TPTP Problem File: SEV674+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV674+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - sums and averages Ravg 0
% 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 : sums.and.averages.Ravg.0.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2685 ( 924 unt; 0 def)
% Number of atoms : 9366 (2471 equ)
% Maximal formula atoms : 82 ( 3 avg)
% Number of connectives : 6896 ( 215 ~; 398 |;1323 &)
% ( 875 <=>;4085 =>; 0 <=; 0 <~>)
% Maximal formula depth : 67 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 444 ( 443 usr; 0 prp; 1-23 aty)
% Number of functors : 1329 (1329 usr; 754 con; 0-22 aty)
% Number of variables : 9246 (8707 !; 539 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$48852',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ( ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(Vv__CANONICAL__0,cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2448852___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(Vv__CANONICAL__0,cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_2448852___24a1(Vv__CANONICAL__0) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eQArith_2eQreals_2eQ2R___24a1(Vv__CANONICAL__0)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.comparison$43770',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eEq
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eLt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eGt
& c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$2850',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_242850___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__2851] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2851)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2851)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_242850___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__2869__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__2851,Vv__CANONICAL__2)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$35588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435588___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35589] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35589)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35589)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435588___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__35589)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$35610',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35611] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35611)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35611)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__35611)) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$5547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__5373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__5559___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__5560___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_245547___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__5516__5520__5529___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__5561___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__5562___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_245547___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__5516__5520__5529___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$35605',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35606] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35606)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35606)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35606) )
| ? [Vvar__0___24Anonymous__35607] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35607)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35607)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35607) ) ) ) ).
fof('$_case_Coq.setoid_ring.Ring_polynom.Pol$33389',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> ( ? [Vvar__1___24Anonymous__33392] :
( t(Vvar__1___24Anonymous__33392,Vv__CANONICAL__8)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__8)
=> ( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ( c_24__type__33412___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__11)
=> ( cType___24t(Vv__CANONICAL__13)
=> ( t(Vvar__1___24Anonymous__33392,Vv__CANONICAL__8)
=> ( Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vv__CANONICAL__8,Vvar__1___24Anonymous__33392)
& ( ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__33392),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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) = c_24__let__20__lnum__33085___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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) )
| ( happ(happ(Vv__CANONICAL__11,Vvar__1___24Anonymous__33392),Vv__CANONICAL__10) = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__33085___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__33395] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__33395)
& ? [Vvar__2___24Anonymous__33396] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__2___24Anonymous__33396)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vv__CANONICAL__8,Vvar__1___24Anonymous__33395,Vvar__2___24Anonymous__33396)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__33085___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) )
| ? [Vvar__1___24Anonymous__33399] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__1___24Anonymous__33399)
& ? [Vvar__2___24Anonymous__33400] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__33400)
& ? [Vvar__3___24Anonymous__33401] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vvar__3___24Anonymous__33401)
& Vv__CANONICAL__19 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vv__CANONICAL__8,Vvar__1___24Anonymous__33399,Vvar__2___24Anonymous__33400,Vvar__3___24Anonymous__33401)
& c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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) = happ(happ(Vv__CANONICAL__7,c_24__let__20__lnum__33085___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,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__19)) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_1093',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__1093___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_25884',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__25887] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25887)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25887)
& c_24__let__16__mkpow__25884___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__25888] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25888)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25888)
& c_24__let__16__mkpow__25884___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__25884___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_25885',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__25885___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__25884___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_25886',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__25886___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__25884___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_20_lnum_33085',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num] : c_24__let__20__lnum__33085___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num) ).
fof('$_def_$_let_33_lmp_1818',axiom,
! [V0__R,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V21__Cpow,V25__cdiv,V29__lpe] : c_24__let__33__lmp__1818___24a12(V0__R,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V21__Cpow,V25__cdiv,V29__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V25__cdiv,V29__lpe) ).
fof('$_def_$_let_6_lmp_32509',axiom,
! [V2__lpe] : c_24__let__6__lmp__32509___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_6_lmp_32527',axiom,
! [V2__lpe] : c_24__let__6__lmp__32527___24a1(V2__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) ).
fof('$_def_$_let_var_11_x_24677_24727',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676] : c_24__let__var__11__x__24677__24727___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676) ).
fof('$_def_$_let_var_11_x_24680_24728',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679] : c_24__let__var__11__x__24680__24728___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679) ).
fof('$_def_$_let_var_6_p_43998_44001',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43997] : c_24__let__var__6__p__43998__44001___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43997) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43997) ).
fof('$_def_$_let_var_6_p_44000_44002',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43999] : c_24__let__var__6__p__44000__44002___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43999) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43999) ).
