( c_24__type__40140___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__16__ceqb__36245)
=> ( c_24__type__40486___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__17__cleb__36250)
=> ( c_24__type__40809___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__18__phi__36255)
=> ( cType___24t(Vvar__19__E__36258)
=> ( c_24__type__41132___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__20__pow__phi__36259)
=> ( c_24__type__41478___24t(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262,Vvar__21__rpow__36262)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__8__rle__36219,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__17__cleb__36250,Vvar__18__phi__36255,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__36193,Vvar__1__rO__36194,Vvar__2__rI__36195,Vvar__3__rplus__36196,Vvar__4__rtimes__36201,Vvar__5__rminus__36206,Vvar__6__ropp__36211,Vvar__7__req__36214,Vvar__9__C__36224,Vvar__10__cO__36225,Vvar__11__cI__36226,Vvar__12__cplus__36227,Vvar__13__ctimes__36232,Vvar__14__cminus__36237,Vvar__15__copp__36242,Vvar__16__ceqb__36245,Vvar__18__phi__36255)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__36193,Vvar__2__rI__36195,Vvar__4__rtimes__36201,Vvar__7__req__36214,Vvar__19__E__36258,Vvar__20__pow__phi__36259,Vvar__21__rpow__36262)
& ! [Vvar__var__var__var__var__var__24__x__36345__36348__36358__36361__36364__36367] :
( t(Vvar__var__var__var__var__var__24__x__36345__36348__36358__36361__36364__36367,Vvar__9__C__36224)
=> ! [Vvar__var__var__var__var__var__25__y__36346__36349__36359__36362__36365__36368] :
( t(Vvar__var__var__var__var__var__25__y__36346__36349__36359__36362__36365__36368,Vvar__9__C__36224)
=> ( happ(happ(Vvar__16__ceqb__36245,Vvar__var__var__var__var__var__24__x__36345__36348__36358__36361__36364__36367),Vvar__var__var__var__var__var__25__y__36346__36349__36359__36362__36365__36368) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__36214,happ(Vvar__18__phi__36255,Vvar__var__var__var__var__var__24__x__36345__36348__36358__36361__36364__36367)),happ(Vvar__18__phi__36255,Vvar__var__var__var__var__var__25__y__36346__36349__36359__36362__36365__36368))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__36352__36355__36370__36373__36376__36379] :
( t(Vvar__var__var__var__var__var__25__x__36352__36355__36370__36373__36376__36379,Vvar__9__C__36224)
=> ! [Vvar__var__var__var__var__var__26__y__36353__36356__36371__36374__36377__36380] :
( t(Vvar__var__var__var__var__var__26__y__36353__36356__36371__36374__36377__36380,Vvar__9__C__36224)
=> ( happ(happ(Vvar__17__cleb__36250,Vvar__var__var__var__var__var__25__x__36352__36355__36370__36373__36376__36379),Vvar__var__var__var__var__var__26__y__36353__36356__36371__36374__36377__36380) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__36219,happ(Vvar__18__phi__36255,Vvar__var__var__var__var__var__25__x__36352__36355__36370__36373__36376__36379)),happ(Vvar__18__phi__36255,Vvar__var__var__var__var__var__26__y__36353__36356__36371__36374__36377__36380))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,VX42756] :
( cType___24t(Vvar__0__TA__42752)
=> ( cType___24t(Vvar__1__TX__42753)
=> ( cType___24t(Vvar__2__AA__42754)
=> ( cType___24t(Vvar__3__AF__42755)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,VX42756)
=> ( VX42756 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755)
| VX42756 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755)
| ? [Vvar__4___24Anonymous__42769] :
( t(Vvar__4___24Anonymous__42769,Vvar__1__TX__42753)
& VX42756 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42769) )
| ? [Vvar__4___24Anonymous__42774] :
( t(Vvar__4___24Anonymous__42774,Vvar__0__TA__42752)
& ? [Vvar__5___24Anonymous__42775] :
( t(Vvar__5___24Anonymous__42775,Vvar__2__AA__42754)
& VX42756 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42774,Vvar__5___24Anonymous__42775) ) )
| ? [Vvar__4___24Anonymous__42780] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42780)
& ? [Vvar__5___24Anonymous__42781] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__5___24Anonymous__42781)
& VX42756 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42780,Vvar__5___24Anonymous__42781) ) )
| ? [Vvar__4___24Anonymous__42786] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42786)
& ? [Vvar__5___24Anonymous__42787] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__5___24Anonymous__42787)
& VX42756 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42786,Vvar__5___24Anonymous__42787) ) )
| ? [Vvar__4___24Anonymous__42792] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42792)
& VX42756 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42792) )
| ? [Vvar__4___24Anonymous__42797] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42797)
& ? [Vvar__5___24Anonymous__42798] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__42755,Vvar__5___24Anonymous__42798)
& ? [Vvar__6___24Anonymous__42799] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__6___24Anonymous__42799)
& VX42756 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__42752,Vvar__1__TX__42753,Vvar__2__AA__42754,Vvar__3__AF__42755,Vvar__4___24Anonymous__42797,Vvar__5___24Anonymous__42798,Vvar__6___24Anonymous__42799) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__43353] :
( cProp___24t(Vvar__0___24Anonymous__43353)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__43353)
=> ( ? [Vvar__0__S__43355] :
( cType___24t(Vvar__0__S__43355)
& ? [Vvar__1__x__43356] :
( t(Vvar__1__x__43356,Vvar__0__S__43355)
& ? [Vvar__2__y__43357] :
( t(Vvar__2__y__43357,Vvar__0__S__43355)
& Vvar__0___24Anonymous__43353 = c_24__prop__43377___24a4(Vvar__0___24Anonymous__43353,Vvar__0__S__43355,Vvar__1__x__43356,Vvar__2__y__43357) ) ) )
| ? [Vvar__0__x__43358] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__43358)
& ? [Vvar__1__y__43359] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__43359)
& Vvar__0___24Anonymous__43353 = c_24__prop__43378___24a3(Vvar__0___24Anonymous__43353,Vvar__0__x__43358,Vvar__1__y__43359) ) )
| ? [Vvar__0__x__43360] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__43360)
& ? [Vvar__1__s__43361] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__43361)
& Vvar__0___24Anonymous__43353 = c_24__prop__43379___24a3(Vvar__0___24Anonymous__43353,Vvar__0__x__43360,Vvar__1__s__43361) ) )
| Vvar__0___24Anonymous__43353 = c_24True
| Vvar__0___24Anonymous__43353 = c_24False
| ? [Vvar__0__P__43362] :
( cProp___24t(Vvar__0__P__43362)
& ? [Vvar__1__Q__43363] :
( cProp___24t(Vvar__1__Q__43363)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__43362)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__43363)
& Vvar__0___24Anonymous__43353 = c_24__prop__43380___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43362,Vvar__1__Q__43363) ) )
| ? [Vvar__0__P__43366] :
( cProp___24t(Vvar__0__P__43366)
& ? [Vvar__1__Q__43367] :
( cProp___24t(Vvar__1__Q__43367)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__43366)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__43367)
& Vvar__0___24Anonymous__43353 = c_24__prop__43381___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43366,Vvar__1__Q__43367) ) )
| ? [Vvar__0__P__43370] :
( cProp___24t(Vvar__0__P__43370)
& ? [Vvar__1__Q__43371] :
( cProp___24t(Vvar__1__Q__43371)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__43370)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__43371)
& Vvar__0___24Anonymous__43353 = c_24__prop__43382___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43370,Vvar__1__Q__43371) ) )
| ? [Vvar__0__P__43375] :
( cProp___24t(Vvar__0__P__43375)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__43375)
& Vvar__0___24Anonymous__43353 = c_24__prop__43383___24a2(Vvar__0___24Anonymous__43353,Vvar__0__P__43375) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__43234,Vvar__1__env__43235,Vvar__2__env_27__43238,Vvar__3__x__43241] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__43234)
=> ( c_24__type__43262___24t(Vvar__0__fr__43234,Vvar__1__env__43235,Vvar__2__env_27__43238,Vvar__3__x__43241,Vvar__1__env__43235)
=> ( c_24__type__43271___24t(Vvar__0__fr__43234,Vvar__1__env__43235,Vvar__2__env_27__43238,Vvar__3__x__43241,Vvar__2__env_27__43238)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__43241)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__43234,Vvar__1__env__43235,Vvar__2__env_27__43238,Vvar__3__x__43241)
=> ( happ(Vvar__1__env__43235,Vvar__3__x__43241) = happ(Vvar__2__env_27__43238,Vvar__3__x__43241)
& happ(Vvar__1__env__43235,Vvar__3__x__43241) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__43238,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__43234,Vvar__3__x__43241))),happ(Vvar__2__env_27__43238,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__43234,Vvar__3__x__43241))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__43238,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__43234,Vvar__3__x__43241))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__43238,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__43234,Vvar__3__x__43241))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__8527,VX8528] :
( cType___24t(Vvar__0__C__8527)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,VX8528)
=> ( VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8527)
| VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8527)
| ? [Vvar__1___24Anonymous__8532] :
( t(Vvar__1___24Anonymous__8532,Vvar__0__C__8527)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8527,Vvar__1___24Anonymous__8532) )
| ? [Vvar__1___24Anonymous__8534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8534)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8527,Vvar__1___24Anonymous__8534) )
| ? [Vvar__1___24Anonymous__8536] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8536)
& ? [Vvar__2___24Anonymous__8537] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__2___24Anonymous__8537)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8527,Vvar__1___24Anonymous__8536,Vvar__2___24Anonymous__8537) ) )
| ? [Vvar__1___24Anonymous__8539] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8539)
& ? [Vvar__2___24Anonymous__8540] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__2___24Anonymous__8540)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8527,Vvar__1___24Anonymous__8539,Vvar__2___24Anonymous__8540) ) )
| ? [Vvar__1___24Anonymous__8542] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8542)
& ? [Vvar__2___24Anonymous__8543] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__2___24Anonymous__8543)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8527,Vvar__1___24Anonymous__8542,Vvar__2___24Anonymous__8543) ) )
| ? [Vvar__1___24Anonymous__8545] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8545)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8527,Vvar__1___24Anonymous__8545) )
| ? [Vvar__1___24Anonymous__8547] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8547)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8527,Vvar__1___24Anonymous__8547) )
| ? [Vvar__1___24Anonymous__8549] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8549)
& ? [Vvar__2___24Anonymous__8550] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__2___24Anonymous__8550)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8527,Vvar__1___24Anonymous__8549,Vvar__2___24Anonymous__8550) ) )
| ? [Vvar__1___24Anonymous__8552] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8527,Vvar__1___24Anonymous__8552)
& ? [Vvar__2___24Anonymous__8553] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8553)
& VX8528 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8527,Vvar__1___24Anonymous__8552,Vvar__2___24Anonymous__8553) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070] :
( cType___24t(Vvar__0__R__32041)
=> ( t(Vvar__1__rO__32042,Vvar__0__R__32041)
=> ( t(Vvar__2__rI__32043,Vvar__0__R__32041)
=> ( c_24__type__32235___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__3__radd__32044)
=> ( c_24__type__32328___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__4__rmul__32049)
=> ( c_24__type__32421___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__5__rsub__32054)
=> ( c_24__type__32503___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__6__ropp__32059)
=> ( c_24__type__32596___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__7__rdiv__32062)
=> ( c_24__type__32678___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__8__rinv__32067)
=> ( c_24__type__32771___24t(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070,Vvar__9__req__32070)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__7__rdiv__32062,Vvar__8__rinv__32067,Vvar__9__req__32070)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__32041,Vvar__1__rO__32042,Vvar__2__rI__32043,Vvar__3__radd__32044,Vvar__4__rmul__32049,Vvar__5__rsub__32054,Vvar__6__ropp__32059,Vvar__9__req__32070)
& ~ p(happ(happ(Vvar__9__req__32070,Vvar__2__rI__32043),Vvar__1__rO__32042))
& ! [Vvar__var__var__var__var__var__var__12__p__32113__32115__32122__32124__32126__32128__32130] :
( t(Vvar__var__var__var__var__var__var__12__p__32113__32115__32122__32124__32126__32128__32130,Vvar__0__R__32041)
=> ! [Vvar__var__var__var__var__var__var__13__q__32114__32116__32123__32125__32127__32129__32131] :
( t(Vvar__var__var__var__var__var__var__13__q__32114__32116__32123__32125__32127__32129__32131,Vvar__0__R__32041)
=> p(happ(happ(Vvar__9__req__32070,happ(happ(Vvar__7__rdiv__32062,Vvar__var__var__var__var__var__var__12__p__32113__32115__32122__32124__32126__32128__32130),Vvar__var__var__var__var__var__var__13__q__32114__32116__32123__32125__32127__32129__32131)),happ(happ(Vvar__4__rmul__32049,Vvar__var__var__var__var__var__var__12__p__32113__32115__32122__32124__32126__32128__32130),happ(Vvar__8__rinv__32067,Vvar__var__var__var__var__var__var__13__q__32114__32116__32123__32125__32127__32129__32131)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__32118__32120__32132__32134__32136__32138__32140__32142] :
( t(Vvar__var__var__var__var__var__var__var__13__p__32118__32120__32132__32134__32136__32138__32140__32142,Vvar__0__R__32041)
=> ( ~ p(happ(happ(Vvar__9__req__32070,Vvar__var__var__var__var__var__var__var__13__p__32118__32120__32132__32134__32136__32138__32140__32142),Vvar__1__rO__32042))
=> p(happ(happ(Vvar__9__req__32070,happ(happ(Vvar__4__rmul__32049,happ(Vvar__8__rinv__32067,Vvar__var__var__var__var__var__var__var__13__p__32118__32120__32132__32134__32136__32138__32140__32142)),Vvar__var__var__var__var__var__var__var__13__p__32118__32120__32132__32134__32136__32138__32140__32142)),Vvar__2__rI__32043)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__9154,VX9155] :
( cType___24t(Vvar__0__C__9154)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__9154,VX9155)
=> ? [Vvar__1__num__9157] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9154,Vvar__1__num__9157)
& ? [Vvar__2__denum__9158] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9154,Vvar__2__denum__9158)
& ? [Vvar__3__condition__9159] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__9154),Vvar__3__condition__9159)
& VX9155 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__9154,Vvar__1__num__9157,Vvar__2__denum__9158,Vvar__3__condition__9159) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__32777,VX32778] :
( cType___24t(Vvar__0__C__32777)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__32777,VX32778)
=> ? [Vvar__1__rsplit__left__32780] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32777,Vvar__1__rsplit__left__32780)
& ? [Vvar__2__rsplit__common__32781] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32777,Vvar__2__rsplit__common__32781)
& ? [Vvar__3__rsplit__right__32782] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__32777,Vvar__3__rsplit__right__32782)
& VX32778 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__32777,Vvar__1__rsplit__left__32780,Vvar__2__rsplit__common__32781,Vvar__3__rsplit__right__32782) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX13009] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX13009)
=> ( VX13009 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__13010] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13010)
& ? [Vvar__1___24Anonymous__13011] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__13011)
& VX13009 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__13010,Vvar__1___24Anonymous__13011) ) )
| ? [Vvar__0___24Anonymous__13012] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13012)
& ? [Vvar__1___24Anonymous__13013] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__13013)
& VX13009 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__13012,Vvar__1___24Anonymous__13013) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__13030,VX13031] :
( cType___24t(Vvar__0__C__13030)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,VX13031)
=> ( VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__13030)
| VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__13030)
| ? [Vvar__1___24Anonymous__13035] :
( t(Vvar__1___24Anonymous__13035,Vvar__0__C__13030)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__13030,Vvar__1___24Anonymous__13035) )
| ? [Vvar__1___24Anonymous__13037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13037)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__13030,Vvar__1___24Anonymous__13037) )
| ? [Vvar__1___24Anonymous__13039] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__1___24Anonymous__13039)
& ? [Vvar__2___24Anonymous__13040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__2___24Anonymous__13040)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__13030,Vvar__1___24Anonymous__13039,Vvar__2___24Anonymous__13040) ) )
| ? [Vvar__1___24Anonymous__13042] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__1___24Anonymous__13042)
& ? [Vvar__2___24Anonymous__13043] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__2___24Anonymous__13043)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__13030,Vvar__1___24Anonymous__13042,Vvar__2___24Anonymous__13043) ) )
| ? [Vvar__1___24Anonymous__13045] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__1___24Anonymous__13045)
& ? [Vvar__2___24Anonymous__13046] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__2___24Anonymous__13046)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__13030,Vvar__1___24Anonymous__13045,Vvar__2___24Anonymous__13046) ) )
| ? [Vvar__1___24Anonymous__13048] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__1___24Anonymous__13048)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__13030,Vvar__1___24Anonymous__13048) )
| ? [Vvar__1___24Anonymous__13050] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__13030,Vvar__1___24Anonymous__13050)
& ? [Vvar__2___24Anonymous__13051] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13051)
& VX13031 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__13030,Vvar__1___24Anonymous__13050,Vvar__2___24Anonymous__13051) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__12830,VX12831] :
( cType___24t(Vvar__0__C__12830)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12830,VX12831)
=> ( ? [Vvar__1___24Anonymous__12833] :
( t(Vvar__1___24Anonymous__12833,Vvar__0__C__12830)
& VX12831 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12830,Vvar__1___24Anonymous__12833) )
| ? [Vvar__1___24Anonymous__12835] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12835)
& ? [Vvar__2___24Anonymous__12836] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12830,Vvar__2___24Anonymous__12836)
& VX12831 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12830,Vvar__1___24Anonymous__12835,Vvar__2___24Anonymous__12836) ) )
| ? [Vvar__1___24Anonymous__12838] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12830,Vvar__1___24Anonymous__12838)
& ? [Vvar__2___24Anonymous__12839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12839)
& ? [Vvar__3___24Anonymous__12840] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12830,Vvar__3___24Anonymous__12840)
& VX12831 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12830,Vvar__1___24Anonymous__12838,Vvar__2___24Anonymous__12839,Vvar__3___24Anonymous__12840) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901] :
( cType___24t(Vvar__0__R__33880)
=> ( t(Vvar__1__rO__33881,Vvar__0__R__33880)
=> ( t(Vvar__2__rI__33882,Vvar__0__R__33880)
=> ( c_24__type__34129___24t(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901,Vvar__3__radd__33883)
=> ( c_24__type__34192___24t(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901,Vvar__4__rmul__33888)
=> ( c_24__type__34255___24t(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901,Vvar__5__rsub__33893)
=> ( c_24__type__34309___24t(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901,Vvar__6__ropp__33898)
=> ( c_24__type__34372___24t(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901,Vvar__7__req__33901)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__33880,Vvar__1__rO__33881,Vvar__2__rI__33882,Vvar__3__radd__33883,Vvar__4__rmul__33888,Vvar__5__rsub__33893,Vvar__6__ropp__33898,Vvar__7__req__33901)
=> ( ! [Vvar__var__var__var__var__var__8__x__33934__33935__33988__33989__33990__33991] :
( t(Vvar__var__var__var__var__var__8__x__33934__33935__33988__33989__33990__33991,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__3__radd__33883,Vvar__1__rO__33881),Vvar__var__var__var__var__var__8__x__33934__33935__33988__33989__33990__33991)),Vvar__var__var__var__var__var__8__x__33934__33935__33988__33989__33990__33991)) )
& ! [Vvar__var__var__var__var__9__x__33937__33939__33992__33994__33996] :
( t(Vvar__var__var__var__var__9__x__33937__33939__33992__33994__33996,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__10__y__33938__33940__33993__33995__33997] :
( t(Vvar__var__var__var__var__10__y__33938__33940__33993__33995__33997,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__9__x__33937__33939__33992__33994__33996),Vvar__var__var__var__var__10__y__33938__33940__33993__33995__33997)),happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__10__y__33938__33940__33993__33995__33997),Vvar__var__var__var__var__9__x__33937__33939__33992__33994__33996))) ) )
& ! [Vvar__var__var__var__var__10__x__33942__33945__33998__34001__34004] :
( t(Vvar__var__var__var__var__10__x__33942__33945__33998__34001__34004,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__11__y__33943__33946__33999__34002__34005] :
( t(Vvar__var__var__var__var__11__y__33943__33946__33999__34002__34005,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__12__z__33944__33947__34000__34003__34006] :
( t(Vvar__var__var__var__var__12__z__33944__33947__34000__34003__34006,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__10__x__33942__33945__33998__34001__34004),happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__11__y__33943__33946__33999__34002__34005),Vvar__var__var__var__var__12__z__33944__33947__34000__34003__34006))),happ(happ(Vvar__3__radd__33883,happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__10__x__33942__33945__33998__34001__34004),Vvar__var__var__var__var__11__y__33943__33946__33999__34002__34005)),Vvar__var__var__var__var__12__z__33944__33947__34000__34003__34006))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__33949__33950__34007__34008__34009__34010] :
( t(Vvar__var__var__var__var__var__11__x__33949__33950__34007__34008__34009__34010,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__4__rmul__33888,Vvar__2__rI__33882),Vvar__var__var__var__var__var__11__x__33949__33950__34007__34008__34009__34010)),Vvar__var__var__var__var__var__11__x__33949__33950__34007__34008__34009__34010)) )
& ! [Vvar__var__var__var__var__var__12__x__33952__33953__34011__34012__34013__34014] :
( t(Vvar__var__var__var__var__var__12__x__33952__33953__34011__34012__34013__34014,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__4__rmul__33888,Vvar__1__rO__33881),Vvar__var__var__var__var__var__12__x__33952__33953__34011__34012__34013__34014)),Vvar__1__rO__33881)) )
& ! [Vvar__var__var__var__var__13__x__33955__33957__34015__34017__34019] :
( t(Vvar__var__var__var__var__13__x__33955__33957__34015__34017__34019,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__14__y__33956__33958__34016__34018__34020] :
( t(Vvar__var__var__var__var__14__y__33956__33958__34016__34018__34020,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__13__x__33955__33957__34015__34017__34019),Vvar__var__var__var__var__14__y__33956__33958__34016__34018__34020)),happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__14__y__33956__33958__34016__34018__34020),Vvar__var__var__var__var__13__x__33955__33957__34015__34017__34019))) ) )
& ! [Vvar__var__var__var__var__14__x__33960__33963__34021__34024__34027] :
( t(Vvar__var__var__var__var__14__x__33960__33963__34021__34024__34027,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__15__y__33961__33964__34022__34025__34028] :
( t(Vvar__var__var__var__var__15__y__33961__33964__34022__34025__34028,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__16__z__33962__33965__34023__34026__34029] :
( t(Vvar__var__var__var__var__16__z__33962__33965__34023__34026__34029,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__14__x__33960__33963__34021__34024__34027),happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__15__y__33961__33964__34022__34025__34028),Vvar__var__var__var__var__16__z__33962__33965__34023__34026__34029))),happ(happ(Vvar__4__rmul__33888,happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__14__x__33960__33963__34021__34024__34027),Vvar__var__var__var__var__15__y__33961__33964__34022__34025__34028)),Vvar__var__var__var__var__16__z__33962__33965__34023__34026__34029))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__33967__33970__34030__34033__34036__34039] :
( t(Vvar__var__var__var__var__var__15__x__33967__33970__34030__34033__34036__34039,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__var__16__y__33968__33971__34031__34034__34037__34040] :
( t(Vvar__var__var__var__var__var__16__y__33968__33971__34031__34034__34037__34040,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__var__17__z__33969__33972__34032__34035__34038__34041] :
( t(Vvar__var__var__var__var__var__17__z__33969__33972__34032__34035__34038__34041,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__4__rmul__33888,happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__var__15__x__33967__33970__34030__34033__34036__34039),Vvar__var__var__var__var__var__16__y__33968__33971__34031__34034__34037__34040)),Vvar__var__var__var__var__var__17__z__33969__33972__34032__34035__34038__34041)),happ(happ(Vvar__3__radd__33883,happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__var__15__x__33967__33970__34030__34033__34036__34039),Vvar__var__var__var__var__var__17__z__33969__33972__34032__34035__34038__34041)),happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__var__16__y__33968__33971__34031__34034__34037__34040),Vvar__var__var__var__var__var__17__z__33969__33972__34032__34035__34038__34041)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__33974__33976__34042__34044__34046__34048] :
( t(Vvar__var__var__var__var__var__16__x__33974__33976__34042__34044__34046__34048,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__var__17__y__33975__33977__34043__34045__34047__34049] :
( t(Vvar__var__var__var__var__var__17__y__33975__33977__34043__34045__34047__34049,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(Vvar__6__ropp__33898,happ(happ(Vvar__4__rmul__33888,Vvar__var__var__var__var__var__16__x__33974__33976__34042__34044__34046__34048),Vvar__var__var__var__var__var__17__y__33975__33977__34043__34045__34047__34049))),happ(happ(Vvar__4__rmul__33888,happ(Vvar__6__ropp__33898,Vvar__var__var__var__var__var__16__x__33974__33976__34042__34044__34046__34048)),Vvar__var__var__var__var__var__17__y__33975__33977__34043__34045__34047__34049))) ) )
& ! [Vvar__var__var__var__var__var__17__x__33979__33981__34050__34052__34054__34056] :
( t(Vvar__var__var__var__var__var__17__x__33979__33981__34050__34052__34054__34056,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__var__18__y__33980__33982__34051__34053__34055__34057] :
( t(Vvar__var__var__var__var__var__18__y__33980__33982__34051__34053__34055__34057,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(Vvar__6__ropp__33898,happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__var__17__x__33979__33981__34050__34052__34054__34056),Vvar__var__var__var__var__var__18__y__33980__33982__34051__34053__34055__34057))),happ(happ(Vvar__3__radd__33883,happ(Vvar__6__ropp__33898,Vvar__var__var__var__var__var__17__x__33979__33981__34050__34052__34054__34056)),happ(Vvar__6__ropp__33898,Vvar__var__var__var__var__var__18__y__33980__33982__34051__34053__34055__34057)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__33984__33986__34058__34060__34062__34064__34066] :
( t(Vvar__var__var__var__var__var__var__18__x__33984__33986__34058__34060__34062__34064__34066,Vvar__0__R__33880)
=> ! [Vvar__var__var__var__var__var__var__19__y__33985__33987__34059__34061__34063__34065__34067] :
( t(Vvar__var__var__var__var__var__var__19__y__33985__33987__34059__34061__34063__34065__34067,Vvar__0__R__33880)
=> p(happ(happ(Vvar__7__req__33901,happ(happ(Vvar__5__rsub__33893,Vvar__var__var__var__var__var__var__18__x__33984__33986__34058__34060__34062__34064__34066),Vvar__var__var__var__var__var__var__19__y__33985__33987__34059__34061__34063__34065__34067)),happ(happ(Vvar__3__radd__33883,Vvar__var__var__var__var__var__var__18__x__33984__33986__34058__34060__34062__34064__34066),happ(Vvar__6__ropp__33898,Vvar__var__var__var__var__var__var__19__y__33985__33987__34059__34061__34063__34065__34067)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120] :
( cType___24t(Vvar__0__R__42100)
=> ( c_24__type__42240___24t(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__1__req__42101)
=> ( cType___24t(Vvar__2__C__42106)
=> ( c_24__type__42290___24t(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__3__cadd__42107)
=> ( c_24__type__42340___24t(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__4__cmul__42112)
=> ( c_24__type__42382___24t(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__5__phi__42117)
=> ( c_24__type__42432___24t(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__6__cdiv__42120)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__42152__42157__42162__42167__42172__42177__42182__42187] :
( t(Vvar__var__var__var__var__var__var__var__7__a__42152__42157__42162__42167__42172__42177__42182__42187,Vvar__2__C__42106)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__42153__42158__42163__42168__42173__42178__42183__42188] :
( t(Vvar__var__var__var__var__var__var__var__8__b__42153__42158__42163__42168__42173__42178__42183__42188,Vvar__2__C__42106)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2442495___24a9(Vvar__0__R__42100,Vvar__1__req__42101,Vvar__2__C__42106,Vvar__3__cadd__42107,Vvar__4__cmul__42112,Vvar__5__phi__42117,Vvar__6__cdiv__42120,Vvar__var__var__var__var__var__var__var__7__a__42152__42157__42162__42167__42172__42177__42182__42187,Vvar__var__var__var__var__var__var__var__8__b__42153__42158__42163__42168__42173__42178__42183__42188) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410] :
( cType___24t(Vvar__0__R__35394)
=> ( t(Vvar__1__rI__35395,Vvar__0__R__35394)
=> ( c_24__type__35496___24t(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410,Vvar__2__rmul__35396)
=> ( c_24__type__35540___24t(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410,Vvar__3__req__35401)
=> ( cType___24t(Vvar__4__Cpow__35406)
=> ( c_24__type__35576___24t(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410,Vvar__5__Cp__phi__35407)
=> ( c_24__type__35620___24t(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410,Vvar__6__rpow__35410)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__3__req__35401,Vvar__4__Cpow__35406,Vvar__5__Cp__phi__35407,Vvar__6__rpow__35410)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__35438__35440__35442__35444__35446__35448__35450__35452] :
( t(Vvar__var__var__var__var__var__var__var__7__r__35438__35440__35442__35444__35446__35448__35450__35452,Vvar__0__R__35394)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__35439__35441__35443__35445__35447__35449__35451__35453] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__35439__35441__35443__35445__35447__35449__35451__35453)
=> p(happ(happ(Vvar__3__req__35401,happ(happ(Vvar__6__rpow__35410,Vvar__var__var__var__var__var__var__var__7__r__35438__35440__35442__35444__35446__35448__35450__35452),happ(Vvar__5__Cp__phi__35407,Vvar__var__var__var__var__var__var__var__8__n__35439__35441__35443__35445__35447__35449__35451__35453))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__35394,Vvar__1__rI__35395,Vvar__2__rmul__35396,Vvar__var__var__var__var__var__var__var__7__r__35438__35440__35442__35444__35446__35448__35450__35452,Vvar__var__var__var__var__var__var__var__8__n__35439__35441__35443__35445__35447__35449__35451__35453))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602] :
( cType___24t(Vvar__0__R__31588)
=> ( c_24__type__31693___24t(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602,Vvar__1__radd__31589)
=> ( c_24__type__31723___24t(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602,Vvar__2__rmul__31594)
=> ( c_24__type__31747___24t(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602,Vvar__3__ropp__31599)
=> ( c_24__type__31777___24t(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602,Vvar__4__req__31602)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31807___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31588,c_24__type__31831___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602),Vvar__4__req__31602,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31588,Vvar__0__R__31588,Vvar__4__req__31602,Vvar__4__req__31602)),Vvar__1__radd__31589)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31864___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31588,c_24__type__31888___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602),Vvar__4__req__31602,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31588,Vvar__0__R__31588,Vvar__4__req__31602,Vvar__4__req__31602)),Vvar__2__rmul__31594)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31915___24a5(Vvar__0__R__31588,Vvar__1__radd__31589,Vvar__2__rmul__31594,Vvar__3__ropp__31599,Vvar__4__req__31602),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31588,Vvar__0__R__31588,Vvar__4__req__31602,Vvar__4__req__31602),Vvar__3__ropp__31599)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX5560] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX5560)
=> ( VX5560 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__5561] :
( cType___24t(Vvar__0__R__5561)
& ? [Vvar__1__req__5562] :
( c_24__type__1449___24t(Vvar__0__R__5561,Vvar__1__req__5562)
& ? [Vvar__2__reqb__5567] :
( c_24__type__5641___24t(Vvar__0__R__5561,Vvar__2__reqb__5567)
& ! [Vvar__var__3__x__5573__5576] :
( t(Vvar__var__3__x__5573__5576,Vvar__0__R__5561)
=> ! [Vvar__var__4__y__5574__5577] :
( t(Vvar__var__4__y__5574__5577,Vvar__0__R__5561)
=> ( happ(happ(Vvar__2__reqb__5567,Vvar__var__3__x__5573__5576),Vvar__var__4__y__5574__5577) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__5562,Vvar__var__3__x__5573__5576),Vvar__var__4__y__5574__5577)) ) ) )
& VX5560 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__5561,Vvar__1__req__5562,Vvar__2__reqb__5567) ) ) )
| ? [Vvar__0__R__5579] :
( cType___24t(Vvar__0__R__5579)
& ? [Vvar__1__rO__5580] :
( t(Vvar__1__rO__5580,Vvar__0__R__5579)
& ? [Vvar__2__rI__5581] :
( t(Vvar__2__rI__5581,Vvar__0__R__5579)
& ? [Vvar__3__radd__5582] :
( c_24__type__5649___24t(Vvar__0__R__5579,Vvar__3__radd__5582)
& ? [Vvar__4__rmul__5587] :
( c_24__type__5649___24t(Vvar__0__R__5579,Vvar__4__rmul__5587)
& ? [Vvar__5__rsub__5592] :
( c_24__type__5649___24t(Vvar__0__R__5579,Vvar__5__rsub__5592)
& ? [Vvar__6__ropp__5597] :
( c_24__type__5658___24t(Vvar__0__R__5579,Vvar__6__ropp__5597)
& ? [Vvar__7__req__5600] :
( c_24__type__1449___24t(Vvar__0__R__5579,Vvar__7__req__5600)
& ? [Vvar__8__C__5605] :
( cType___24t(Vvar__8__C__5605)
& ? [Vvar__9__cO__5606] :
( t(Vvar__9__cO__5606,Vvar__8__C__5605)
& ? [Vvar__10__cI__5607] :
( t(Vvar__10__cI__5607,Vvar__8__C__5605)
& ? [Vvar__11__cadd__5608] :
( c_24__type__5668___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__11__cadd__5608)
& ? [Vvar__12__cmul__5613] :
( c_24__type__5668___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__12__cmul__5613)
& ? [Vvar__13__csub__5618] :
( c_24__type__5668___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__13__csub__5618)
& ? [Vvar__14__copp__5623] :
( c_24__type__5682___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__14__copp__5623)
& ? [Vvar__15__ceqb__5626] :
( c_24__type__5689___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__15__ceqb__5626)
& ? [Vvar__16__phi__5631] :
( c_24__type__5693___24t(Vvar__0__R__5579,Vvar__8__C__5605,Vvar__16__phi__5631)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__5579,Vvar__1__rO__5580,Vvar__2__rI__5581,Vvar__3__radd__5582,Vvar__4__rmul__5587,Vvar__5__rsub__5592,Vvar__6__ropp__5597,Vvar__7__req__5600,Vvar__8__C__5605,Vvar__9__cO__5606,Vvar__10__cI__5607,Vvar__11__cadd__5608,Vvar__12__cmul__5613,Vvar__13__csub__5618,Vvar__14__copp__5623,Vvar__15__ceqb__5626,Vvar__16__phi__5631)
& VX5560 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__5579,Vvar__1__rO__5580,Vvar__2__rI__5581,Vvar__3__radd__5582,Vvar__4__rmul__5587,Vvar__5__rsub__5592,Vvar__6__ropp__5597,Vvar__7__req__5600,Vvar__8__C__5605,Vvar__9__cO__5606,Vvar__10__cI__5607,Vvar__11__cadd__5608,Vvar__12__cmul__5613,Vvar__13__csub__5618,Vvar__14__copp__5623,Vvar__15__ceqb__5626,Vvar__16__phi__5631) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128] :
( cType___24t(Vvar__0__R__3076)
=> ( t(Vvar__1__rO__3077,Vvar__0__R__3076)
=> ( t(Vvar__2__rI__3078,Vvar__0__R__3076)
=> ( c_24__type__3472___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__3__radd__3079)
=> ( c_24__type__3685___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__4__rmul__3084)
=> ( c_24__type__3898___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__5__rsub__3089)
=> ( c_24__type__4093___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__6__ropp__3094)
=> ( c_24__type__4306___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__7__req__3097)
=> ( cType___24t(Vvar__8__C__3102)
=> ( t(Vvar__9__cO__3103,Vvar__8__C__3102)
=> ( t(Vvar__10__cI__3104,Vvar__8__C__3102)
=> ( c_24__type__4519___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__11__cadd__3105)
=> ( c_24__type__4732___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__12__cmul__3110)
=> ( c_24__type__4945___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__13__csub__3115)
=> ( c_24__type__5140___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__14__copp__3120)
=> ( c_24__type__5353___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__15__ceqb__3123)
=> ( c_24__type__5548___24t(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128,Vvar__16__phi__3128)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__3076,Vvar__1__rO__3077,Vvar__2__rI__3078,Vvar__3__radd__3079,Vvar__4__rmul__3084,Vvar__5__rsub__3089,Vvar__6__ropp__3094,Vvar__7__req__3097,Vvar__8__C__3102,Vvar__9__cO__3103,Vvar__10__cI__3104,Vvar__11__cadd__3105,Vvar__12__cmul__3110,Vvar__13__csub__3115,Vvar__14__copp__3120,Vvar__15__ceqb__3123,Vvar__16__phi__3128)
=> ( p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,Vvar__9__cO__3103)),Vvar__1__rO__3077))
& p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,Vvar__10__cI__3104)),Vvar__2__rI__3078))
& ! [Vvar__var__var__var__var__var__var__19__x__3190__3192__3214__3216__3218__3220__3222] :
( t(Vvar__var__var__var__var__var__var__19__x__3190__3192__3214__3216__3218__3220__3222,Vvar__8__C__3102)
=> ! [Vvar__var__var__var__var__var__var__20__y__3191__3193__3215__3217__3219__3221__3223] :
( t(Vvar__var__var__var__var__var__var__20__y__3191__3193__3215__3217__3219__3221__3223,Vvar__8__C__3102)
=> p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,happ(happ(Vvar__11__cadd__3105,Vvar__var__var__var__var__var__var__19__x__3190__3192__3214__3216__3218__3220__3222),Vvar__var__var__var__var__var__var__20__y__3191__3193__3215__3217__3219__3221__3223))),happ(happ(Vvar__3__radd__3079,happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__19__x__3190__3192__3214__3216__3218__3220__3222)),happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__20__y__3191__3193__3215__3217__3219__3221__3223)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__3195__3197__3224__3226__3228__3230__3232] :
( t(Vvar__var__var__var__var__var__var__20__x__3195__3197__3224__3226__3228__3230__3232,Vvar__8__C__3102)
=> ! [Vvar__var__var__var__var__var__var__21__y__3196__3198__3225__3227__3229__3231__3233] :
( t(Vvar__var__var__var__var__var__var__21__y__3196__3198__3225__3227__3229__3231__3233,Vvar__8__C__3102)
=> p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,happ(happ(Vvar__13__csub__3115,Vvar__var__var__var__var__var__var__20__x__3195__3197__3224__3226__3228__3230__3232),Vvar__var__var__var__var__var__var__21__y__3196__3198__3225__3227__3229__3231__3233))),happ(happ(Vvar__5__rsub__3089,happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__20__x__3195__3197__3224__3226__3228__3230__3232)),happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__21__y__3196__3198__3225__3227__3229__3231__3233)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__3200__3202__3234__3236__3238__3240__3242] :
( t(Vvar__var__var__var__var__var__var__21__x__3200__3202__3234__3236__3238__3240__3242,Vvar__8__C__3102)
=> ! [Vvar__var__var__var__var__var__var__22__y__3201__3203__3235__3237__3239__3241__3243] :
( t(Vvar__var__var__var__var__var__var__22__y__3201__3203__3235__3237__3239__3241__3243,Vvar__8__C__3102)
=> p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,happ(happ(Vvar__12__cmul__3110,Vvar__var__var__var__var__var__var__21__x__3200__3202__3234__3236__3238__3240__3242),Vvar__var__var__var__var__var__var__22__y__3201__3203__3235__3237__3239__3241__3243))),happ(happ(Vvar__4__rmul__3084,happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__21__x__3200__3202__3234__3236__3238__3240__3242)),happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__22__y__3201__3203__3235__3237__3239__3241__3243)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__3205__3206__3244__3245__3246__3247__3248] :
( t(Vvar__var__var__var__var__var__var__22__x__3205__3206__3244__3245__3246__3247__3248,Vvar__8__C__3102)
=> p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,happ(Vvar__14__copp__3120,Vvar__var__var__var__var__var__var__22__x__3205__3206__3244__3245__3246__3247__3248))),happ(Vvar__6__ropp__3094,happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__var__22__x__3205__3206__3244__3245__3246__3247__3248)))) )
& ! [Vvar__var__var__var__var__var__23__x__3208__3211__3249__3252__3255__3258] :