fof('$_def_$_let_var_var_12_x_24635_24638_24708',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632] : c_24__let__var__var__12__x__24635__24638__24708___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632) ).
fof('$_def_$_let_var_var_12_x_24648_24651_24714',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645] : c_24__let__var__var__12__x__24648__24651__24714___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645) ).
fof('$_def_$_let_var_var_12_x_24661_24665_24723',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658] : c_24__let__var__var__12__x__24661__24665__24723___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658) ).
fof('$_def_$_let_var_var_12_x_24685_24689_24735',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682] : c_24__let__var__var__12__x__24685__24689__24735___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682) ).
fof('$_def_$_let_var_var_12_x_24702_24704_24739',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700] : c_24__let__var__var__12__x__24702__24704__24739___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700) ).
fof('$_def_$_let_var_var_13_y_24636_24639_24709',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633] : c_24__let__var__var__13__y__24636__24639__24709___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633) ).
fof('$_def_$_let_var_var_13_y_24649_24652_24715',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646] : c_24__let__var__var__13__y__24649__24652__24715___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646) ).
fof('$_def_$_let_var_var_13_y_24662_24666_24724',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659] : c_24__let__var__var__13__y__24662__24666__24724___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659) ).
fof('$_def_$_let_var_var_13_y_24686_24690_24736',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683] : c_24__let__var__var__13__y__24686__24690__24736___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683) ).
fof('$_def_$_let_var_var_14_s1_24663_24667_24725',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659] : c_24__let__var__var__14__s1__24663__24667__24725___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__24661__24665__24723___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__24662__24666__24724___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659))) ).
fof('$_def_$_let_var_var_14_s1_24687_24691_24737',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683] : c_24__let__var__var__14__s1__24687__24691__24737___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__24685__24689__24735___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__24686__24690__24736___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683))) ).
fof('$_def_$_let_var_var_14_s_24637_24640_24710',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633] : c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__24635__24638__24708___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__24636__24639__24709___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633))) ).
fof('$_def_$_let_var_var_14_s_24650_24653_24716',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646] : c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__24648__24651__24714___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__24649__24652__24715___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646))) ).
fof('$_def_$_let_var_var_15_s2_24664_24668_24726',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659] : c_24__let__var__var__15__s2__24664__24668__24726___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__24662__24666__24724___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__24661__24665__24723___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658))) ).
fof('$_def_$_let_var_var_15_s2_24688_24692_24738',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683] : c_24__let__var__var__15__s2__24688__24692__24738___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__24685__24689__24735___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682)),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__13__y__24686__24690__24736___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683))) ).
fof('$_def_$_let_var_var_7_n_5516_5520_5529',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__5513] : c_24__let__var__var__7__n__5516__5520__5529___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__5513) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__5513,V4__x) ).
fof('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__30960] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30960)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30960)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30960),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__30960)) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
! [V0__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V0__m,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__19820] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__19820)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__19820) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19836] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__19836)
& ? [Vvar__1___24Anonymous__19837] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__19837)
& ? [Vvar__2___24Anonymous__19838] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__19838)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__19836,Vvar__1___24Anonymous__19837,Vvar__2___24Anonymous__19838)
& ( ? [Vvar__0___24Anonymous__19851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19851)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19851)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__19851,Vvar__2___24Anonymous__19838) )
| ? [Vvar__0___24Anonymous__19852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19852)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19852)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__19852,Vvar__0___24Anonymous__19836) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__19837 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__19834] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__19834)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__19834) ) ).
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__44] :
( t(Vvar__1___24Anonymous__44,V0__A)
& ? [Vvar__2___24Anonymous__45] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__45)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__44,Vvar__2___24Anonymous__45)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__44,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__45,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__3553] :
( t(Vvar__2___24Anonymous__3553,V0__A)
& ? [Vvar__3___24Anonymous__3554] :
( t(Vvar__3___24Anonymous__3554,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__3553,Vvar__3___24Anonymous__3554)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__3553 ) ) ) ) ) ).
fof('$_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__1967] :
( t(Vvar__1___24Anonymous__1967,V0__A)
& ? [Vvar__2___24Anonymous__1968] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1968)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1967,Vvar__2___24Anonymous__1968)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__1968)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__3583___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__3577] :
( t(Vvar__1___24Anonymous__3577,V0__A)
& ? [Vvar__2___24Anonymous__3578] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3578)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3577,Vvar__2___24Anonymous__3578)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__3577),Vvar__2___24Anonymous__3578),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__3578)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__20111___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__20109] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20109)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20109)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__20109),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__20109)) ) ) ) ) ).
fof('$_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__3565] :
( t(Vvar__2___24Anonymous__3565,V0__A)
& ? [Vvar__3___24Anonymous__3566] :
( t(Vvar__3___24Anonymous__3566,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__3565,Vvar__3___24Anonymous__3566)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__3566 ) ) ) ) ) ).