( t(Vvar__var__var__var__var__var__23__x__3208__3211__3249__3252__3255__3258,Vvar__8__C__3102)
=> ! [Vvar__var__var__var__var__var__24__y__3209__3212__3250__3253__3256__3259] :
( t(Vvar__var__var__var__var__var__24__y__3209__3212__3250__3253__3256__3259,Vvar__8__C__3102)
=> ( happ(happ(Vvar__15__ceqb__3123,Vvar__var__var__var__var__var__23__x__3208__3211__3249__3252__3255__3258),Vvar__var__var__var__var__var__24__y__3209__3212__3250__3253__3256__3259) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__3097,happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__23__x__3208__3211__3249__3252__3255__3258)),happ(Vvar__16__phi__3128,Vvar__var__var__var__var__var__24__y__3209__3212__3250__3253__3256__3259))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432] :
( cType___24t(Vvar__0__R__34396)
=> ( t(Vvar__1__rO__34397,Vvar__0__R__34396)
=> ( t(Vvar__2__rI__34398,Vvar__0__R__34396)
=> ( c_24__type__34649___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__3__radd__34399)
=> ( c_24__type__34774___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__4__rmul__34404)
=> ( c_24__type__34899___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__5__req__34409)
=> ( cType___24t(Vvar__6__C__34414)
=> ( t(Vvar__7__cO__34415,Vvar__6__C__34414)
=> ( t(Vvar__8__cI__34416,Vvar__6__C__34414)
=> ( c_24__type__35024___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__9__cadd__34417)
=> ( c_24__type__35149___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__10__cmul__34422)
=> ( c_24__type__35274___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__11__ceqb__34427)
=> ( c_24__type__35385___24t(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432,Vvar__12__phi__34432)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__34396,Vvar__1__rO__34397,Vvar__2__rI__34398,Vvar__3__radd__34399,Vvar__4__rmul__34404,Vvar__5__req__34409,Vvar__6__C__34414,Vvar__7__cO__34415,Vvar__8__cI__34416,Vvar__9__cadd__34417,Vvar__10__cmul__34422,Vvar__11__ceqb__34427,Vvar__12__phi__34432)
=> ( p(happ(happ(Vvar__5__req__34409,happ(Vvar__12__phi__34432,Vvar__7__cO__34415)),Vvar__1__rO__34397))
& p(happ(happ(Vvar__5__req__34409,happ(Vvar__12__phi__34432,Vvar__8__cI__34416)),Vvar__2__rI__34398))
& ! [Vvar__var__var__var__var__var__var__15__x__34478__34480__34494__34496__34498__34500__34502] :
( t(Vvar__var__var__var__var__var__var__15__x__34478__34480__34494__34496__34498__34500__34502,Vvar__6__C__34414)
=> ! [Vvar__var__var__var__var__var__var__16__y__34479__34481__34495__34497__34499__34501__34503] :
( t(Vvar__var__var__var__var__var__var__16__y__34479__34481__34495__34497__34499__34501__34503,Vvar__6__C__34414)
=> p(happ(happ(Vvar__5__req__34409,happ(Vvar__12__phi__34432,happ(happ(Vvar__9__cadd__34417,Vvar__var__var__var__var__var__var__15__x__34478__34480__34494__34496__34498__34500__34502),Vvar__var__var__var__var__var__var__16__y__34479__34481__34495__34497__34499__34501__34503))),happ(happ(Vvar__3__radd__34399,happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__var__15__x__34478__34480__34494__34496__34498__34500__34502)),happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__var__16__y__34479__34481__34495__34497__34499__34501__34503)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__34483__34485__34504__34506__34508__34510__34512] :
( t(Vvar__var__var__var__var__var__var__16__x__34483__34485__34504__34506__34508__34510__34512,Vvar__6__C__34414)
=> ! [Vvar__var__var__var__var__var__var__17__y__34484__34486__34505__34507__34509__34511__34513] :
( t(Vvar__var__var__var__var__var__var__17__y__34484__34486__34505__34507__34509__34511__34513,Vvar__6__C__34414)
=> p(happ(happ(Vvar__5__req__34409,happ(Vvar__12__phi__34432,happ(happ(Vvar__10__cmul__34422,Vvar__var__var__var__var__var__var__16__x__34483__34485__34504__34506__34508__34510__34512),Vvar__var__var__var__var__var__var__17__y__34484__34486__34505__34507__34509__34511__34513))),happ(happ(Vvar__4__rmul__34404,happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__var__16__x__34483__34485__34504__34506__34508__34510__34512)),happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__var__17__y__34484__34486__34505__34507__34509__34511__34513)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__34488__34491__34514__34517__34520__34523] :
( t(Vvar__var__var__var__var__var__17__x__34488__34491__34514__34517__34520__34523,Vvar__6__C__34414)
=> ! [Vvar__var__var__var__var__var__18__y__34489__34492__34515__34518__34521__34524] :
( t(Vvar__var__var__var__var__var__18__y__34489__34492__34515__34518__34521__34524,Vvar__6__C__34414)
=> ( happ(happ(Vvar__11__ceqb__34427,Vvar__var__var__var__var__var__17__x__34488__34491__34514__34517__34520__34523),Vvar__var__var__var__var__var__18__y__34489__34492__34515__34518__34521__34524) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__34409,happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__17__x__34488__34491__34514__34517__34520__34523)),happ(Vvar__12__phi__34432,Vvar__var__var__var__var__var__18__y__34489__34492__34515__34518__34521__34524))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__14633,Vvar__1__copp__14634,Vvar__2__ceqb__14637,Vvar__3__get__sign__14642] :
( cType___24t(Vvar__0__C__14633)
=> ( c_24__type__14689___24t(Vvar__0__C__14633,Vvar__1__copp__14634,Vvar__2__ceqb__14637,Vvar__3__get__sign__14642,Vvar__1__copp__14634)
=> ( c_24__type__14708___24t(Vvar__0__C__14633,Vvar__1__copp__14634,Vvar__2__ceqb__14637,Vvar__3__get__sign__14642,Vvar__2__ceqb__14637)
=> ( c_24__type__14722___24t(Vvar__0__C__14633,Vvar__1__copp__14634,Vvar__2__ceqb__14637,Vvar__3__get__sign__14642,Vvar__3__get__sign__14642)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__14633,Vvar__1__copp__14634,Vvar__2__ceqb__14637,Vvar__3__get__sign__14642)
=> ( ! [Vvar__var__var__var__var__var__4__c__14659__14662__14665__14668__14671__14674] :
( t(Vvar__var__var__var__var__var__4__c__14659__14662__14665__14668__14671__14674,Vvar__0__C__14633)
=> ! [Vvar__var__var__var__var__var__5__c_27__14660__14663__14666__14669__14672__14675] :
( t(Vvar__var__var__var__var__var__5__c_27__14660__14663__14666__14669__14672__14675,Vvar__0__C__14633)
=> ( happ(Vvar__3__get__sign__14642,Vvar__var__var__var__var__var__4__c__14659__14662__14665__14668__14671__14674) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__14633,Vvar__var__var__var__var__var__5__c_27__14660__14663__14666__14669__14672__14675)
=> happ(happ(Vvar__2__ceqb__14637,Vvar__var__var__var__var__var__4__c__14659__14662__14665__14668__14671__14674),happ(Vvar__1__copp__14634,Vvar__var__var__var__var__var__5__c_27__14660__14663__14666__14669__14672__14675)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629] :
( cType___24t(Vvar__0__R__41618)
=> ( c_24__type__41704___24t(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629,Vvar__1__radd__41619)
=> ( c_24__type__41727___24t(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629,Vvar__2__rmul__41624)
=> ( c_24__type__41750___24t(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629,Vvar__3__req__41629)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__41773___24a4(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__41618,c_24__type__41791___24a4(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629),Vvar__3__req__41629,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__41618,Vvar__0__R__41618,Vvar__3__req__41629,Vvar__3__req__41629)),Vvar__1__radd__41619)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__41817___24a4(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__41618,c_24__type__41835___24a4(Vvar__0__R__41618,Vvar__1__radd__41619,Vvar__2__rmul__41624,Vvar__3__req__41629),Vvar__3__req__41629,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__41618,Vvar__0__R__41618,Vvar__3__req__41629,Vvar__3__req__41629)),Vvar__2__rmul__41624)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.elemsR',axiom,
! [Vvar__0__A__43296,Vvar__1__B__43297,Vvar__2__R__43298,Vvar__3___24Anonymous__43303,Vvar__4___24Anonymous__43304] :
( cType___24t(Vvar__0__A__43296)
=> ( cType___24t(Vvar__1__B__43297)
=> ( c_24__type__43341___24t(Vvar__0__A__43296,Vvar__1__B__43297,Vvar__2__R__43298,Vvar__3___24Anonymous__43303,Vvar__4___24Anonymous__43304,Vvar__2__R__43298)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43296,Vvar__3___24Anonymous__43303)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__43297,Vvar__4___24Anonymous__43304)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__43296,Vvar__1__B__43297,Vvar__2__R__43298,Vvar__3___24Anonymous__43303,Vvar__4___24Anonymous__43304)
=> ( ( Vvar__4___24Anonymous__43304 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__43297)
& Vvar__3___24Anonymous__43303 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__43296) )
| ? [Vvar__3__a__43320] :
( t(Vvar__3__a__43320,Vvar__0__A__43296)
& ? [Vvar__4__b__43321] :
( t(Vvar__4__b__43321,Vvar__1__B__43297)
& p(happ(happ(Vvar__2__R__43298,Vvar__3__a__43320),Vvar__4__b__43321))
& ? [Vvar__6__l__43323] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43296,Vvar__6__l__43323)
& ? [Vvar__7__l_27__43324] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__43297,Vvar__7__l_27__43324)
& cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__43296,Vvar__1__B__43297,Vvar__2__R__43298,Vvar__6__l__43323,Vvar__7__l_27__43324)
& Vvar__4___24Anonymous__43304 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__43297,Vvar__4__b__43321,Vvar__7__l_27__43324)
& Vvar__3___24Anonymous__43303 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43296,Vvar__3__a__43320,Vvar__6__l__43323) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.merges_spec',axiom,
! [Vvar__0__T__1838,Vvar__1___24Anonymous__1839,Vvar__2___24Anonymous__1840,Vvar__3___24Anonymous__1841] :
( cType___24t(Vvar__0__T__1838)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__1___24Anonymous__1839)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__2___24Anonymous__1840)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838),Vvar__3___24Anonymous__1841)
=> ( cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__1838,Vvar__1___24Anonymous__1839,Vvar__2___24Anonymous__1840,Vvar__3___24Anonymous__1841)
=> ( ? [Vvar__1__x__1844] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__1__x__1844)
& Vvar__3___24Anonymous__1841 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838),Vvar__1__x__1844,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838)))
& Vvar__2___24Anonymous__1840 = Vvar__1__x__1844
& Vvar__1___24Anonymous__1839 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__1838) )
| ? [Vvar__1__x__1846] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__1__x__1846)
& Vvar__3___24Anonymous__1841 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838),Vvar__1__x__1846,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838)))
& Vvar__2___24Anonymous__1840 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__1838)
& Vvar__1___24Anonymous__1839 = Vvar__1__x__1846 )
| ? [Vvar__1__x__1848] :
( t(Vvar__1__x__1848,Vvar__0__T__1838)
& ? [Vvar__2__y__1849] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__2__y__1849)
& ? [Vvar__3__h__1850] :
( t(Vvar__3__h__1850,Vvar__0__T__1838)
& ? [Vvar__4__t__1851] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__1838,Vvar__4__t__1851)
& ? [Vvar__5__r__1852] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838),Vvar__5__r__1852)
& ? [Vvar__6__r_27__1853] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__1838),Vvar__6__r_27__1853)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__1838,Vvar__2__y__1849,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__1838,Vvar__3__h__1850,Vvar__4__t__1851),Vvar__5__r__1852)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__1838,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__1838,Vvar__1__x__1848,Vvar__2__y__1849),Vvar__4__t__1851,Vvar__6__r_27__1853)
& Vvar__3___24Anonymous__1841 = c_24__case__Coq_2eInit_2eDatatypes_2elist_242348___24a8(Vvar__0__T__1838,Vvar__1___24Anonymous__1839,Vvar__2___24Anonymous__1840,Vvar__3___24Anonymous__1841,Vvar__1__x__1848,Vvar__3__h__1850,Vvar__5__r__1852,Vvar__6__r_27__1853)
& Vvar__2___24Anonymous__1840 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__1838,Vvar__3__h__1850,Vvar__4__t__1851)
& Vvar__1___24Anonymous__1839 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__1838,Vvar__1__x__1848,Vvar__2__y__1849) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_monads.Functor',axiom,
! [VX43531] :
( cmonads_2eFunctor___24t(VX43531)
=> ? [Vvar__0__func__43532] :
( c_24__type__20___24t(Vvar__0__func__43532)
& ? [Vvar__1__func__map__43534] :
( c_24__type__43582___24t(Vvar__0__func__43532,Vvar__1__func__map__43534)
& ! [Vvar__var__2__X__43546__43549] :
( cType___24t(Vvar__var__2__X__43546__43549)
=> happ(happ(happ(Vvar__1__func__map__43534,Vvar__var__2__X__43546__43549),Vvar__var__2__X__43546__43549),c_24__lam__43588___24a2(Vvar__0__func__43532,Vvar__var__2__X__43546__43549)) = c_24__lam__43591___24a2(Vvar__0__func__43532,Vvar__var__2__X__43546__43549) )
& ! [Vvar__var__3__a__43553__43561] :
( cType___24t(Vvar__var__3__a__43553__43561)
=> ! [Vvar__var__4__b__43554__43562] :
( cType___24t(Vvar__var__4__b__43554__43562)
=> ! [Vvar__var__5__c__43555__43563] :
( cType___24t(Vvar__var__5__c__43555__43563)
=> ! [Vvar__var__6__x__43560__43568] :
( t(Vvar__var__6__x__43560__43568,happ(Vvar__0__func__43532,Vvar__var__3__a__43553__43561))
=> ! [Vvar__var__7__f__43558__43566] :
( c_24__type__43599___24t(Vvar__0__func__43532,Vvar__var__3__a__43553__43561,Vvar__var__4__b__43554__43562,Vvar__var__5__c__43555__43563,Vvar__var__7__f__43558__43566)
=> ! [Vvar__var__8__g__43559__43567] :
( c_24__type__43605___24t(Vvar__0__func__43532,Vvar__var__3__a__43553__43561,Vvar__var__4__b__43554__43562,Vvar__var__5__c__43555__43563,Vvar__var__8__g__43559__43567)
=> happ(happ(happ(happ(Vvar__1__func__map__43534,Vvar__var__3__a__43553__43561),Vvar__var__5__c__43555__43563),cCoq_2eProgram_2eBasics_2ecompose___24a5(Vvar__var__3__a__43553__43561,Vvar__var__4__b__43554__43562,Vvar__var__5__c__43555__43563,Vvar__var__7__f__43558__43566,Vvar__var__8__g__43559__43567)),Vvar__var__6__x__43560__43568) = happ(happ(happ(happ(Vvar__1__func__map__43534,Vvar__var__4__b__43554__43562),Vvar__var__5__c__43555__43563),Vvar__var__7__f__43558__43566),happ(happ(happ(happ(Vvar__1__func__map__43534,Vvar__var__3__a__43553__43561),Vvar__var__4__b__43554__43562),Vvar__var__8__g__43559__43567),Vvar__var__6__x__43560__43568)) ) ) ) ) ) )
& VX43531 = cmonads_2eBuild__Functor___24a2(Vvar__0__func__43532,Vvar__1__func__map__43534) ) ) ) ).
fof('$_inversion_monads.Monad',axiom,
! [VX903] :
( cmonads_2eMonad___24t(VX903)
=> ? [Vvar__0__mon__904] :
( c_24__type__20___24t(Vvar__0__mon__904)
& ? [Vvar__1__bind__906] :
( c_24__type__971___24t(Vvar__0__mon__904,Vvar__1__bind__906)
& ? [Vvar__2__ret__917] :
( c_24__type__981___24t(Vvar__0__mon__904,Vvar__2__ret__917)
& ! [Vvar__var__3__a__923__928] :
( cType___24t(Vvar__var__3__a__923__928)
=> ! [Vvar__var__4__b__924__929] :
( cType___24t(Vvar__var__4__b__924__929)
=> ! [Vvar__var__5__x__926__931] :
( t(Vvar__var__5__x__926__931,Vvar__var__3__a__923__928)
=> ! [Vvar__var__6__f__927__932] :
( c_24__type__976___24t(Vvar__0__mon__904,Vvar__var__3__a__923__928,Vvar__var__4__b__924__929,Vvar__var__6__f__927__932)
=> happ(happ(happ(happ(Vvar__1__bind__906,Vvar__var__3__a__923__928),Vvar__var__4__b__924__929),happ(happ(Vvar__2__ret__917,Vvar__var__3__a__923__928),Vvar__var__5__x__926__931)),Vvar__var__6__f__927__932) = happ(Vvar__var__6__f__927__932,Vvar__var__5__x__926__931) ) ) ) )
& ! [Vvar__var__4__a__934__936] :
( cType___24t(Vvar__var__4__a__934__936)
=> ! [Vvar__var__5__f__935__937] :
( t(Vvar__var__5__f__935__937,happ(Vvar__0__mon__904,Vvar__var__4__a__934__936))
=> happ(happ(happ(happ(Vvar__1__bind__906,Vvar__var__4__a__934__936),Vvar__var__4__a__934__936),Vvar__var__5__f__935__937),happ(Vvar__2__ret__917,Vvar__var__4__a__934__936)) = Vvar__var__5__f__935__937 ) )
& ! [Vvar__var__5__a__939__948] :
( cType___24t(Vvar__var__5__a__939__948)
=> ! [Vvar__var__6__b__940__949] :
( cType___24t(Vvar__var__6__b__940__949)
=> ! [Vvar__var__7__c__942__951] :
( cType___24t(Vvar__var__7__c__942__951)
=> ! [Vvar__var__8__n__944__953] :
( t(Vvar__var__8__n__944__953,happ(Vvar__0__mon__904,Vvar__var__5__a__939__948))
=> ! [Vvar__var__9__f__945__954] :
( c_24__type__976___24t(Vvar__0__mon__904,Vvar__var__5__a__939__948,Vvar__var__6__b__940__949,Vvar__var__9__f__945__954)
=> ! [Vvar__var__10__g__946__955] :
( c_24__type__1000___24t(Vvar__0__mon__904,Vvar__var__5__a__939__948,Vvar__var__6__b__940__949,Vvar__var__7__c__942__951,Vvar__var__10__g__946__955)
=> happ(happ(happ(happ(Vvar__1__bind__906,Vvar__var__6__b__940__949),Vvar__var__7__c__942__951),happ(happ(happ(happ(Vvar__1__bind__906,Vvar__var__5__a__939__948),Vvar__var__6__b__940__949),Vvar__var__8__n__944__953),Vvar__var__9__f__945__954)),Vvar__var__10__g__946__955) = happ(happ(happ(happ(Vvar__1__bind__906,Vvar__var__5__a__939__948),Vvar__var__7__c__942__951),Vvar__var__8__n__944__953),c_24__lam__1025___24a7(Vvar__0__mon__904,Vvar__1__bind__906,Vvar__var__5__a__939__948,Vvar__var__6__b__940__949,Vvar__var__7__c__942__951,Vvar__var__9__f__945__954,Vvar__var__10__g__946__955)) ) ) ) ) ) )
& VX903 = cmonads_2eBuild__Monad___24a3(Vvar__0__mon__904,Vvar__1__bind__906,Vvar__2__ret__917) ) ) ) ) ).
fof('$_lam_1025',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] : c_24__lam__1025___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_11827',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11827___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_11835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11835___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_11843',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11843___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_11851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11851___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__203___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cmonads_2ebind___24a5(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__6),Vv__CANONICAL__5) ).
fof('$_lam_35907',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__35907___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_35915',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__35915___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_36127',axiom,
! [Vv__CANONICAL__0] : c_24__lam__36127___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_36128',axiom,
! [Vv__CANONICAL__0] : c_24__lam__36128___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_420',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] : c_24__lam__420___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_43588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__43588___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_43591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__43591___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_43719',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__43719___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_43722',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__43722___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_648',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__648___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_890',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] : c_24__lam__890___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_prop_35880',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__35880___24a2(V0__A,V1__B))
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V1__B,V4__x)) ) ) ).
fof('$_prop_35881',axiom,
! [V0__A,V2__C] :
( p(c_24__prop__35881___24a2(V0__A,V2__C))
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__C,V4__x)) ) ) ).
fof('$_prop_43347',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43347___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_43348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43348___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_43377',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__S__43355,Vvar__1__x__43356,Vvar__2__y__43357] :
( p(c_24__prop__43377___24a4(Vvar__0___24Anonymous__43353,Vvar__0__S__43355,Vvar__1__x__43356,Vvar__2__y__43357))
<=> Vvar__1__x__43356 = Vvar__2__y__43357 ) ).
fof('$_prop_43378',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__x__43358,Vvar__1__y__43359] :
( p(c_24__prop__43378___24a3(Vvar__0___24Anonymous__43353,Vvar__0__x__43358,Vvar__1__y__43359))
<=> Vvar__0__x__43358 = Vvar__1__y__43359 ) ).
fof('$_prop_43379',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__x__43360,Vvar__1__s__43361] :
( p(c_24__prop__43379___24a3(Vvar__0___24Anonymous__43353,Vvar__0__x__43360,Vvar__1__s__43361))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__43360,Vvar__1__s__43361) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_43380',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__P__43362,Vvar__1__Q__43363] :
( p(c_24__prop__43380___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43362,Vvar__1__Q__43363))
<=> ( p(Vvar__0__P__43362)
& p(Vvar__1__Q__43363) ) ) ).
fof('$_prop_43381',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__P__43366,Vvar__1__Q__43367] :
( p(c_24__prop__43381___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43366,Vvar__1__Q__43367))
<=> ( p(Vvar__0__P__43366)
| p(Vvar__1__Q__43367) ) ) ).