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__81] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__81,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__7197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7197)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7197)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__7200] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7200)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7200)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__7197,Vvar__0___24Anonymous__7200)) ) ) ) ) ) ) ) ).
fof('$_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__7203] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7203)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7203)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__7206] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7206)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7206)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__7203,Vvar__0___24Anonymous__7206)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__439] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__439)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__439)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__439,V2__m)) ) ) ) ).
fof('$_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__7195] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7195)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7195)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__7195 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2662] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2662)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2662)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2665] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2665)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2665)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__2662,Vvar__0___24Anonymous__2665) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.sumbool_rec',axiom,
! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V0__A,V1__B,V2__P) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__1977] :
( t(Vvar__1___24Anonymous__1977,V0__A)
& ? [Vvar__2___24Anonymous__1978] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1978)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1977,Vvar__2___24Anonymous__1978)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__1977 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__1978)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.combine',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__6571] :
( t(Vvar__1___24Anonymous__6571,V0__A)
& ? [Vvar__2___24Anonymous__6572] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6572)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6571,Vvar__2___24Anonymous__6572)
& ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__6583] :
( t(Vvar__1___24Anonymous__6583,V1__B)
& ? [Vvar__2___24Anonymous__6584] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__6584)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__6583,Vvar__2___24Anonymous__6584)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__6571,Vvar__1___24Anonymous__6583),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__6572,Vvar__2___24Anonymous__6584)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__5512] :
( t(Vvar__1___24Anonymous__5512,V0__A)
& ? [Vvar__2___24Anonymous__5513] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5513)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5512,Vvar__2___24Anonymous__5513)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_245547___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__5512,Vvar__2___24Anonymous__5513) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.existsb',axiom,
! [V0__A,V1__f,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_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__21139] :
( t(Vvar__1___24Anonymous__21139,V0__A)
& ? [Vvar__2___24Anonymous__21140] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__21140)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__21139,Vvar__2___24Anonymous__21140)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__21139),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__21140)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__6472] :
( t(Vvar__1___24Anonymous__6472,V0__A)
& ? [Vvar__2___24Anonymous__6473] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6473)
& ( cType___24t(V0__A)
=> ( c_24__type__6478___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__6472,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6472,Vvar__2___24Anonymous__6473)
& ( ( happ(V1__f,Vvar__1___24Anonymous__6472) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6472,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__6473)) )
| ( happ(V1__f,Vvar__1___24Anonymous__6472) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__6473) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.find',axiom,
! [V0__A,V1__f,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_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__34092] :
( t(Vvar__1___24Anonymous__34092,V0__A)
& ? [Vvar__2___24Anonymous__34093] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__34093)
& ( cType___24t(V0__A)
=> ( c_24__type__6478___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__34092,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__34092,Vvar__2___24Anonymous__34093)
& ( ( happ(V1__f,Vvar__1___24Anonymous__34092) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__34092) )
| ( happ(V1__f,Vvar__1___24Anonymous__34092) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,Vvar__2___24Anonymous__34093) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.flat_map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__6397] :
( t(Vvar__1___24Anonymous__6397,V0__A)
& ? [Vvar__2___24Anonymous__6398] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6398)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6397,Vvar__2___24Anonymous__6398)
& cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__6397),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__6398)) ) ) ) ) ) ) ).
fof('$_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__2020] :
( t(Vvar__1___24Anonymous__2020,V1__B)
& ? [Vvar__2___24Anonymous__2021] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__2021)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__2020,Vvar__2___24Anonymous__2021)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__2020),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__2021)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ).