fof('$_prop_43382',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__P__43370,Vvar__1__Q__43371] :
( p(c_24__prop__43382___24a3(Vvar__0___24Anonymous__43353,Vvar__0__P__43370,Vvar__1__Q__43371))
<=> ( p(Vvar__0__P__43370)
=> p(Vvar__1__Q__43371) ) ) ).
fof('$_prop_43383',axiom,
! [Vvar__0___24Anonymous__43353,Vvar__0__P__43375] :
( p(c_24__prop__43383___24a2(Vvar__0___24Anonymous__43353,Vvar__0__P__43375))
<=> ~ p(Vvar__0__P__43375) ) ).
fof('$_prop_43384',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__43384___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_43515',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__43515___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_8494',axiom,
! [V0__X,V1__x] :
( p(c_24__prop__8494___24a2(V0__X,V1__x))
<=> V1__x = V1__x ) ).
fof('$_prop_8507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__8507___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_8508',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__8508___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_type_1',axiom,
! [Vvar__2] :
( c_24__type__1___24t(Vvar__2)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cmonads_2emon___24t(cM,cB,happ(Vvar__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10',axiom,
! [Vvar__11] :
( c_24__type__10___24t(Vvar__11)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1001] :
( c_24__type__1000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1001)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__1001,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_10526',axiom,
! [Vvar__10527] :
( c_24__type__10526___24t(Vvar__10527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__10527,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10531',axiom,
! [Vv__CANONICAL__0,Vvar__10532] :
( c_24__type__10531___24t(Vv__CANONICAL__0,Vvar__10532)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__10532,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_10704',axiom,
! [Vvar__10705] :
( c_24__type__10704___24t(Vvar__10705)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(Vvar__10705,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11052',axiom,
! [Vvar__11053] :
( c_24__type__11052___24t(Vvar__11053)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5658___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__11053,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_11093',axiom,
! [Vvar__11094] :
( c_24__type__11093___24t(Vvar__11094)
<=> ! [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__11094,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_11245',axiom,
! [Vv__CANONICAL__0,Vvar__11246] :
( c_24__type__11245___24t(Vv__CANONICAL__0,Vvar__11246)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__11246,Vv__CANONICAL__1)) ) ) ).
fof('$_type_11353',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11354] :
( c_24__type__11353___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11354)
<=> ! [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__11354,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_11372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11373] :
( c_24__type__11372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__11373)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__11373,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_11392',axiom,
! [Vvar__11393] :
( c_24__type__11392___24t(Vvar__11393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___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__11393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_11495',axiom,
! [Vvar__11496] :
( c_24__type__11495___24t(Vvar__11496)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__11496,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_11526',axiom,
! [Vvar__11527] :
( c_24__type__11526___24t(Vvar__11527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___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__11527,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_11557',axiom,
! [Vvar__11558] :
( c_24__type__11557___24t(Vvar__11558)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__11558,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_11568',axiom,
! [Vv__CANONICAL__0,Vvar__11569] :
( c_24__type__11568___24t(Vv__CANONICAL__0,Vvar__11569)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__11569,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_11570',axiom,
! [Vvar__11571] :
( c_24__type__11570___24t(Vvar__11571)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__11571,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11590',axiom,
! [Vvar__11591] :
( c_24__type__11590___24t(Vvar__11591)
<=> ! [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__11591,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11594',axiom,
! [Vvar__11595] :
( c_24__type__11594___24t(Vvar__11595)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11595,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11602',axiom,
! [Vvar__11603] :
( c_24__type__11602___24t(Vvar__11603)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__11603,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11669',axiom,
! [Vvar__11670] :
( c_24__type__11669___24t(Vvar__11670)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__11670,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11888',axiom,
! [Vvar__11889] :
( c_24__type__11888___24t(Vvar__11889)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__11889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_12504',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12505] :
( c_24__type__12504___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12505)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__12505,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1285',axiom,
! [Vvar__1286] :
( c_24__type__1285___24t(Vvar__1286)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1286,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1295',axiom,
! [Vvar__1296] :
( c_24__type__1295___24t(Vvar__1296)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__131] :
( c_24__type__130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__131)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__58___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__131,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__2) ) ) ) ) ).
fof('$_type_13004',axiom,
! [Vvar__13005] :
( c_24__type__13004___24t(Vvar__13005)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__13005,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1311',axiom,
! [Vvar__1312] :
( c_24__type__1311___24t(Vvar__1312)
<=> ! [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__1312,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1323',axiom,
! [Vvar__1324] :
( c_24__type__1323___24t(Vvar__1324)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__1324,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_13253',axiom,
! [Vvar__13254] :
( c_24__type__13253___24t(Vvar__13254)
<=> ! [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__13254,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13256',axiom,
! [Vvar__13257] :
( c_24__type__13256___24t(Vvar__13257)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__13257,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13261',axiom,
! [Vvar__13262] :
( c_24__type__13261___24t(Vvar__13262)
<=> ! [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__13262,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1335',axiom,
! [Vvar__1336] :
( c_24__type__1335___24t(Vvar__1336)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__1336,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_1337',axiom,
! [Vvar__1338] :
( c_24__type__1337___24t(Vvar__1338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1338,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1345',axiom,
! [Vvar__1346] :
( c_24__type__1345___24t(Vvar__1346)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1346,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13454',axiom,
! [Vvar__13455] :
( c_24__type__13454___24t(Vvar__13455)
<=> ! [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__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__5658___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__5693___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__9143___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__9152___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__13455,Vv__CANONICAL__0),Vv__CANONICAL__1),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__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1362',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1363] :
( c_24__type__1362___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1363)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1363,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1366',axiom,
! [Vvar__1367] :
( c_24__type__1366___24t(Vvar__1367)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1367,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1369',axiom,
! [Vv__CANONICAL__0,Vvar__1370] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vvar__1370)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1370,Vv__CANONICAL__1)) ) ) ).
fof('$_type_137',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__138] :
( c_24__type__137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__138)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__138,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_1449',axiom,
! [Vv__CANONICAL__0,Vvar__1450] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vvar__1450)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1450,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1452',axiom,
! [Vv__CANONICAL__0,Vvar__1453] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vvar__1453)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1453,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14628',axiom,
! [Vvar__14629] :
( c_24__type__14628___24t(Vvar__14629)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__14629,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_14689',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14690] :
( c_24__type__14689___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14690)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__14690,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_14708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14709] :
( c_24__type__14708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14709)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14709,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_14722',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14723] :
( c_24__type__14722___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14723)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__14723,Vv__CANONICAL__4)) ) ) ).
fof('$_type_14780',axiom,
! [Vvar__14781] :
( c_24__type__14780___24t(Vvar__14781)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__14781,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14791',axiom,
! [Vvar__14792] :
( c_24__type__14791___24t(Vvar__14792)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11245___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__14792,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14804',axiom,
! [Vvar__14805] :
( c_24__type__14804___24t(Vvar__14805)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__14805,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_14831',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14832] :
( c_24__type__14831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14832)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14832,Vv__CANONICAL__3)) ) ) ).
fof('$_type_14839',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14840] :
( c_24__type__14839___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14840)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14840,Vv__CANONICAL__3)) ) ) ).
fof('$_type_14847',axiom,
! [Vvar__14848] :
( c_24__type__14847___24t(Vvar__14848)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__14848,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14881',axiom,
! [Vvar__14882] :
( c_24__type__14881___24t(Vvar__14882)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__14882,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_14909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14910] :
( c_24__type__14909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14910)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14910,Vv__CANONICAL__3)) ) ) ).
fof('$_type_14917',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14918] :
( c_24__type__14917___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14918)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14918,Vv__CANONICAL__3)) ) ) ).
fof('$_type_14925',axiom,
! [Vvar__14926] :
( c_24__type__14925___24t(Vvar__14926)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__14926,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14959',axiom,
! [Vvar__14960] :
( c_24__type__14959___24t(Vvar__14960)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__14960,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_14977',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14978] :
( c_24__type__14977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14978)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14978,Vv__CANONICAL__2)) ) ) ).
fof('$_type_14983',axiom,
! [Vvar__14984] :
( c_24__type__14983___24t(Vvar__14984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__14984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__152] :
( c_24__type__151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__152)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__152,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_15157',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15158] :
( c_24__type__15157___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15158)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15158,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15163',axiom,
! [Vvar__15164] :
( c_24__type__15163___24t(Vvar__15164)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___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__15164,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_15180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15181] :
( c_24__type__15180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15181)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15181,Vv__CANONICAL__2)) ) ) ).
fof('$_type_15186',axiom,
! [Vvar__15187] :
( c_24__type__15186___24t(Vvar__15187)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___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__15187,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eprojT1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__173] :
( c_24__type__172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__173)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cmonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vvar__173,Vv__CANONICAL__3)) ) ) ).
fof('$_type_177',axiom,
! [Vvar__178] :
( c_24__type__177___24t(Vvar__178)
<=> ! [Vv__CANONICAL__0] :
( cmonads_2eMonad___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__178,Vv__CANONICAL__0)) ) ) ).
fof('$_type_186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__187] :
( c_24__type__186___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__187)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> cmonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__187,Vv__CANONICAL__4)) ) ) ).
fof('$_type_20',axiom,
! [Vvar__21] :
( c_24__type__20___24t(Vvar__21)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__21,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2664',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2665] :
( c_24__type__2664___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2665)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(Vvar__2665,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2672',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2673] :
( c_24__type__2672___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2673)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__2673,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2685',axiom,
! [Vvar__2686] :
( c_24__type__2685___24t(Vvar__2686)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__2686,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2698',axiom,
! [Vvar__2699] :
( c_24__type__2698___24t(Vvar__2699)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2699,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2703',axiom,
! [Vvar__2704] :
( c_24__type__2703___24t(Vvar__2704)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2704,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2708',axiom,
! [Vvar__2709] :
( c_24__type__2708___24t(Vvar__2709)
<=> ! [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__2709,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2713',axiom,
! [Vv__CANONICAL__0,Vvar__2714] :
( c_24__type__2713___24t(Vv__CANONICAL__0,Vvar__2714)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__2714,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_2729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2730] :
( c_24__type__2729___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2730)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2730,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2733',axiom,
! [Vvar__2734] :
( c_24__type__2733___24t(Vvar__2734)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2734,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2751',axiom,
! [Vvar__2752] :
( c_24__type__2751___24t(Vvar__2752)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___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__2752,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27590',axiom,
! [Vvar__27591] :
( c_24__type__27590___24t(Vvar__27591)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__27591,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2761',axiom,
! [Vvar__2762] :
( c_24__type__2761___24t(Vvar__2762)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2762,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27613',axiom,
! [Vvar__27614] :
( c_24__type__27613___24t(Vvar__27614)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__27614,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_27618',axiom,
! [Vvar__27619] :
( c_24__type__27618___24t(Vvar__27619)
<=> ! [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__27619,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_27630',axiom,
! [Vvar__27631] :
( c_24__type__27630___24t(Vvar__27631)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__27631,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2767',axiom,
! [Vvar__2768] :
( c_24__type__2767___24t(Vvar__2768)
<=> ! [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__2768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27750',axiom,
! [Vvar__27751] :
( c_24__type__27750___24t(Vvar__27751)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__27751,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27767',axiom,
! [Vvar__27768] :
( c_24__type__27767___24t(Vvar__27768)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__27768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27775',axiom,
! [Vvar__27776] :
( c_24__type__27775___24t(Vvar__27776)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__27776,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2824',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2825] :
( c_24__type__2824___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2825)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(Vvar__2825,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_2840',axiom,
! [Vvar__2841] :
( c_24__type__2840___24t(Vvar__2841)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__2841,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2844',axiom,
! [Vvar__2845] :
( c_24__type__2844___24t(Vvar__2845)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2845,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28786',axiom,
! [Vvar__28787] :
( c_24__type__28786___24t(Vvar__28787)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28787,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28978',axiom,
! [Vvar__28979] :
( c_24__type__28978___24t(Vvar__28979)
<=> ! [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__28979,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29218',axiom,
! [Vvar__29219] :
( c_24__type__29218___24t(Vvar__29219)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__29219,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29227',axiom,
! [Vvar__29228] :
( c_24__type__29227___24t(Vvar__29228)
<=> ! [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__29228,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29236',axiom,
! [Vvar__29237] :
( c_24__type__29236___24t(Vvar__29237)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__29237,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29246',axiom,
! [Vvar__29247] :
( c_24__type__29246___24t(Vvar__29247)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__29247,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29268',axiom,
! [Vvar__29269] :
( c_24__type__29268___24t(Vvar__29269)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29269,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29279',axiom,
! [Vvar__29280] :
( c_24__type__29279___24t(Vvar__29280)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29280,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29404',axiom,
! [Vvar__29405] :
( c_24__type__29404___24t(Vvar__29405)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29405,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29439',axiom,
! [Vvar__29440] :
( c_24__type__29439___24t(Vvar__29440)
<=> ! [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__29440,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29449',axiom,
! [Vvar__29450] :
( c_24__type__29449___24t(Vvar__29450)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__29450,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29457',axiom,
! [Vvar__29458] :
( c_24__type__29457___24t(Vvar__29458)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29458,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29464',axiom,
! [Vvar__29465] :
( c_24__type__29464___24t(Vvar__29465)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__29465,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29467',axiom,
! [Vvar__29468] :
( c_24__type__29467___24t(Vvar__29468)
<=> ! [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__29468,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29607',axiom,
! [Vvar__29608] :
( c_24__type__29607___24t(Vvar__29608)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29608,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2961',axiom,
! [Vvar__2962] :
( c_24__type__2961___24t(Vvar__2962)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2962,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29610',axiom,
! [Vvar__29611] :
( c_24__type__29610___24t(Vvar__29611)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29611,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2981',axiom,
! [Vvar__2982] :
( c_24__type__2981___24t(Vvar__2982)
<=> ! [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__2982,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2983',axiom,
! [Vvar__2984] :
( c_24__type__2983___24t(Vvar__2984)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__2984,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2986',axiom,
! [Vv__CANONICAL__0,Vvar__2987] :
( c_24__type__2986___24t(Vv__CANONICAL__0,Vvar__2987)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__2987,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2995',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2996] :
( c_24__type__2995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2996)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__2996,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3001] :
( c_24__type__3000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3001)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__3001,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3025',axiom,
! [Vvar__3026] :
( c_24__type__3025___24t(Vvar__3026)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__3026,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3039',axiom,
! [Vvar__3040] :
( c_24__type__3039___24t(Vvar__3040)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3040,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3049',axiom,
! [Vvar__3050] :
( c_24__type__3049___24t(Vvar__3050)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3050,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31008',axiom,
! [Vvar__31009] :
( c_24__type__31008___24t(Vvar__31009)
<=> ! [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__31009,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31032',axiom,
! [Vvar__31033] :
( c_24__type__31032___24t(Vvar__31033)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31033,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31035',axiom,
! [Vvar__31036] :
( c_24__type__31035___24t(Vvar__31036)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31036,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31558',axiom,
! [Vvar__31559] :
( c_24__type__31558___24t(Vvar__31559)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__31559,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31570',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31571] :
( c_24__type__31570___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31571)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__31571,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31576] :
( c_24__type__31575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31576)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__31576,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31694] :
( c_24__type__31693___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31694)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31694,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31723',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31724] :
( c_24__type__31723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31724)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31724,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31747',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31748] :
( c_24__type__31747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31748)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31748,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31778] :
( c_24__type__31777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31778)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31778,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_31807',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31808] :
( c_24__type__31807___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31808)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31808,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31831',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31832] :
( c_24__type__31831___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31832)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31832,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31864',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31865] :
( c_24__type__31864___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31865)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31865,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31889] :
( c_24__type__31888___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31889)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31889,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31915',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31916] :
( c_24__type__31915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31916)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31916,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31926',axiom,
! [Vvar__31927] :
( c_24__type__31926___24t(Vvar__31927)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31927,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31968',axiom,
! [Vvar__31969] :
( c_24__type__31968___24t(Vvar__31969)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31969,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32030',axiom,
! [Vvar__32031] :
( c_24__type__32030___24t(Vvar__32031)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1452___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> cProp___24t(happ(happ(happ(happ(Vvar__32031,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32235',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__32236] :
( c_24__type__32235___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__32236)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32236,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32329] :
( c_24__type__32328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32329)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32329,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32421',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__32422] :
( c_24__type__32421___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__32422)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32422,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32503',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32504] :
( c_24__type__32503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32504)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__32504,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_32596',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__32597] :
( c_24__type__32596___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__32597)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32597,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32679] :
( c_24__type__32678___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__32679)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__32679,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_32771',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__32772] :
( c_24__type__32771___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__32772)
<=> ! [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__32772,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_33223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33224] :
( c_24__type__33223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33224)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33224,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33324',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__33325] :
( c_24__type__33324___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__33325)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33325,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33425',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33426] :
( c_24__type__33425___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33426)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33426,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33515',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__33516] :
( c_24__type__33515___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__33516)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__33516,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_33616',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33617] :
( c_24__type__33616___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33617)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33617,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_33717',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__33718] :
( c_24__type__33717___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__33718)
<=> ! [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__33718,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_33818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33819] :
( c_24__type__33818___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__33819)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33819,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_33877',axiom,
! [Vvar__33878] :
( c_24__type__33877___24t(Vvar__33878)
<=> ! [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__33878,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34129',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34130] :
( c_24__type__34129___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34130)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34130,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34192',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__34193] :
( c_24__type__34192___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__34193)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34193,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34256] :
( c_24__type__34255___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34256)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34256,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34309',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__34310] :
( c_24__type__34309___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__34310)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__34310,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_34372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34373] :
( c_24__type__34372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__34373)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34373,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_34649',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__34650] :
( c_24__type__34649___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__34650)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34650,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3473] :
( c_24__type__3472___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3473)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3473,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34774',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__34775] :
( c_24__type__34774___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__34775)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34775,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34899',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__34900] :
( c_24__type__34899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__34900)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34900,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_35024',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__35025] :
( c_24__type__35024___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__35025)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__35025,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_35149',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35150] :
( c_24__type__35149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35150)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__35150,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_35274',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__35275] :
( c_24__type__35274___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__35275)
<=> ! [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__35275,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_35385',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35386] :
( c_24__type__35385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35386)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__35386,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_35496',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35497] :
( c_24__type__35496___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35497)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35497,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35540',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35541] :
( c_24__type__35540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35541)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35541,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_35576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35577] :
( c_24__type__35576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35577)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__35577,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_35620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35621] :
( c_24__type__35620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35621)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__35621,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35643',axiom,
! [Vvar__35644] :
( c_24__type__35643___24t(Vvar__35644)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__35653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__35644,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35653',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35654] :
( c_24__type__35653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35654)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__35654,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_35665',axiom,
! [Vvar__35666] :
( c_24__type__35665___24t(Vvar__35666)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35666,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35698',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35699] :
( c_24__type__35698___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35699)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35699,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_35720',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35721] :
( c_24__type__35720___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35721)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__35721,Vv__CANONICAL__3)) ) ) ).
fof('$_type_35722',axiom,
! [Vvar__35723] :
( c_24__type__35722___24t(Vvar__35723)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35723,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35728',axiom,
! [Vvar__35729] :
( c_24__type__35728___24t(Vvar__35729)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35729,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35767',axiom,
! [Vvar__35768] :
( c_24__type__35767___24t(Vvar__35768)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__35768,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35769',axiom,
! [Vvar__35770] :
( c_24__type__35769___24t(Vvar__35770)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__35770,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35775',axiom,
! [Vvar__35776] :
( c_24__type__35775___24t(Vvar__35776)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__35776,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_35778',axiom,
! [Vvar__35779] :
( c_24__type__35778___24t(Vvar__35779)
<=> ! [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__35779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35781',axiom,
! [Vvar__35782] :
( c_24__type__35781___24t(Vvar__35782)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35786',axiom,
! [Vvar__35787] :
( c_24__type__35786___24t(Vvar__35787)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35795',axiom,
! [Vvar__35796] :
( c_24__type__35795___24t(Vvar__35796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__35796,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35800',axiom,
! [Vvar__35801] :
( c_24__type__35800___24t(Vvar__35801)
<=> ! [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__35801,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35808',axiom,
! [Vvar__35809] :
( c_24__type__35808___24t(Vvar__35809)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__35809,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35820',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35821] :
( c_24__type__35820___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35821)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__35821,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_35834',axiom,
! [Vvar__35835] :
( c_24__type__35834___24t(Vvar__35835)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35835,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35843',axiom,
! [Vvar__35844] :
( c_24__type__35843___24t(Vvar__35844)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1452___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__35844,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35850',axiom,
! [Vvar__35851] :
( c_24__type__35850___24t(Vvar__35851)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35851,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35870',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35871] :
( c_24__type__35870___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35871)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35871,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35875',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35876] :
( c_24__type__35875___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35876)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35876,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35889] :
( c_24__type__35888___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35889)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35889,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35893',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35894] :
( c_24__type__35893___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35894)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35894,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35899',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35900] :
( c_24__type__35899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35900)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__35900,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35948',axiom,
! [Vvar__35949] :
( c_24__type__35948___24t(Vvar__35949)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__35949,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_35981',axiom,
! [Vvar__35982] :
( c_24__type__35981___24t(Vvar__35982)
<=> ! [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__5641___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__35982,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_36017',axiom,
! [Vvar__36018] :
( c_24__type__36017___24t(Vvar__36018)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__36018,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_36041',axiom,
! [Vvar__36042] :
( c_24__type__36041___24t(Vvar__36042)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__12504___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__36042,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_36070',axiom,
! [Vvar__36071] :
( c_24__type__36070___24t(Vvar__36071)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__36071,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_36077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36078] :
( c_24__type__36077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36078)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36078,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36102] :
( c_24__type__36101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36102)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__36102,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36117',axiom,
! [Vvar__36118] :
( c_24__type__36117___24t(Vvar__36118)
<=> ! [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__36118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36133',axiom,
! [Vv__CANONICAL__0,Vvar__36134] :
( c_24__type__36133___24t(Vv__CANONICAL__0,Vvar__36134)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__36134,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36162',axiom,
! [Vvar__36163] :
( c_24__type__36162___24t(Vvar__36163)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__36163,Vv__CANONICAL__0)) ) ) ).
fof('$_type_36187',axiom,
! [Vvar__36188] :
( c_24__type__36187___24t(Vvar__36188)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__36188,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36190',axiom,
! [Vvar__36191] :
( c_24__type__36190___24t(Vvar__36191)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(Vvar__36191,Vv__CANONICAL__0)) ) ) ).
fof('$_type_366',axiom,
! [Vv__CANONICAL__0,Vvar__367] :
( c_24__type__366___24t(Vv__CANONICAL__0,Vvar__367)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__367,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_36726',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__36727] :
( c_24__type__36726___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__36727)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36727,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3685',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3686] :
( c_24__type__3685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3686)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3686,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37',axiom,
! [Vvar__38] :
( c_24__type__37___24t(Vvar__38)
<=> ! [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__38,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37072',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37073] :
( c_24__type__37072___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37073)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__37073,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__372] :
( c_24__type__371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__372)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__372,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_37418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37419] :
( c_24__type__37418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37419)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__37419,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_376',axiom,
! [Vv__CANONICAL__0,Vvar__377] :
( c_24__type__376___24t(Vv__CANONICAL__0,Vvar__377)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__377,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37742] :
( c_24__type__37741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37742)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__37742,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_38087',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__38088] :
( c_24__type__38087___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__38088)
<=> ! [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__38088,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_38433',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38434] :
( c_24__type__38433___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38434)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38434,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_38779',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__38780] :
( c_24__type__38779___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__38780)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__38780,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_3898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3899] :
( c_24__type__3898___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__3899)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3899,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39125',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__39126] :
( c_24__type__39125___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__39126)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__39126,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_39471',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39472] :
( c_24__type__39471___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39472)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__39472,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__396] :
( c_24__type__395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__396)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__396,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_39794',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39795] :
( c_24__type__39794___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39795)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__39795,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_40140',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__40141] :
( c_24__type__40140___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__40141)
<=> ! [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__40141,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_40486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40487] :
( c_24__type__40486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40487)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__40487,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_40809',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__40810] :
( c_24__type__40809___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__40810)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__40810,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_4093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4094] :
( c_24__type__4093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4094)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__4094,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_41132',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__41133] :
( c_24__type__41132___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__41133)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__41133,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_41478',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41479] :
( c_24__type__41478___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__41479)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__41479,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41488',axiom,
! [Vvar__41489] :
( c_24__type__41488___24t(Vvar__41489)
<=> ! [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__41489,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41493',axiom,
! [Vvar__41494] :
( c_24__type__41493___24t(Vvar__41494)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__41494,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41501',axiom,
! [Vvar__41502] :
( c_24__type__41501___24t(Vvar__41502)
<=> ! [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__41502,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_41503',axiom,
! [Vvar__41504] :
( c_24__type__41503___24t(Vvar__41504)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__41504,Vv__CANONICAL__0)) ) ) ).
fof('$_type_41512',axiom,
! [Vvar__41513] :
( c_24__type__41512___24t(Vvar__41513)
<=> ! [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__41513,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41517',axiom,
! [Vvar__41518] :
( c_24__type__41517___24t(Vvar__41518)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__41518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41535',axiom,
! [Vvar__41536] :
( c_24__type__41535___24t(Vvar__41536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5649___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__41536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_41704',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41705] :
( c_24__type__41704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41705)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41705,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41727',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41728] :
( c_24__type__41727___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41728)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41728,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41751] :
( c_24__type__41750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41751)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__41751,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_41773',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41774] :
( c_24__type__41773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41774)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41774,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41792] :
( c_24__type__41791___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41792)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__41792,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_41817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41818] :
( c_24__type__41817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41818)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__41818,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41836] :
( c_24__type__41835___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41836)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__41836,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_42240',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42241] :
( c_24__type__42240___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42241)
<=> ! [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__42241,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_42290',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42291] :
( c_24__type__42290___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42291)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__42291,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_42340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42341] :
( c_24__type__42340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42341)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__42341,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_42382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42383] :
( c_24__type__42382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42383)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__42383,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_42432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42433] :
( c_24__type__42432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__42433)
<=> ! [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__42433,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_42508',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42509] :
( c_24__type__42508___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42509)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__42509,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_42530',axiom,
! [Vvar__42531] :
( c_24__type__42530___24t(Vvar__42531)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5649___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__42531,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_42615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42616] :
( c_24__type__42615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42616)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__42616,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_42650',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42651] :
( c_24__type__42650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42651)
<=> ! [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__42651,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_42690',axiom,
! [Vvar__42691] :
( c_24__type__42690___24t(Vvar__42691)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__42700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__35653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__42691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_42700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42701] :
( c_24__type__42700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42701)
<=> ! [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__42701,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_42740',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42741] :
( c_24__type__42740___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42741)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__42741,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_42745',axiom,
! [Vvar__42746] :
( c_24__type__42745___24t(Vvar__42746)
<=> ! [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__42746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42750',axiom,
! [Vvar__42751] :
( c_24__type__42750___24t(Vvar__42751)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__42751,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_42806',axiom,
! [Vvar__42807] :
( c_24__type__42806___24t(Vvar__42807)
<=> ! [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__42807,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4307] :
( c_24__type__4306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4307)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4307,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_43230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43231] :
( c_24__type__43230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43231)
<=> ! [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__43231,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_43262',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43263] :
( c_24__type__43262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43263)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__43263,Vv__CANONICAL__4)) ) ) ).
fof('$_type_43271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43272] :
( c_24__type__43271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43272)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__43272,Vv__CANONICAL__4)) ) ) ).
fof('$_type_43293',axiom,
! [Vvar__43294] :
( c_24__type__43293___24t(Vvar__43294)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__11245___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__43294,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_433',axiom,
! [Vvar__434] :
( c_24__type__433___24t(Vvar__434)
<=> ! [Vv__CANONICAL__0] :
( cmonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cmonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__43342] :
( c_24__type__43341___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__43342)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43342,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_43345',axiom,
! [Vvar__43346] :
( c_24__type__43345___24t(Vvar__43346)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__43347___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43348___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43346,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43388',axiom,
! [Vvar__43389] :
( c_24__type__43388___24t(Vvar__43389)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__43389,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43394',axiom,
! [Vvar__43395] :
( c_24__type__43394___24t(Vvar__43395)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__43395,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43398',axiom,
! [Vvar__43399] :
( c_24__type__43398___24t(Vvar__43399)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__29246___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__29246___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43399,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43404',axiom,
! [Vvar__43405] :
( c_24__type__43404___24t(Vvar__43405)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__3039___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3039___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43405,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43421',axiom,
! [Vvar__43422] :
( c_24__type__43421___24t(Vvar__43422)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5658___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__43422,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_43425',axiom,
! [Vvar__43426] :
( c_24__type__43425___24t(Vvar__43426)
<=> ! [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__43426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43439',axiom,
! [Vvar__43440] :
( c_24__type__43439___24t(Vvar__43440)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__43440,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_43447',axiom,
! [Vvar__43448] :
( c_24__type__43447___24t(Vvar__43448)
<=> ! [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__43448,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43465',axiom,
! [Vvar__43466] :
( c_24__type__43465___24t(Vvar__43466)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__43466,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43471',axiom,
! [Vvar__43472] :
( c_24__type__43471___24t(Vvar__43472)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__43472,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43478',axiom,
! [Vvar__43479] :
( c_24__type__43478___24t(Vvar__43479)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43479,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43498',axiom,
! [Vvar__43499] :
( c_24__type__43498___24t(Vvar__43499)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__43499,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43519',axiom,
! [Vvar__43520] :
( c_24__type__43519___24t(Vvar__43520)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__43520,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_43521',axiom,
! [Vvar__43522] :
( c_24__type__43521___24t(Vvar__43522)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__43522,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43525',axiom,
! [Vvar__43526] :
( c_24__type__43525___24t(Vvar__43526)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__43527___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__43527___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__43526,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43527',axiom,
! [Vvar__43528] :
( c_24__type__43527___24t(Vvar__43528)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__43528,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43582',axiom,
! [Vv__CANONICAL__0,Vvar__43583] :
( c_24__type__43582___24t(Vv__CANONICAL__0,Vvar__43583)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__58___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__43583,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_43599',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43600] :
( c_24__type__43599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43600)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__43600,Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ).
fof('$_type_43605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43606] :
( c_24__type__43605___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43606)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(Vvar__43606,Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ).
fof('$_type_43698',axiom,
! [Vvar__43699] :
( c_24__type__43698___24t(Vvar__43699)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__20___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__43713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__2),c_24__lam__43719___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)) = c_24__lam__43722___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
=> ( ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__7] :
( c_24__type__43730___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__43736___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__8)
=> happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__5),cCoq_2eProgram_2eBasics_2ecompose___24a5(Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__8)),Vv__CANONICAL__6) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__7),happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__8),Vv__CANONICAL__6)) ) ) ) ) ) )
=> cmonads_2eFunctor___24t(happ(happ(Vvar__43699,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_43713',axiom,
! [Vv__CANONICAL__0,Vvar__43714] :
( c_24__type__43713___24t(Vv__CANONICAL__0,Vvar__43714)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__58___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__43714,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_43730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43731] :
( c_24__type__43730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43731)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__43731,Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ).
fof('$_type_43736',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43737] :
( c_24__type__43736___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43737)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(Vvar__43737,Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ).
fof('$_type_4519',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__4520] :
( c_24__type__4519___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__4520)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__4520,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_4732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4733] :
( c_24__type__4732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__4733)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__4733,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_4945',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__4946] :
( c_24__type__4945___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__4946)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__4946,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_5140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5141] :
( c_24__type__5140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__5141)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__5141,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_5353',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__5354] :
( c_24__type__5353___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__5354)
<=> ! [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__5354,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_54',axiom,
! [Vvar__55] :
( c_24__type__54___24t(Vvar__55)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__55,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5548',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__5549] :
( c_24__type__5548___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__5549)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__5549,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_5641',axiom,
! [Vv__CANONICAL__0,Vvar__5642] :
( c_24__type__5641___24t(Vv__CANONICAL__0,Vvar__5642)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5642,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_5649',axiom,
! [Vv__CANONICAL__0,Vvar__5650] :
( c_24__type__5649___24t(Vv__CANONICAL__0,Vvar__5650)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5650,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5658',axiom,
! [Vv__CANONICAL__0,Vvar__5659] :
( c_24__type__5658___24t(Vv__CANONICAL__0,Vvar__5659)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__5659,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_5668',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5669] :
( c_24__type__5668___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5669)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__5669,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_5682',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5683] :
( c_24__type__5682___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5683)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__5683,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_5689',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5690] :
( c_24__type__5689___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5690)
<=> ! [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__5690,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_5693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5694] :
( c_24__type__5693___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5694)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__5694,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_58',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__59] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__59)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__59,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_5809',axiom,
! [Vvar__5810] :
( c_24__type__5809___24t(Vvar__5810)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5641___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(happ(happ(happ(Vvar__5810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_594',axiom,
! [Vv__CANONICAL__0,Vvar__595] :
( c_24__type__594___24t(Vv__CANONICAL__0,Vvar__595)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__595,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_599',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__600] :
( c_24__type__599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__600)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__600,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_604',axiom,
! [Vv__CANONICAL__0,Vvar__605] :
( c_24__type__604___24t(Vv__CANONICAL__0,Vvar__605)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__605,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_61',axiom,
! [Vvar__62] :
( c_24__type__61___24t(Vvar__62)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__62,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__624] :
( c_24__type__623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__624)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__624,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_672',axiom,
! [Vvar__673] :
( c_24__type__672___24t(Vvar__673)
<=> ! [Vv__CANONICAL__0] :
( cmonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cmonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cmonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__673,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_69',axiom,
! [Vvar__70] :
( c_24__type__69___24t(Vvar__70)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__70,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7350',axiom,
! [Vvar__7351] :
( c_24__type__7350___24t(Vvar__7351)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__7351,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__75,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7402',axiom,
! [Vvar__7403] :
( c_24__type__7402___24t(Vvar__7403)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__7403,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7777',axiom,
! [Vvar__7778] :
( c_24__type__7777___24t(Vvar__7778)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__7778,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7794',axiom,
! [Vvar__7795] :
( c_24__type__7794___24t(Vvar__7795)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__7795,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7816',axiom,
! [Vvar__7817] :
( c_24__type__7816___24t(Vvar__7817)
<=> ! [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__7817,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7818',axiom,
! [Vvar__7819] :
( c_24__type__7818___24t(Vvar__7819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__7819,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7882',axiom,
! [Vvar__7883] :
( c_24__type__7882___24t(Vvar__7883)
<=> ! [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__7883,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7907',axiom,
! [Vvar__7908] :
( c_24__type__7907___24t(Vvar__7908)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__7908,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7980',axiom,
! [Vvar__7981] :
( c_24__type__7980___24t(Vvar__7981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1449___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)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__5)
=> cType___24t(happ(happ(happ(happ(happ(happ(Vvar__7981,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_8',axiom,
! [Vvar__9] :
( c_24__type__8___24t(Vvar__9)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__9,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8059',axiom,
! [Vvar__8060] :
( c_24__type__8059___24t(Vvar__8060)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__8060,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_8255',axiom,
! [Vvar__8256] :
( c_24__type__8255___24t(Vvar__8256)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__8256,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8297',axiom,
! [Vv__CANONICAL__0,Vvar__8298] :
( c_24__type__8297___24t(Vv__CANONICAL__0,Vvar__8298)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__8298,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_8323',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__8324] :
( c_24__type__8323___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__8324)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8324,Vv__CANONICAL__6)) ) ) ).
fof('$_type_8351',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__8352] :
( c_24__type__8351___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__8352)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8352,Vv__CANONICAL__6)) ) ) ).
fof('$_type_836',axiom,
! [Vv__CANONICAL__0,Vvar__837] :
( c_24__type__836___24t(Vv__CANONICAL__0,Vvar__837)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__837,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__842] :
( c_24__type__841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__842)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__842,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_846',axiom,
! [Vv__CANONICAL__0,Vvar__847] :
( c_24__type__846___24t(Vv__CANONICAL__0,Vvar__847)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__847,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8478',axiom,
! [Vvar__8479] :
( c_24__type__8478___24t(Vvar__8479)
<=> ! [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__8479,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_8481',axiom,
! [Vvar__8482] :
( c_24__type__8481___24t(Vvar__8482)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8482,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8488',axiom,
! [Vvar__8489] :
( c_24__type__8488___24t(Vvar__8489)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8492___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__8489,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8492',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8493] :
( c_24__type__8492___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8493)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__8493) ) ) ).
fof('$_type_8505',axiom,
! [Vv__CANONICAL__0,Vvar__8506] :
( c_24__type__8505___24t(Vv__CANONICAL__0,Vvar__8506)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__8507___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__8508___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__8506,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__866] :
( c_24__type__865___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__866)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__866,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_87',axiom,
! [Vvar__88] :
( c_24__type__87___24t(Vvar__88)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__58___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__88,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8855',axiom,
! [Vvar__8856] :
( c_24__type__8855___24t(Vvar__8856)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8856,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8860',axiom,
! [Vvar__8861] :
( c_24__type__8860___24t(Vvar__8861)
<=> ! [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__8861,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8863',axiom,
! [Vvar__8864] :
( c_24__type__8863___24t(Vvar__8864)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8864,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_901',axiom,
! [Vvar__902] :
( c_24__type__901___24t(Vvar__902)
<=> ! [Vv__CANONICAL__0] :
( cmonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__902,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9144] :
( c_24__type__9143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9144)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__9144,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_9152',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9153] :
( c_24__type__9152___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9153)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__9153,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9174',axiom,
! [Vvar__9175] :
( c_24__type__9174___24t(Vvar__9175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__9175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_9185',axiom,
! [Vvar__9186] :
( c_24__type__9185___24t(Vvar__9186)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__9186,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9205',axiom,
! [Vvar__9206] :
( c_24__type__9205___24t(Vvar__9206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__9206,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_971',axiom,
! [Vv__CANONICAL__0,Vvar__972] :
( c_24__type__971___24t(Vv__CANONICAL__0,Vvar__972)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__972,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_976',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__977] :
( c_24__type__976___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__977)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__977,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_981',axiom,
! [Vv__CANONICAL__0,Vvar__982] :
( c_24__type__981___24t(Vv__CANONICAL__0,Vvar__982)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__982,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__1345___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__29404___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__1345___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__43404___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__35728___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__2981___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__31926___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__3039___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__29610___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__29607___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__43465___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__29610___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_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__29610___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__7402___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__43471___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
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.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('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__35769___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompSpecT',axiom,
c_24__type__7980___24t(cCoq_2eInit_2eDatatypes_2eCompSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__7907___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__7818___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__8___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__7816___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__2981___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__7882___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__37___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__1323___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__35767___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__20___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__2983___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__1337___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__20___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__2981___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__1311___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__1295___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__1335___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__1295___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__2981___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__36117___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__3049___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__3039___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__3039___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__2708___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__3049___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__1345___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__1345___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__14804___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.exist2',axiom,
c_24__type__14881___24t(cCoq_2eInit_2eSpecif_2eexist2) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__2751___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.existT2',axiom,
c_24__type__14959___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__42745___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__42750___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__27613___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__14983___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__15163___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__15186___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__27618___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__1366___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__14847___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__2733___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__14925___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__27590___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__35665___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__2761___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__3025___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__36041___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__36070___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__11093___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__54___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__36017___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_bool',axiom,
c_24__type__14791___24t(cCoq_2eLists_2eSetoidList_2ecompat__bool) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__42690___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__35643___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__31968___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__35843___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__35834___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
c_24__type__32030___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__8488___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_',axiom,
c_24__type__35834___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__8478___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
c_24__type__8481___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__) ).
fof('$_typeof_Coq.Logic.FinFun.Bijective',axiom,
c_24__type__31558___24t(cCoq_2eLogic_2eFinFun_2eBijective) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__31558___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__31558___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.Logic.FinFun.bInjective',axiom,
c_24__type__2703___24t(cCoq_2eLogic_2eFinFun_2ebInjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__43394___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__7350___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__43398___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__7350___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__7350___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__29227___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__29236___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__29246___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__29246___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sqrt',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__2685___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__29218___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__29236___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__29268___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__1285___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__2698___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__2698___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__7777___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__7777___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__29467___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__29467___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__43447___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__29449___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__29439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__43425___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__43421___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__43439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__29439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__29439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__29439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__29464___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__29464___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__7777___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__29439___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__7777___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__29457___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__33877___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__11570___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__11602___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('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__11590___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__11594___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__11594___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__11570___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__11594___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__11594___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__11590___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__11590___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__11570___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__11590___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__36162___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__11669___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__36190___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__14780___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__61___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__61___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__61___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__61___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_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__27630___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__11392___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedType.EQ',axiom,
c_24__type__11526___24t(cCoq_2eStructures_2eOrderedType_2eEQ) ).
fof('$_typeof_Coq.Structures.OrderedType.GT',axiom,
c_24__type__11557___24t(cCoq_2eStructures_2eOrderedType_2eGT) ).
fof('$_typeof_Coq.Structures.OrderedType.LT',axiom,
c_24__type__11495___24t(cCoq_2eStructures_2eOrderedType_2eLT) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__7350___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__7350___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__1345___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__1345___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.eq',axiom,
c_24__type__29467___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__43345___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__29467___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__29467___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__43478___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__43478___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__2767___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__2767___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.F1',axiom,
c_24__type__10704___24t(cCoq_2eVectors_2eFin_2eF1) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__7794___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__27775___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__27767___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__27750___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Bezout',axiom,
c_24__type__43519___24t(cCoq_2eZArith_2eBinInt_2eZ_2eBezout) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__43521___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__43525___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__31008___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__28786___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__28786___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__31035___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__31032___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__2840___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__2844___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__43498___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__28786___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__2767___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__11669___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__28978___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.Env.jump',axiom,
c_24__type__8059___24t(cCoq_2emicromega_2eEnv_2ejump) ).
fof('$_typeof_Coq.micromega.Env.nth',axiom,
c_24__type__35775___24t(cCoq_2emicromega_2eEnv_2enth) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__35781___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__35786___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__35778___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__35786___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__35786___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__35808___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__35795___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__35800___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__8255___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__8255___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__36187___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__11888___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__42806___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__43388___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__8855___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__35850___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__8863___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__8860___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__10526___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__9205___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__9185___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__9174___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__9185___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__29218___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__35948___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__11052___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__35981___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__2981___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__41503___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__41503___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__13256___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__13261___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__13253___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__13454___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__13261___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__41512___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__41517___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__13261___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__41501___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__41488___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__13004___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__41493___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Computational',axiom,
c_24__type__5809___24t(cCoq_2esetoid__ring_2eRing__theory_2eComputational) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__74___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__74___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__42530___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__7816___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__29218___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__41535___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__14628___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_M',axiom,
cmonads_2eMonad___24t(cM) ).
fof('$_typeof_QuicksortComplexity.list_utils.count',axiom,
c_24__type__43293___24t(cQuicksortComplexity_2elist__utils_2ecount) ).
fof('$_typeof_QuicksortComplexity.list_utils.repeat',axiom,
c_24__type__69___24t(cQuicksortComplexity_2elist__utils_2erepeat) ).
fof('$_typeof_QuicksortComplexity.util.ext_eq',axiom,
c_24__type__87___24t(cQuicksortComplexity_2eutil_2eext__eq) ).
fof('$_typeof_QuicksortComplexity.util.id',axiom,
c_24__type__74___24t(cQuicksortComplexity_2eutil_2eid) ).
fof('$_typeof_f',axiom,
c_24__type__1___24t(cf) ).
fof('$_typeof_g',axiom,
c_24__type__1___24t(cg) ).
fof('$_typeof_m',axiom,
cmonads_2emon___24t(cM,cA,cm) ).
fof('$_typeof_monads.Build_Functor',axiom,
c_24__type__43698___24t(cmonads_2eBuild__Functor) ).
fof('$_typeof_monads.Functor',axiom,
cType___24t(cmonads_2eFunctor) ).
fof('$_typeof_monads.Monad',axiom,
cType___24t(cmonads_2eMonad) ).
fof('$_typeof_monads.bind',axiom,
c_24__type__672___24t(cmonads_2ebind) ).
fof('$_typeof_monads.extMonad',axiom,
c_24__type__177___24t(cmonads_2eextMonad) ).
fof('$_typeof_monads.mon',axiom,
c_24__type__901___24t(cmonads_2emon) ).
fof('$_typeof_monads.ret',axiom,
c_24__type__433___24t(cmonads_2eret) ).
fof('$_typeof_n',axiom,
cmonads_2emon___24t(cM,cA,cn) ).
fof('Coq.Arith.Between.bet_eq',axiom,
! [V0__P] :
( c_24__type__10___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( V2__l = V1__k
=> cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V2__l) ) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_eq',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_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.EqNat.eq_eq_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.EqNat.eq_nat_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',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_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.nat_total_order',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_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
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_neq_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(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_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)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
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_neq_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(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_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.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2708,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__8,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2eadd) ).
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.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2egcd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2egcd___24a2(V1__m,V0__n) ) ) ).
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_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_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.le_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)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eInit_2ePeano_2ele___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
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__1345,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__10,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_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_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_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)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_r',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1345,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__10,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_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_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_cancel_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( V2__p != cCoq_2eInit_2eDatatypes_2eO
=> ( cCoq_2eInit_2eNat_2emul___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
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.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2708,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__8,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2emul) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
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.andb_true_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.eq_iff_eq_true',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = V1__b2
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_false_abs',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
=> p(c_24False) ) ) ) ).
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.not_false_is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2efalse
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.not_true_is_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2etrue
=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.orb_true_intro',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 )
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Bool.Bool.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Init.Datatypes.comparison_eq_stable',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ~ ( V0__c != V1__c_27 )
=> V0__c = V1__c_27 ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2986___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__10___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_equal2_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__36133___24t(V0__B,V1__f)
=> ! [V2__x1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x1)
=> ! [V3__y1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y1)
=> ! [V4__x2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x2)
=> ! [V5__y2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y2)
=> ( V2__x1 = V3__y1
=> ( V4__x2 = V5__y2
=> happ(happ(V1__f,V2__x1),V4__x2) = happ(happ(V1__f,V3__y1),V5__y2) ) ) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__2713___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_S',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(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
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.not_eq_S',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_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1369___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__58___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
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.Eqdep.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__8492___24t(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('Coq.Logic.Eqdep.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.UIP_refl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__1452___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [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('Coq.Logic.Eqdep.EqdepTheory.eq_rec_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.UIP_shift_on',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__X,V1__x)
=> ( V1__x = V1__x
=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a1(c_24__prop__8494___24a2(V0__X,V1__x)) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__1452___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_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__2824___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
=> V2__y = V1__x ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__8492___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__P] :
( c_24__type__8492___24t(V0__A,V1__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ( V1__x = V1__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_type',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__8505___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__8492___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.UIP_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__8505___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_dep_eq_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__8505___24t(V0__A,V1___24Anonymous)
=> ! [V2__P] :
( c_24__type__1452___24t(V0__A,V2__P)
=> ! [V3__p] :
( t(V3__p,V0__A)
=> ! [V4__x] :
( t(V4__x,happ(V2__P,V3__p))
=> ! [V5__y] :
( t(V5__y,happ(V2__P,V3__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__A,V2__P,V3__p,V4__x,V3__p,V5__y)
=> V4__x = V5__y ) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V1__x = V3__y
=> ( V1__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__58___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1452___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__31570___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__31575___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__35915___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1452___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__35899___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__35907___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1452___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__1452___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__type__35870___24a2(V0__A,V1__B) = c_24__type__35875___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionalityP',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1369___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__1369___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__prop__35880___24a2(V0__A,V1__B) = c_24__prop__35881___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionalityS',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1452___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__1452___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__type__35888___24a2(V0__A,V1__B) = c_24__type__35893___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__58___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__1452___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__2995___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__3000___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.JMeq.JMeq_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(V0__A,V1__x,V0__A,V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Logic.JMeq.JMeq_eq_dep',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__1452___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__q] :
( t(V3__q,V0__U)
=> ! [V4__x] :
( t(V4__x,happ(V1__P,V2__p))
=> ! [V5__y] :
( t(V5__y,happ(V1__P,V3__q))
=> ( V2__p = V3__q
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(happ(V1__P,V2__p),V4__x,happ(V1__P,V3__q),V5__y)
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V4__x,V3__q,V5__y) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.PI.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__8492___24t(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('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP_refl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__1452___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [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('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_rec_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__1452___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__2824___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
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_neq_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(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_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)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
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_neq_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(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
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.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.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_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_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.le_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)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7350,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__29279,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_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_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_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)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eN0
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__35722___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__35698___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__5682___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.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.Pnat.Pos2Nat.inj',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)
=> V0__p = V1__q ) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.Reals.DiscrR.IZR_eq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 = V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Rdichotomy',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_eq_compat',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)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( V0__r1 = V1__r2
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V3__r4)
=> ( V3__r4 = V2__r3
=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_eq_compat',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)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( V0__r1 = V1__r2
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V3__r4)
=> ( V3__r4 = V2__r3
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r) ) ).
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.RIneq.Rmult_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r) ) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r) ) ) ) ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.f_equal_R',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__11568___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.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.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_sym',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',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
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
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.eq_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)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(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_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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> 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)
=> ( ~ 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.eq_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)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ 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_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono',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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_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_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_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_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V3__q)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ).
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__43515___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_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_l',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_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V1__m,V0__n) ) ) ).
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))
| 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))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__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_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2767,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__2961,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,
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,
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_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( 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_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepr',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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_add_distr_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
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_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
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_nonneg_nonneg',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(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_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)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
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_shuffle3',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(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.BinInt.Z.opp_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj_wd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_null',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z_eq_mult',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zeq_minus',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zplus_eq_compat',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)
=> ( V0__n = V1__m
=> ( V2__p = V3__q
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zpos_eq',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( V0__p = V1__q
=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V1__q) ) ) ) ).
fof('Coq.ZArith.BinInt.Zsucc_eq_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.Zcompare.Zcompare_eq_case',axiom,
! [V0__c1] :
( cProp___24t(V0__c1)
=> ! [V1__c2] :
( cProp___24t(V1__c2)
=> ! [V2__c3] :
( cProp___24t(V2__c3)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( p(V0__c1)
=> ( V3__n = V4__m
=> c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278___24a5(V0__c1,V1__c2,V2__c3,V3__n,V4__m) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.micromega.EnvRing.Mphi_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__5649___24t(V0__R,V2__rmul)
=> ! [V3__M] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V3__M)
=> ! [V4__e1] :
( c_24__type__8297___24t(V0__R,V4__e1)
=> ! [V5__e2] :
( c_24__type__8297___24t(V0__R,V5__e2)
=> ( ! [V6__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__x)
=> happ(V4__e1,V6__x) = happ(V5__e2,V6__x) )
=> cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V4__e1,V3__M) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V5__e2,V3__M) ) ) ) ) ) ) ) ).
fof('Coq.micromega.EnvRing.env_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5649___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5649___24t(V0__R,V2__rmul)
=> ! [V3__C] :
( cType___24t(V3__C)
=> ! [V4__phi] :
( c_24__type__5693___24t(V0__R,V3__C,V4__phi)
=> ! [V5__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,V5__p)
=> ! [V6__e1] :
( c_24__type__35820___24t(V0__R,V3__C,V6__e1)
=> ! [V7__e2] :
( c_24__type__35820___24t(V0__R,V3__C,V7__e2)
=> ( ! [V8__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V8__x)
=> happ(V6__e1,V8__x) = happ(V7__e2,V8__x) )
=> cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__e1,V5__p) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V7__e2,V5__p) ) ) ) ) ) ) ) ) ) ).
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.F.In_eq_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__y)
=> ( V1__x = V2__y
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s) ) ) ) ) ) ).
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__43384___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.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = 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)) ) ) ) ) ).
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.OMEGA5',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 = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',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))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
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.omega.PreOmega.Z.div_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.mod_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.quot_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.rem_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y) = V0__x ) ) ) ).
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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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_1_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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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),V2__rI)),V10__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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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.ARopp_zero',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,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)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___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__5649___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5649___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__5658___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5649___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5649___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,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) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_add',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V18__x),V19__y))),happ(happ(V3__radd,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_eq',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_mul',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V18__x),V19__y))),happ(happ(V4__rmul,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_opp',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V18__x))),happ(V6__ropp,happ(V16__phi,V18__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_sub',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__5649___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5649___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5649___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__5658___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1449___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5668___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5668___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5668___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5682___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5689___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__5693___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V18__x),V19__y))),happ(happ(V5__rsub,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.map_ext_eq_mor',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2664___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__58___24a2(V0__A,V1__B),c_24__type__2672___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B))),cCoq_2eLists_2eList_2emap___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.util.compose_ext_eq_morph',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> ! [V3__x] :
( c_24__type__58___24t(V1__Y,V2__Z,V3__x)
=> ! [V4__y] :
( c_24__type__58___24t(V1__Y,V2__Z,V4__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V1__Y,V2__Z,V3__x,V4__y)
=> ! [V6__x] :
( c_24__type__137___24t(V0__X,V1__Y,V2__Z,V6__x)
=> ! [V7__y] :
( c_24__type__137___24t(V0__X,V1__Y,V2__Z,V7__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__X,V1__Y,V6__x,V7__y)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__X,V2__Z,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,V1__Y,V2__Z,V3__x,V6__x),cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,V1__Y,V2__Z,V4__y,V7__y)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.compose_ext_eq_morph_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__130___24a3(V0__X,V1__Y,V2__Z),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__58___24a2(V1__Y,V2__Z),c_24__type__151___24a3(V0__X,V1__Y,V2__Z),cQuicksortComplexity_2eutil_2eext__eq___24a2(V1__Y,V2__Z),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__58___24a2(V0__X,V1__Y),c_24__type__58___24a2(V0__X,V2__Z),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V2__Z))),cCoq_2eProgram_2eBasics_2ecompose___24a3(V0__X,V1__Y,V2__Z)) ) ) ) ).
fof('QuicksortComplexity.util.compose_lunit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V1__B,cQuicksortComplexity_2eutil_2eid___24a1(V1__B),V2__f),V2__f) ) ) ) ).
fof('QuicksortComplexity.util.compose_runit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V0__A,V1__B,V2__f,cQuicksortComplexity_2eutil_2eid___24a1(V0__A)),V2__f) ) ) ) ).
fof('QuicksortComplexity.util.eq_trans',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__a] :
( t(V1__a,V0__X)
=> ! [V2__b] :
( t(V2__b,V0__X)
=> ! [V3__c] :
( t(V3__c,V0__X)
=> ( V1__a = V2__b
=> ( V2__b = V3__c
=> V1__a = V3__c ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.ext_eq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__58___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Reflexive',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(c_24__type__58___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Symmetric',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(c_24__type__58___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Transitive',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(c_24__type__58___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_relation',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(c_24__type__58___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rw',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__58___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__58___24t(V0__A,V1__B,V3__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__f,V3__g)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.ext_eq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(c_24__type__58___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(c_24__type__58___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof(e,axiom,
cmonads_2eextMonad___24a1(cM) ).
fof('monads.mon_assoc',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__b] :
( cType___24t(V2__b)
=> ! [V3__c] :
( cType___24t(V3__c)
=> ! [V4__n] :
( cmonads_2emon___24t(V0__m,V1__a,V4__n)
=> ! [V5__f] :
( c_24__type__172___24t(V0__m,V1__a,V2__b,V5__f)
=> ! [V6__g] :
( c_24__type__186___24t(V0__m,V1__a,V2__b,V3__c,V6__g)
=> cmonads_2ebind___24a5(V0__m,V2__b,V3__c,cmonads_2ebind___24a5(V0__m,V1__a,V2__b,V4__n,V5__f),V6__g) = cmonads_2ebind___24a5(V0__m,V1__a,V3__c,V4__n,c_24__lam__203___24a6(V0__m,V1__a,V2__b,V3__c,V5__f,V6__g)) ) ) ) ) ) ) ) ).
fof('monads.mon_lunit',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__b] :
( cType___24t(V2__b)
=> ! [V3__x] :
( t(V3__x,V1__a)
=> ! [V4__f] :
( c_24__type__172___24t(V0__m,V1__a,V2__b,V4__f)
=> cmonads_2ebind___24a5(V0__m,V1__a,V2__b,cmonads_2eret___24a3(V0__m,V1__a,V3__x),V4__f) = happ(V4__f,V3__x) ) ) ) ) ) ).
fof('monads.mon_runit',axiom,
! [V0__m] :
( cmonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__f] :
( cmonads_2emon___24t(V0__m,V1__a,V2__f)
=> cmonads_2ebind___24a5(V0__m,V1__a,V1__a,V2__f,cmonads_2eret___24a2(V0__m,V1__a)) = V2__f ) ) ) ).
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_$_fix_2591_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__2591__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__2591__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_$_prop_43377_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__43377,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__43377___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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_monads.ret_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cmonads_2eret,V_24X1),V_24X2) = cmonads_2eret___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_420_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__420,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__420___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_$_let_var_6_p_14614_14617_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14614__14617,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14614__14617___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_648_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__648,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__648___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_$_lam_43588_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43588,V_24X1),V_24X2) = c_24__lam__43588___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43381_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__43381,V_24X1),V_24X2),V_24X3) = c_24__prop__43381___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.JMeq.JMeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eJMeq_2eJMeq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eJMeq_2eJMeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_monads.mon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cmonads_2emon,V_24X1),V_24X2) = cmonads_2emon___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('$adef_$_lam_43719_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43719,V_24X1),V_24X2) = c_24__lam__43719___24a2(V_24X1,V_24X2) ).
fof('$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_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.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_36127_$a1',axiom,
! [V_24X1] : happ(c_24__lam__36127,V_24X1) = c_24__lam__36127___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sig_$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('$adef_$_let_var_6_p_14616_14618_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__14616__14618,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__14616__14618___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.ZArith.BinIntDef.Z.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V_24X1) ).
fof('$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_$_prop_8507_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__8507,V_24X1),V_24X2),V_24X3) = c_24__prop__8507___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Specif.sumbool_$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('$adef_Coq.Init.Logic.eq_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rec___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('$adef_QuicksortComplexity.util.ext_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eutil_2eext__eq,V_24X1),V_24X2) = cQuicksortComplexity_2eutil_2eext__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$11662_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2411662___24a1(V_24X1) ).
fof('$adef_$_lam_43722_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43722,V_24X1),V_24X2),V_24X3) = c_24__lam__43722___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ediv,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_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.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.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_35907_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__35907,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__35907___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP__$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.FinFun.Surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eSurjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_monads.bind_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cmonads_2ebind,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cmonads_2ebind___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___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('$adef_Coq.Init.Nat.eqb_$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('$adef_$_lam_890_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__890,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__890___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_QuicksortComplexity.util.id_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eutil_2eid,V_24X1) = cQuicksortComplexity_2eutil_2eid___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.RewriteRelation_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eRewriteRelation,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(V_24X1,V_24X2) ) ).
fof('$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.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.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_$_lam_11827_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11827,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11827___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_prop_43348_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43348,V_24X1),V_24X2) = c_24__prop__43348___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Datatypes.CompareSpecT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.micromega.Env.jump_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Logic.EqdepFacts.UIP_refl_on__$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a1(V_24X1) ) ).
fof('$adef_$_lam_11827_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11827,V_24X1),V_24X2) = c_24__lam__11827___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11835_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11835,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11835___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.list_utils.count_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2ecount,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43382_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__43382,V_24X1),V_24X2),V_24X3) = c_24__prop__43382___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Logic.FinFun.Bijective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eBijective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eBijective___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('$adef_Coq.Init.Nat.add_$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('$adef_$_prop_8494_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__8494,V_24X1),V_24X2) = c_24__prop__8494___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_43591_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43591,V_24X1),V_24X2),V_24X3) = c_24__lam__43591___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_890_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__890,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__890___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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_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.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.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_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_$_lam_11851_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11851,V_24X1),V_24X2) = c_24__lam__11851___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_monads.extMonad_$a1',axiom,
! [V_24X1] :
( p(happ(cmonads_2eextMonad,V_24X1))
<=> cmonads_2eextMonad___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.util.ext_eq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2eext__eq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.modulo_$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('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$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('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_lam_35907_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__35907,V_24X1),V_24X2),V_24X3) = c_24__lam__35907___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_43347_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43347,V_24X1),V_24X2) = c_24__prop__43347___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_35915_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__35915,V_24X1),V_24X2),V_24X3) = c_24__lam__35915___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_monads.Build_Monad_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cmonads_2eBuild__Monad,V_24X1),V_24X2),V_24X3) = cmonads_2eBuild__Monad___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_monads.ret_$a1',axiom,
! [V_24X1] : happ(cmonads_2eret,V_24X1) = cmonads_2eret___24a1(V_24X1) ).
fof('$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.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_36128_$a1',axiom,
! [V_24X1] : happ(c_24__lam__36128,V_24X1) = c_24__lam__36128___24a1(V_24X1) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_Coq.NArith.BinNatDef.N.pred_$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('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$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('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_$_lam_203_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__203,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__203___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.CompSpecT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompSpecT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_monads.Build_Functor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cmonads_2eBuild__Functor,V_24X1),V_24X2) = cmonads_2eBuild__Functor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Program.Basics.compose_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3) = cCoq_2eProgram_2eBasics_2ecompose___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$11657_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2411657___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('$adef_QuicksortComplexity.list_utils.merges_spec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges__spec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_prop_8508_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__8508,V_24X1),V_24X2),V_24X3) = c_24__prop__8508___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Logic.FinFun.Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eInjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eInjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$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.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.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_420_$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(c_24__lam__420,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__420___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_QuicksortComplexity.util.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eutil_2eid,V_24X1),V_24X2) = cQuicksortComplexity_2eutil_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.comparison$43278_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443278___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_fix_2494_v_CANONICAL_2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__2494__v__CANONICAL__2,V_24X1),V_24X2),V_24X3) = c_24__fix__2494__v__CANONICAL__2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_43515_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43515,V_24X1),V_24X2) = c_24__prop__43515___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.elemsR_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_monads.bind_$a1',axiom,
! [V_24X1] : happ(cmonads_2ebind,V_24X1) = cmonads_2ebind___24a1(V_24X1) ).
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('$adef_$_prop_43380_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__43380,V_24X1),V_24X2),V_24X3) = c_24__prop__43380___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.shiftl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1) = cCoq_2eInit_2eNat_2eshiftl___24a1(V_24X1) ).
fof('$adef_$_prop_43379_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__43379,V_24X1),V_24X2),V_24X3) = c_24__prop__43379___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_43719_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43719,V_24X1),V_24X2),V_24X3) = c_24__lam__43719___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11851_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11851,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11851___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_648_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__648,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__648___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.Env.nth_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2enth,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2enth___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_11835_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11835,V_24X1),V_24X2) = c_24__lam__11835___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$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('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.Mphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2eMphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.Between.between_$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('$adef_monads.mon_$a1',axiom,
! [V_24X1] : happ(cmonads_2emon,V_24X1) = cmonads_2emon___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inright_$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('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_refl_on__$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_35880_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35880,V_24X1),V_24X2) = c_24__prop__35880___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.repeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2erepeat,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2erepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.nat$11640_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2411640,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2411640___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$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('$adef_$_lam_1025_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1025,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__1025___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_prop_43384_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43384,V_24X1),V_24X2) = c_24__prop__43384___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('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$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('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$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('$adef_Coq.Program.Basics.compose_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_29409_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__29409__1__add__carry,V_24X1),V_24X2) = c_24__fix__29409__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$42495_$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_2442495,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_2442495___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
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('$adef_$_lam_43722_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43722,V_24X1),V_24X2) = c_24__lam__43722___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$2348_$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(c_24__case__Coq_2eInit_2eDatatypes_2elist_242348,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2elist_242348___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_Coq.ZArith.BinInt.Z.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$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('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___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('$adef_Coq.micromega.Tauto.A_$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('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Specif.sumor_$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('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$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('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$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('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
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('$adef_$_prop_43383_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43383,V_24X1),V_24X2) = c_24__prop__43383___24a2(V_24X1,V_24X2) ).
fof('$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.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$2455_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_242455,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_242455___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Nat.sqrt_iter_$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('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_monads.ret_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cmonads_2eret,V_24X1),V_24X2),V_24X3) = cmonads_2eret___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_$_prop_43378_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__43378,V_24X1),V_24X2),V_24X3) = c_24__prop__43378___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35881_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35881,V_24X1),V_24X2) = c_24__prop__35881___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.map_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2) = cCoq_2eLists_2eList_2emap___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$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('$adef_$_lam_35915_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__35915,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__35915___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_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_$_lam_11843_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11843,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11843___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_$_lam_203_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__203,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__203___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_lam_43588_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__43588,V_24X1),V_24X2),V_24X3) = c_24__lam__43588___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Logic.FinFun.bInjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebInjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_11843_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11843,V_24X1),V_24X2) = c_24__lam__11843___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_lam_43591_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__43591,V_24X1),V_24X2) = c_24__lam__43591___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Lists.SetoidList.compat_bool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__bool,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.ZArith.BinIntDef.Z.pow_$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('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$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('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___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('$adef_$_lam_1025_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__1025,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__1025___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_type_43713',axiom,
! [V_24X1,V_24Y] :
( c_24__type__43713___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__43713___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.Env.Env',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___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_$_type_35893',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35893___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35893___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31035',axiom,
! [V_24Y] :
( c_24__type__31035___24t(V_24Y)
<=> t(V_24Y,c_24__type__31035) ) ).
fof('$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_37072',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__37072___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__37072___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_15186',axiom,
! [V_24Y] :
( c_24__type__15186___24t(V_24Y)
<=> t(V_24Y,c_24__type__15186) ) ).
fof('$tdef_$_type_32596',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__32596___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__32596___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35981',axiom,
! [V_24Y] :
( c_24__type__35981___24t(V_24Y)
<=> t(V_24Y,c_24__type__35981) ) ).
fof('$tdef_$_type_4519',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__4519___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__4519___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_31693',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31693___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31693___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_14722',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__14722___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__14722___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37418',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__37418___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__37418___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_31570',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31570___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31570___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3039',axiom,
! [V_24Y] :
( c_24__type__3039___24t(V_24Y)
<=> t(V_24Y,c_24__type__3039) ) ).
fof('$tdef_$_type_42382',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__42382___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__42382___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_594',axiom,
! [V_24X1,V_24Y] :
( c_24__type__594___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__594___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43527',axiom,
! [V_24Y] :
( c_24__type__43527___24t(V_24Y)
<=> t(V_24Y,c_24__type__43527) ) ).
fof('$tdef_$_type_8351',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__8351___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__8351___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_36726',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__36726___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__36726___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_672',axiom,
! [V_24Y] :
( c_24__type__672___24t(V_24Y)
<=> t(V_24Y,c_24__type__672) ) ).
fof('$tdef_$_type_43394',axiom,
! [V_24Y] :
( c_24__type__43394___24t(V_24Y)
<=> t(V_24Y,c_24__type__43394) ) ).
fof('$tdef_$_type_29218',axiom,
! [V_24Y] :
( c_24__type__29218___24t(V_24Y)
<=> t(V_24Y,c_24__type__29218) ) ).
fof('$tdef_$_type_43605',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43605___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43605___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__841___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__841___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_69',axiom,
! [V_24Y] :
( c_24__type__69___24t(V_24Y)
<=> t(V_24Y,c_24__type__69) ) ).
fof('$tdef_$_type_186',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_29227',axiom,
! [V_24Y] :
( c_24__type__29227___24t(V_24Y)
<=> t(V_24Y,c_24__type__29227) ) ).
fof('$tdef_$_type_35728',axiom,
! [V_24Y] :
( c_24__type__35728___24t(V_24Y)
<=> t(V_24Y,c_24__type__35728) ) ).
fof('$tdef_$_type_2983',axiom,
! [V_24Y] :
( c_24__type__2983___24t(V_24Y)
<=> t(V_24Y,c_24__type__2983) ) ).
fof('$tdef_$_type_15157',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15157___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15157___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14628',axiom,
! [V_24Y] :
( c_24__type__14628___24t(V_24Y)
<=> t(V_24Y,c_24__type__14628) ) ).
fof('$tdef_$_type_42650',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42650___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42650___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35834',axiom,
! [V_24Y] :
( c_24__type__35834___24t(V_24Y)
<=> t(V_24Y,c_24__type__35834) ) ).
fof('$tdef_$_type_14977',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14977___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14977___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27618',axiom,
! [V_24Y] :
( c_24__type__27618___24t(V_24Y)
<=> t(V_24Y,c_24__type__27618) ) ).
fof('$tdef_$_type_35274',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__35274___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__35274___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_34899',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__34899___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__34899___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_2840',axiom,
! [V_24Y] :
( c_24__type__2840___24t(V_24Y)
<=> t(V_24Y,c_24__type__2840) ) ).
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_$_type_13256',axiom,
! [V_24Y] :
( c_24__type__13256___24t(V_24Y)
<=> t(V_24Y,c_24__type__13256) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_8860',axiom,
! [V_24Y] :
( c_24__type__8860___24t(V_24Y)
<=> t(V_24Y,c_24__type__8860) ) ).
fof('$tdef_$_type_9152',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9152___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9152___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_43262',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43262___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43262___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_1452',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1452___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1452___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35778',axiom,
! [V_24Y] :
( c_24__type__35778___24t(V_24Y)
<=> t(V_24Y,c_24__type__35778) ) ).
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_28786',axiom,
! [V_24Y] :
( c_24__type__28786___24t(V_24Y)
<=> t(V_24Y,c_24__type__28786) ) ).
fof('$tdef_$_type_11495',axiom,
! [V_24Y] :
( c_24__type__11495___24t(V_24Y)
<=> t(V_24Y,c_24__type__11495) ) ).
fof('$tdef_$_type_37',axiom,
! [V_24Y] :
( c_24__type__37___24t(V_24Y)
<=> t(V_24Y,c_24__type__37) ) ).
fof('$tdef_$_type_14708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__14708___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__14708___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1449',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1449___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1449___24a1(V_24X1)) ) ).
fof('$tdef_$_type_7980',axiom,
! [V_24Y] :
( c_24__type__7980___24t(V_24Y)
<=> t(V_24Y,c_24__type__7980) ) ).
fof('$tdef_$_type_27590',axiom,
! [V_24Y] :
( c_24__type__27590___24t(V_24Y)
<=> t(V_24Y,c_24__type__27590) ) ).
fof('$tdef_$_type_31777',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31777___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31777___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8255',axiom,
! [V_24Y] :
( c_24__type__8255___24t(V_24Y)
<=> t(V_24Y,c_24__type__8255) ) ).
fof('$tdef_$_type_14791',axiom,
! [V_24Y] :
( c_24__type__14791___24t(V_24Y)
<=> t(V_24Y,c_24__type__14791) ) ).
fof('$tdef_$_type_29610',axiom,
! [V_24Y] :
( c_24__type__29610___24t(V_24Y)
<=> t(V_24Y,c_24__type__29610) ) ).
fof('$tdef_$_type_1345',axiom,
! [V_24Y] :
( c_24__type__1345___24t(V_24Y)
<=> t(V_24Y,c_24__type__1345) ) ).
fof('$tdef_$_type_172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__172___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__172___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_9185',axiom,
! [V_24Y] :
( c_24__type__9185___24t(V_24Y)
<=> t(V_24Y,c_24__type__9185) ) ).
fof('$tdef_$_type_43498',axiom,
! [V_24Y] :
( c_24__type__43498___24t(V_24Y)
<=> t(V_24Y,c_24__type__43498) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_35786',axiom,
! [V_24Y] :
( c_24__type__35786___24t(V_24Y)
<=> t(V_24Y,c_24__type__35786) ) ).
fof('$tdef_$_type_35385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__35385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__35385___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_34129',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__34129___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__34129___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_41503',axiom,
! [V_24Y] :
( c_24__type__41503___24t(V_24Y)
<=> t(V_24Y,c_24__type__41503) ) ).
fof('$tdef_$_type_28978',axiom,
! [V_24Y] :
( c_24__type__28978___24t(V_24Y)
<=> t(V_24Y,c_24__type__28978) ) ).
fof('$tdef_$_type_11888',axiom,
! [V_24Y] :
( c_24__type__11888___24t(V_24Y)
<=> t(V_24Y,c_24__type__11888) ) ).
fof('$tdef_$_type_41493',axiom,
! [V_24Y] :
( c_24__type__41493___24t(V_24Y)
<=> t(V_24Y,c_24__type__41493) ) ).
fof('$tdef_$_type_1369',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1369___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1369___24a1(V_24X1)) ) ).
fof('$tdef_$_type_42508',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42508___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42508___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7816',axiom,
! [V_24Y] :
( c_24__type__7816___24t(V_24Y)
<=> t(V_24Y,c_24__type__7816) ) ).
fof('$tdef_$_type_42750',axiom,
! [V_24Y] :
( c_24__type__42750___24t(V_24Y)
<=> t(V_24Y,c_24__type__42750) ) ).
fof('$tdef_$_type_2981',axiom,
! [V_24Y] :
( c_24__type__2981___24t(V_24Y)
<=> t(V_24Y,c_24__type__2981) ) ).
fof('$tdef_$_type_29246',axiom,
! [V_24Y] :
( c_24__type__29246___24t(V_24Y)
<=> t(V_24Y,c_24__type__29246) ) ).
fof('$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_$_type_901',axiom,
! [V_24Y] :
( c_24__type__901___24t(V_24Y)
<=> t(V_24Y,c_24__type__901) ) ).
fof('$tdef_$_type_31575',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31575___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31575___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29268',axiom,
! [V_24Y] :
( c_24__type__29268___24t(V_24Y)
<=> t(V_24Y,c_24__type__29268) ) ).
fof('$tdef_monads.mon',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cmonads_2emon___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cmonads_2emon___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15180',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15180___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15180___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9143',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9143___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9143___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8481',axiom,
! [V_24Y] :
( c_24__type__8481___24t(V_24Y)
<=> t(V_24Y,c_24__type__8481) ) ).
fof('$tdef_$_type_41773',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41773___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41773___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2733',axiom,
! [V_24Y] :
( c_24__type__2733___24t(V_24Y)
<=> t(V_24Y,c_24__type__2733) ) ).
fof('$tdef_$_type_10704',axiom,
! [V_24Y] :
( c_24__type__10704___24t(V_24Y)
<=> t(V_24Y,c_24__type__10704) ) ).
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('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35653',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35653___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35653___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27630',axiom,
! [V_24Y] :
( c_24__type__27630___24t(V_24Y)
<=> t(V_24Y,c_24__type__27630) ) ).
fof('$tdef_$_type_39125',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39125___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39125___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_29449',axiom,
! [V_24Y] :
( c_24__type__29449___24t(V_24Y)
<=> t(V_24Y,c_24__type__29449) ) ).
fof('$tdef_$_type_43271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43271___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11353',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11353___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11353___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumbool',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14959',axiom,
! [V_24Y] :
( c_24__type__14959___24t(V_24Y)
<=> t(V_24Y,c_24__type__14959) ) ).
fof('$tdef_$_type_599',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__599___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__599___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11052',axiom,
! [V_24Y] :
( c_24__type__11052___24t(V_24Y)
<=> t(V_24Y,c_24__type__11052) ) ).
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_$_type_41727',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41727___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41727___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11602',axiom,
! [V_24Y] :
( c_24__type__11602___24t(V_24Y)
<=> t(V_24Y,c_24__type__11602) ) ).
fof('$tdef_$_type_42240',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__42240___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__42240___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_43698',axiom,
! [V_24Y] :
( c_24__type__43698___24t(V_24Y)
<=> t(V_24Y,c_24__type__43698) ) ).
fof('$tdef_$_type_3000',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3000___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3000___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29464',axiom,
! [V_24Y] :
( c_24__type__29464___24t(V_24Y)
<=> t(V_24Y,c_24__type__29464) ) ).
fof('$tdef_$_type_14780',axiom,
! [V_24Y] :
( c_24__type__14780___24t(V_24Y)
<=> t(V_24Y,c_24__type__14780) ) ).
fof('$tdef_$_type_8323',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__8323___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__8323___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_35899',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35899___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35899___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13454',axiom,
! [V_24Y] :
( c_24__type__13454___24t(V_24Y)
<=> t(V_24Y,c_24__type__13454) ) ).
fof('$tdef_$_type_42615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__42615___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__42615___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29457',axiom,
! [V_24Y] :
( c_24__type__29457___24t(V_24Y)
<=> t(V_24Y,c_24__type__29457) ) ).
fof('$tdef_$_type_40140',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40140___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40140___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31864',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31864___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31864___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32328',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32328___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32328___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29404',axiom,
! [V_24Y] :
( c_24__type__29404___24t(V_24Y)
<=> t(V_24Y,c_24__type__29404) ) ).
fof('$tdef_$_type_27767',axiom,
! [V_24Y] :
( c_24__type__27767___24t(V_24Y)
<=> t(V_24Y,c_24__type__27767) ) ).
fof('$tdef_$_type_36187',axiom,
! [V_24Y] :
( c_24__type__36187___24t(V_24Y)
<=> t(V_24Y,c_24__type__36187) ) ).
fof('$tdef_$_type_33515',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__33515___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__33515___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9174',axiom,
! [V_24Y] :
( c_24__type__9174___24t(V_24Y)
<=> t(V_24Y,c_24__type__9174) ) ).
fof('$tdef_$_type_7818',axiom,
! [V_24Y] :
( c_24__type__7818___24t(V_24Y)
<=> t(V_24Y,c_24__type__7818) ) ).
fof('$tdef_$_type_1',axiom,
! [V_24Y] :
( c_24__type__1___24t(V_24Y)
<=> t(V_24Y,c_24__type__1) ) ).
fof('$tdef_$_type_4306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__4306___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__4306___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_604',axiom,
! [V_24X1,V_24Y] :
( c_24__type__604___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__604___24a1(V_24X1)) ) ).
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_$_type_35767',axiom,
! [V_24Y] :
( c_24__type__35767___24t(V_24Y)
<=> t(V_24Y,c_24__type__35767) ) ).
fof('$tdef_$_type_2685',axiom,
! [V_24Y] :
( c_24__type__2685___24t(V_24Y)
<=> t(V_24Y,c_24__type__2685) ) ).
fof('$tdef_$_type_1295',axiom,
! [V_24Y] :
( c_24__type__1295___24t(V_24Y)
<=> t(V_24Y,c_24__type__1295) ) ).
fof('$tdef_$_type_10531',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10531___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10531___24a1(V_24X1)) ) ).
fof('$tdef_$_type_61',axiom,
! [V_24Y] :
( c_24__type__61___24t(V_24Y)
<=> t(V_24Y,c_24__type__61) ) ).
fof('$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_3025',axiom,
! [V_24Y] :
( c_24__type__3025___24t(V_24Y)
<=> t(V_24Y,c_24__type__3025) ) ).
fof('$tdef_$_type_7882',axiom,
! [V_24Y] :
( c_24__type__7882___24t(V_24Y)
<=> t(V_24Y,c_24__type__7882) ) ).
fof('$tdef_$_type_36041',axiom,
! [V_24Y] :
( c_24__type__36041___24t(V_24Y)
<=> t(V_24Y,c_24__type__36041) ) ).
fof('$tdef_$_type_371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__371___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__371___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2824',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2824___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2824___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38087',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__38087___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__38087___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_33818',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__33818___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__33818___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_42690',axiom,
! [V_24Y] :
( c_24__type__42690___24t(V_24Y)
<=> t(V_24Y,c_24__type__42690) ) ).
fof('$tdef_$_type_35875',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35875___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35875___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35722',axiom,
! [V_24Y] :
( c_24__type__35722___24t(V_24Y)
<=> t(V_24Y,c_24__type__35722) ) ).
fof('$tdef_$_type_35643',axiom,
! [V_24Y] :
( c_24__type__35643___24t(V_24Y)
<=> t(V_24Y,c_24__type__35643) ) ).
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_$_type_5693',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5693___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5693___24a2(V_24X1,V_24X2)) ) ).
fof('$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_29279',axiom,
! [V_24Y] :
( c_24__type__29279___24t(V_24Y)
<=> t(V_24Y,c_24__type__29279) ) ).
fof('$tdef_$_type_2698',axiom,
! [V_24Y] :
( c_24__type__2698___24t(V_24Y)
<=> t(V_24Y,c_24__type__2698) ) ).
fof('$tdef_$_type_41704',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41704___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41704___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_2961',axiom,
! [V_24Y] :
( c_24__type__2961___24t(V_24Y)
<=> t(V_24Y,c_24__type__2961) ) ).
fof('$tdef_$_type_31968',axiom,
! [V_24Y] :
( c_24__type__31968___24t(V_24Y)
<=> t(V_24Y,c_24__type__31968) ) ).
fof('$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_31807',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31807___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31807___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2672',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2672___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2672___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35820',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35820___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35820___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10',axiom,
! [V_24Y] :
( c_24__type__10___24t(V_24Y)
<=> t(V_24Y,c_24__type__10) ) ).
fof('$tdef_$_type_32503',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32503___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32503___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_38779',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__38779___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__38779___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1362',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1362___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1362___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_1323',axiom,
! [V_24Y] :
( c_24__type__1323___24t(V_24Y)
<=> t(V_24Y,c_24__type__1323) ) ).
fof('$tdef_$_type_35781',axiom,
! [V_24Y] :
( c_24__type__35781___24t(V_24Y)
<=> t(V_24Y,c_24__type__35781) ) ).
fof('$tdef_$_type_623',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__623___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__623___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_42700',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42700___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42700___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8863',axiom,
! [V_24Y] :
( c_24__type__8863___24t(V_24Y)
<=> t(V_24Y,c_24__type__8863) ) ).
fof('$tdef_$_type_29467',axiom,
! [V_24Y] :
( c_24__type__29467___24t(V_24Y)
<=> t(V_24Y,c_24__type__29467) ) ).
fof('$tdef_$_type_33425',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__33425___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__33425___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8297',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8297___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8297___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14831',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14831___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14831___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36162',axiom,
! [V_24Y] :
( c_24__type__36162___24t(V_24Y)
<=> t(V_24Y,c_24__type__36162) ) ).
fof('$tdef_$_type_151',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__151___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__151___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_41501',axiom,
! [V_24Y] :
( c_24__type__41501___24t(V_24Y)
<=> t(V_24Y,c_24__type__41501) ) ).
fof('$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_3685',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__3685___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__3685___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('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_40809',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40809___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40809___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1285',axiom,
! [V_24Y] :
( c_24__type__1285___24t(V_24Y)
<=> t(V_24Y,c_24__type__1285) ) ).
fof('$tdef_$_type_34309',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__34309___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__34309___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_36117',axiom,
! [V_24Y] :
( c_24__type__36117___24t(V_24Y)
<=> t(V_24Y,c_24__type__36117) ) ).
fof('$tdef_$_type_31831',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31831___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31831___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32421',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32421___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32421___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5658',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5658___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5658___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35888',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35888___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35888___24a2(V_24X1,V_24X2)) ) ).
fof('$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_43736',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43736___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43736___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35620',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35620___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35620___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31558',axiom,
! [V_24Y] :
( c_24__type__31558___24t(V_24Y)
<=> t(V_24Y,c_24__type__31558) ) ).
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_$_type_5641',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5641___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5641___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33223',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__33223___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__33223___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7350',axiom,
! [V_24Y] :
( c_24__type__7350___24t(V_24Y)
<=> t(V_24Y,c_24__type__7350) ) ).
fof('$tdef_$_type_3049',axiom,
! [V_24Y] :
( c_24__type__3049___24t(V_24Y)
<=> t(V_24Y,c_24__type__3049) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34372',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__34372___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__34372___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_31723',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31723___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31723___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7777',axiom,
! [V_24Y] :
( c_24__type__7777___24t(V_24Y)
<=> t(V_24Y,c_24__type__7777) ) ).
fof('$tdef_$_type_31915',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31915___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31915___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_41750',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41750___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41750___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_32235',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__32235___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__32235___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_2664',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2664___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2664___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35850',axiom,
! [V_24Y] :
( c_24__type__35850___24t(V_24Y)
<=> t(V_24Y,c_24__type__35850) ) ).
fof('$tdef_$_type_5649',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5649___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5649___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41517',axiom,
! [V_24Y] :
( c_24__type__41517___24t(V_24Y)
<=> t(V_24Y,c_24__type__41517) ) ).
fof('$tdef_$_type_14925',axiom,
! [V_24Y] :
( c_24__type__14925___24t(V_24Y)
<=> t(V_24Y,c_24__type__14925) ) ).
fof('$tdef_$_type_43730',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43730___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35775',axiom,
! [V_24Y] :
( c_24__type__35775___24t(V_24Y)
<=> t(V_24Y,c_24__type__35775) ) ).
fof('$tdef_$_type_42340',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__42340___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__42340___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35795',axiom,
! [V_24Y] :
( c_24__type__35795___24t(V_24Y)
<=> t(V_24Y,c_24__type__35795) ) ).
fof('$tdef_$_type_395',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__395___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_8478',axiom,
! [V_24Y] :
( c_24__type__8478___24t(V_24Y)
<=> t(V_24Y,c_24__type__8478) ) ).
fof('$tdef_$_type_43519',axiom,
! [V_24Y] :
( c_24__type__43519___24t(V_24Y)
<=> t(V_24Y,c_24__type__43519) ) ).
fof('$tdef_$_type_35698',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35698___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35698___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14983',axiom,
! [V_24Y] :
( c_24__type__14983___24t(V_24Y)
<=> t(V_24Y,c_24__type__14983) ) ).
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_35870',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35870___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35870___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_40486',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__40486___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__40486___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('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31888',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31888___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31888___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7907',axiom,
! [V_24Y] :
( c_24__type__7907___24t(V_24Y)
<=> t(V_24Y,c_24__type__7907) ) ).
fof('$tdef_$_type_41835',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41835___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41835___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_43465',axiom,
! [V_24Y] :
( c_24__type__43465___24t(V_24Y)
<=> t(V_24Y,c_24__type__43465) ) ).
fof('$tdef_$_type_27775',axiom,
! [V_24Y] :
( c_24__type__27775___24t(V_24Y)
<=> t(V_24Y,c_24__type__27775) ) ).
fof('$tdef_$_type_39794',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39794___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39794___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_7794',axiom,
! [V_24Y] :
( c_24__type__7794___24t(V_24Y)
<=> t(V_24Y,c_24__type__7794) ) ).
fof('$tdef_$_type_42432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__42432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__42432___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33324',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__33324___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__33324___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_43439',axiom,
! [V_24Y] :
( c_24__type__43439___24t(V_24Y)
<=> t(V_24Y,c_24__type__43439) ) ).
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_$_type_8059',axiom,
! [V_24Y] :
( c_24__type__8059___24t(V_24Y)
<=> t(V_24Y,c_24__type__8059) ) ).
fof('$tdef_$_type_11590',axiom,
! [V_24Y] :
( c_24__type__11590___24t(V_24Y)
<=> t(V_24Y,c_24__type__11590) ) ).
fof('$tdef_$_type_14917',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14917___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14917___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_976',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__976___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__976___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32771',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__32771___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__32771___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1000',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__1000___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__1000___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_35800',axiom,
! [V_24Y] :
( c_24__type__35800___24t(V_24Y)
<=> t(V_24Y,c_24__type__35800) ) ).
fof('$tdef_$_type_11568',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11568___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11568___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11557',axiom,
! [V_24Y] :
( c_24__type__11557___24t(V_24Y)
<=> t(V_24Y,c_24__type__11557) ) ).
fof('$tdef_$_type_34774',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__34774___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__34774___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_2713',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2713___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2713___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11526',axiom,
! [V_24Y] :
( c_24__type__11526___24t(V_24Y)
<=> t(V_24Y,c_24__type__11526) ) ).
fof('$tdef_$_type_38433',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__38433___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__38433___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_43525',axiom,
! [V_24Y] :
( c_24__type__43525___24t(V_24Y)
<=> t(V_24Y,c_24__type__43525) ) ).
fof('$tdef_$_type_43293',axiom,
! [V_24Y] :
( c_24__type__43293___24t(V_24Y)
<=> t(V_24Y,c_24__type__43293) ) ).
fof('$tdef_$_type_177',axiom,
! [V_24Y] :
( c_24__type__177___24t(V_24Y)
<=> t(V_24Y,c_24__type__177) ) ).
fof('$tdef_$_type_2761',axiom,
! [V_24Y] :
( c_24__type__2761___24t(V_24Y)
<=> t(V_24Y,c_24__type__2761) ) ).
fof('$tdef_$_type_58',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__58___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__58___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_41488',axiom,
! [V_24Y] :
( c_24__type__41488___24t(V_24Y)
<=> t(V_24Y,c_24__type__41488) ) ).
fof('$tdef_$_type_35808',axiom,
! [V_24Y] :
( c_24__type__35808___24t(V_24Y)
<=> t(V_24Y,c_24__type__35808) ) ).
fof('$tdef_$_type_2995',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2995___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2995___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5668',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5668___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5668___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_865',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__865___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__865___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_42530',axiom,
! [V_24Y] :
( c_24__type__42530___24t(V_24Y)
<=> t(V_24Y,c_24__type__42530) ) ).
fof('$tdef_$_type_34192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__34192___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__34192___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_846',axiom,
! [V_24X1,V_24Y] :
( c_24__type__846___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__846___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39471',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__39471___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__39471___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_42290',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__42290___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__42290___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_42745',axiom,
! [V_24Y] :
( c_24__type__42745___24t(V_24Y)
<=> t(V_24Y,c_24__type__42745) ) ).
fof('$tdef_$_type_1311',axiom,
! [V_24Y] :
( c_24__type__1311___24t(V_24Y)
<=> t(V_24Y,c_24__type__1311) ) ).
fof('$tdef_$_type_20',axiom,
! [V_24Y] :
( c_24__type__20___24t(V_24Y)
<=> t(V_24Y,c_24__type__20) ) ).
fof('$tdef_$_type_2767',axiom,
! [V_24Y] :
( c_24__type__2767___24t(V_24Y)
<=> t(V_24Y,c_24__type__2767) ) ).
fof('$tdef_$_type_10526',axiom,
! [V_24Y] :
( c_24__type__10526___24t(V_24Y)
<=> t(V_24Y,c_24__type__10526) ) ).
fof('$tdef_$_type_36070',axiom,
! [V_24Y] :
( c_24__type__36070___24t(V_24Y)
<=> t(V_24Y,c_24__type__36070) ) ).
fof('$tdef_$_type_1337',axiom,
! [V_24Y] :
( c_24__type__1337___24t(V_24Y)
<=> t(V_24Y,c_24__type__1337) ) ).
fof('$tdef_$_type_13253',axiom,
! [V_24Y] :
( c_24__type__13253___24t(V_24Y)
<=> t(V_24Y,c_24__type__13253) ) ).
fof('$tdef_$_type_31747',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31747___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31747___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_31008',axiom,
! [V_24Y] :
( c_24__type__31008___24t(V_24Y)
<=> t(V_24Y,c_24__type__31008) ) ).
fof('$tdef_$_type_366',axiom,
! [V_24X1,V_24Y] :
( c_24__type__366___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__366___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43447',axiom,
! [V_24Y] :
( c_24__type__43447___24t(V_24Y)
<=> t(V_24Y,c_24__type__43447) ) ).
fof('$tdef_$_type_41132',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41132___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41132___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_27750',axiom,
! [V_24Y] :
( c_24__type__27750___24t(V_24Y)
<=> t(V_24Y,c_24__type__27750) ) ).
fof('$tdef_$_type_13004',axiom,
! [V_24Y] :
( c_24__type__13004___24t(V_24Y)
<=> t(V_24Y,c_24__type__13004) ) ).
fof('$tdef_$_type_376',axiom,
! [V_24X1,V_24Y] :
( c_24__type__376___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__376___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35948',axiom,
! [V_24Y] :
( c_24__type__35948___24t(V_24Y)
<=> t(V_24Y,c_24__type__35948) ) ).
fof('$tdef_$_type_29439',axiom,
! [V_24Y] :
( c_24__type__29439___24t(V_24Y)
<=> t(V_24Y,c_24__type__29439) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43404',axiom,
! [V_24Y] :
( c_24__type__43404___24t(V_24Y)
<=> t(V_24Y,c_24__type__43404) ) ).
fof('$tdef_$_type_31032',axiom,
! [V_24Y] :
( c_24__type__31032___24t(V_24Y)
<=> t(V_24Y,c_24__type__31032) ) ).
fof('$tdef_$_type_971',axiom,
! [V_24X1,V_24Y] :
( c_24__type__971___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__971___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43425',axiom,
! [V_24Y] :
( c_24__type__43425___24t(V_24Y)
<=> t(V_24Y,c_24__type__43425) ) ).
fof('$tdef_$_type_836',axiom,
! [V_24X1,V_24Y] :
( c_24__type__836___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__836___24a1(V_24X1)) ) ).
fof('$tdef_$_type_433',axiom,
! [V_24Y] :
( c_24__type__433___24t(V_24Y)
<=> t(V_24Y,c_24__type__433) ) ).
fof('$tdef_$_type_2708',axiom,
! [V_24Y] :
( c_24__type__2708___24t(V_24Y)
<=> t(V_24Y,c_24__type__2708) ) ).
fof('$tdef_$_type_43599',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43599___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43599___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_43521',axiom,
! [V_24Y] :
( c_24__type__43521___24t(V_24Y)
<=> t(V_24Y,c_24__type__43521) ) ).
fof('$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_8492',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8492___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8492___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_43421',axiom,
! [V_24Y] :
( c_24__type__43421___24t(V_24Y)
<=> t(V_24Y,c_24__type__43421) ) ).
fof('$tdef_$_type_43388',axiom,
! [V_24Y] :
( c_24__type__43388___24t(V_24Y)
<=> t(V_24Y,c_24__type__43388) ) ).
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_$_type_4732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__4732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__4732___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_11372',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__11372___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__11372___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7402',axiom,
! [V_24Y] :
( c_24__type__7402___24t(V_24Y)
<=> t(V_24Y,c_24__type__7402) ) ).
fof('$tdef_$_type_36190',axiom,
! [V_24Y] :
( c_24__type__36190___24t(V_24Y)
<=> t(V_24Y,c_24__type__36190) ) ).
fof('$tdef_$_type_35665',axiom,
! [V_24Y] :
( c_24__type__35665___24t(V_24Y)
<=> t(V_24Y,c_24__type__35665) ) ).
fof('$tdef_$_type_2844',axiom,
! [V_24Y] :
( c_24__type__2844___24t(V_24Y)
<=> t(V_24Y,c_24__type__2844) ) ).
fof('$tdef_$_type_1366',axiom,
! [V_24Y] :
( c_24__type__1366___24t(V_24Y)
<=> t(V_24Y,c_24__type__1366) ) ).
fof('$tdef_$_type_11093',axiom,
! [V_24Y] :
( c_24__type__11093___24t(V_24Y)
<=> t(V_24Y,c_24__type__11093) ) ).
fof('$tdef_monads.Monad',axiom,
! [V_24Y] :
( cmonads_2eMonad___24t(V_24Y)
<=> t(V_24Y,cmonads_2eMonad) ) ).
fof('$tdef_$_type_41817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41817___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_41512',axiom,
! [V_24Y] :
( c_24__type__41512___24t(V_24Y)
<=> t(V_24Y,c_24__type__41512) ) ).
fof('$tdef_$_type_1335',axiom,
! [V_24Y] :
( c_24__type__1335___24t(V_24Y)
<=> t(V_24Y,c_24__type__1335) ) ).
fof('$tdef_$_type_36101',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36101___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36101___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35720',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35720___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35720___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_11669',axiom,
! [V_24Y] :
( c_24__type__11669___24t(V_24Y)
<=> t(V_24Y,c_24__type__11669) ) ).
fof('$tdef_$_type_14881',axiom,
! [V_24Y] :
( c_24__type__14881___24t(V_24Y)
<=> t(V_24Y,c_24__type__14881) ) ).
fof('$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_43478',axiom,
! [V_24Y] :
( c_24__type__43478___24t(V_24Y)
<=> t(V_24Y,c_24__type__43478) ) ).
fof('$tdef_$_type_43471',axiom,
! [V_24Y] :
( c_24__type__43471___24t(V_24Y)
<=> t(V_24Y,c_24__type__43471) ) ).
fof('$tdef_$_type_35769',axiom,
! [V_24Y] :
( c_24__type__35769___24t(V_24Y)
<=> t(V_24Y,c_24__type__35769) ) ).
fof('$tdef_$_type_5353',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__5353___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__5353___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_14909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14909___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14909___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36077',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36077___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36077___24a2(V_24X1,V_24X2)) ) ).
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_$_type_43582',axiom,
! [V_24X1,V_24Y] :
( c_24__type__43582___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__43582___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41478',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__41478___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__41478___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_35149',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__35149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__35149___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$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('$tdef_$_type_3898',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__3898___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__3898___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_35540',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35540___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35540___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_4945',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__4945___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__4945___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_130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__130___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__130___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11570',axiom,
! [V_24Y] :
( c_24__type__11570___24t(V_24Y)
<=> t(V_24Y,c_24__type__11570) ) ).
fof('$tdef_$_type_87',axiom,
! [V_24Y] :
( c_24__type__87___24t(V_24Y)
<=> t(V_24Y,c_24__type__87) ) ).
fof('$tdef_$_type_8488',axiom,
! [V_24Y] :
( c_24__type__8488___24t(V_24Y)
<=> t(V_24Y,c_24__type__8488) ) ).
fof('$tdef_$_type_9205',axiom,
! [V_24Y] :
( c_24__type__9205___24t(V_24Y)
<=> t(V_24Y,c_24__type__9205) ) ).
fof('$tdef_$_type_13261',axiom,
! [V_24Y] :
( c_24__type__13261___24t(V_24Y)
<=> t(V_24Y,c_24__type__13261) ) ).
fof('$tdef_$_type_3472',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__3472___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__3472___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_2729',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2729___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2729___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11594',axiom,
! [V_24Y] :
( c_24__type__11594___24t(V_24Y)
<=> t(V_24Y,c_24__type__11594) ) ).
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_$_type_37741',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__37741___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__37741___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_43230',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__43230___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__43230___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_981',axiom,
! [V_24X1,V_24Y] :
( c_24__type__981___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__981___24a1(V_24X1)) ) ).
fof('$tdef_$_type_54',axiom,
! [V_24Y] :
( c_24__type__54___24t(V_24Y)
<=> t(V_24Y,c_24__type__54) ) ).
fof('$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_2703',axiom,
! [V_24Y] :
( c_24__type__2703___24t(V_24Y)
<=> t(V_24Y,c_24__type__2703) ) ).
fof('$tdef_$_type_42740',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__42740___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__42740___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29236',axiom,
! [V_24Y] :
( c_24__type__29236___24t(V_24Y)
<=> t(V_24Y,c_24__type__29236) ) ).
fof('$tdef_$_type_5682',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5682___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5682___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34649',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__34649___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__34649___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_5809',axiom,
! [V_24Y] :
( c_24__type__5809___24t(V_24Y)
<=> t(V_24Y,c_24__type__5809) ) ).
fof('$tdef_$_type_36133',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36133___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36133___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14804',axiom,
! [V_24Y] :
( c_24__type__14804___24t(V_24Y)
<=> t(V_24Y,c_24__type__14804) ) ).
fof('$tdef_$_type_33717',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__33717___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__33717___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_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_31926',axiom,
! [V_24Y] :
( c_24__type__31926___24t(V_24Y)
<=> t(V_24Y,c_24__type__31926) ) ).
fof('$tdef_$_type_43341',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__43341___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__43341___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35843',axiom,
! [V_24Y] :
( c_24__type__35843___24t(V_24Y)
<=> t(V_24Y,c_24__type__35843) ) ).
fof('$tdef_$_type_11392',axiom,
! [V_24Y] :
( c_24__type__11392___24t(V_24Y)
<=> t(V_24Y,c_24__type__11392) ) ).
fof('$tdef_$_type_35024',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__35024___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__35024___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_14847',axiom,
! [V_24Y] :
( c_24__type__14847___24t(V_24Y)
<=> t(V_24Y,c_24__type__14847) ) ).
fof('$tdef_$_type_14689',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__14689___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__14689___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_5548',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__5548___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__5548___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_5689',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5689___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5689___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35496',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35496___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35496___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_34255',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__34255___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__34255___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_8855',axiom,
! [V_24Y] :
( c_24__type__8855___24t(V_24Y)
<=> t(V_24Y,c_24__type__8855) ) ).
fof('$tdef_$_type_42806',axiom,
! [V_24Y] :
( c_24__type__42806___24t(V_24Y)
<=> t(V_24Y,c_24__type__42806) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24Y] :
( c_24__type__8___24t(V_24Y)
<=> t(V_24Y,c_24__type__8) ) ).
fof('$tdef_$_type_36017',axiom,
! [V_24Y] :
( c_24__type__36017___24t(V_24Y)
<=> t(V_24Y,c_24__type__36017) ) ).
fof('$tdef_$_type_33616',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__33616___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__33616___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15163',axiom,
! [V_24Y] :
( c_24__type__15163___24t(V_24Y)
<=> t(V_24Y,c_24__type__15163) ) ).
fof('$tdef_$_type_2751',axiom,
! [V_24Y] :
( c_24__type__2751___24t(V_24Y)
<=> t(V_24Y,c_24__type__2751) ) ).
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_43398',axiom,
! [V_24Y] :
( c_24__type__43398___24t(V_24Y)
<=> t(V_24Y,c_24__type__43398) ) ).
fof('$tdef_$_type_41791',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41791___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41791___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2986',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2986___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2986___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43345',axiom,
! [V_24Y] :
( c_24__type__43345___24t(V_24Y)
<=> t(V_24Y,c_24__type__43345) ) ).
fof('$tdef_$_type_11245',axiom,
! [V_24X1,V_24Y] :
( c_24__type__11245___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__11245___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12504',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12504___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12504___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14839',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14839___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14839___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_137',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__137___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__137___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35576___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35576___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_8505',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8505___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8505___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33877',axiom,
! [V_24Y] :
( c_24__type__33877___24t(V_24Y)
<=> t(V_24Y,c_24__type__33877) ) ).
fof('$tdef_$_type_4093',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__4093___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__4093___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_32678',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__32678___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__32678___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27613',axiom,
! [V_24Y] :
( c_24__type__27613___24t(V_24Y)
<=> t(V_24Y,c_24__type__27613) ) ).
fof('$tdef_$_type_29607',axiom,
! [V_24Y] :
( c_24__type__29607___24t(V_24Y)
<=> t(V_24Y,c_24__type__29607) ) ).
fof('$tdef_$_type_5140',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__5140___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__5140___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('$tdef_monads.Functor',axiom,
! [V_24Y] :
( cmonads_2eFunctor___24t(V_24Y)
<=> t(V_24Y,cmonads_2eFunctor) ) ).
fof('$tdef_$_type_41535',axiom,
! [V_24Y] :
( c_24__type__41535___24t(V_24Y)
<=> t(V_24Y,c_24__type__41535) ) ).
fof('$tdef_$_type_32030',axiom,
! [V_24Y] :
( c_24__type__32030___24t(V_24Y)
<=> t(V_24Y,c_24__type__32030) ) ).
fof('_HAMMER_GOAL',conjecture,
( cm = cn
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(cA,cmonads_2emon___24a2(cM,cB),cf,cg)
=> cmonads_2ebind___24a5(cM,cA,cB,cm,cf) = cmonads_2ebind___24a5(cM,cA,cB,cn,cg) ) ) ).
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