fof('$_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__56] :
( t(Vvar__1___24Anonymous__56,V0__A)
& ? [Vvar__2___24Anonymous__57] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__57)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__56,Vvar__2___24Anonymous__57)
& 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__56),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__57)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nodup',axiom,
! [V0__A,V1__decA,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_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__6686] :
( t(Vvar__1___24Anonymous__6686,V0__A)
& ? [Vvar__2___24Anonymous__6687] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6687)
& ( cType___24t(V0__A)
=> ( c_24__type__5373___24t(V0__A,V1__decA)
=> ( t(Vvar__1___24Anonymous__6686,V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6687)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687),c_24__prop__6706___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__6687) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
& cCoq_2eLists_2eList_2ein__dec___24a4(V0__A,V1__decA,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687),c_24__prop__6718___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
& cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6686,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,Vvar__2___24Anonymous__6687)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__417] :
( t(Vvar__1___24Anonymous__417,V0__A)
& ? [Vvar__2___24Anonymous__418] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__418)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__417,Vvar__2___24Anonymous__418)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__417 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__420] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__420)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__420)
& ( ( 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__427] :
( t(Vvar__1___24Anonymous__427,V0__A)
& ? [Vvar__2___24Anonymous__428] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__428)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__427,Vvar__2___24Anonymous__428)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__420,Vvar__2___24Anonymous__428,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__5382] :
( t(Vvar__1___24Anonymous__5382,V0__A)
& ? [Vvar__2___24Anonymous__5383] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5383)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5382,Vvar__2___24Anonymous__5383)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__5382) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5385] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5385)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5385)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__5392] :
( t(Vvar__1___24Anonymous__5392,V0__A)
& ? [Vvar__2___24Anonymous__5393] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5393)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5392,Vvar__2___24Anonymous__5393)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__5393,Vvar__0___24Anonymous__5385) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.remove',axiom,
! [V0__A,V1__eq__dec,V3__x,V4__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__5404] :
( t(Vvar__1___24Anonymous__5404,V0__A)
& ? [Vvar__2___24Anonymous__5405] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5405)
& ( cType___24t(V0__A)
=> ( c_24__type__5373___24t(V0__A,V1__eq__dec)
=> ( t(V3__x,V0__A)
=> ( t(Vvar__1___24Anonymous__5404,V0__A)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5404,Vvar__2___24Anonymous__5405)
& ( ( V3__x = Vvar__1___24Anonymous__5404
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__5404) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__5424___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404),c_24__prop__5425___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__5405) )
| ( V3__x != Vvar__1___24Anonymous__5404
& happ(happ(V1__eq__dec,V3__x),Vvar__1___24Anonymous__5404) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__5426___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404),c_24__prop__5427___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
& cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5404,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,Vvar__2___24Anonymous__5405)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__5587] :
( t(Vvar__1___24Anonymous__5587,V0__A)
& ? [Vvar__2___24Anonymous__5588] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__5588)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5587,Vvar__2___24Anonymous__5588)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__5588),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__5587,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.ListDec.In_dec',axiom,
! [V0__A,V1__dec] : cCoq_2eLists_2eListDec_2eIn__dec___24a2(V0__A,V1__dec) = cCoq_2eLists_2eList_2ein__dec___24a2(V0__A,V1__dec) ).
fof('$_def_Coq.Lists.ListDec.decidable_eq',axiom,
! [V0__A] :
( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
<=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__30978___24a3(V0__A,V1__x,V2__y)) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.FinFun.Full',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V1__l)) ) ) ).
fof('$_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__2518] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2518)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2518)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__2521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2521)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2521)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2518,Vvar__0___24Anonymous__2521)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__2539] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2539)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2539)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__2542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2542)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2542)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2539,V1__b) ) ) ) ) ) ) ) ).
fof('$_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__2531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2531)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2531)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__2532] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2532)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2532)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__2535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2535)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2535)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__2532,Vvar__0___24Anonymous__2535) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2525] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2525)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2525)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__2528] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2528)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2528)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2525,Vvar__0___24Anonymous__2528)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__19678] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19678)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19678)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__19678)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__2546] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2546)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2546)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__2546) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( p(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.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__19748] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19748)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19748)
& ( ? [Vvar__0___24Anonymous__19752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19752)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19752)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__19747__1__add__carry___24a2(Vvar__0___24Anonymous__19748,Vvar__0___24Anonymous__19752)) )
| ? [Vvar__0___24Anonymous__19753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19753)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19753)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19748,Vvar__0___24Anonymous__19753)) )
| ( 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__19748)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19754] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19754)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19754)
& ( ? [Vvar__0___24Anonymous__19758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19758)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19758)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19754,Vvar__0___24Anonymous__19758)) )
| ? [Vvar__0___24Anonymous__19759] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19759)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19759)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19754,Vvar__0___24Anonymous__19759)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19754) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__19760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19760)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19760)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19760)) )
| ? [Vvar__0___24Anonymous__19761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19761)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19761)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19761) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__32474] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32474)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32474)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__32474,V2__y))) )
| ? [Vvar__0___24Anonymous__32475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32475)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32475)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__32475,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_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__32512] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32512)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32512)
& 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__32512)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__21023] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21023)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__21023)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__21023 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__3327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3327)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3327)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__3327)) )
| ? [Vvar__0___24Anonymous__3328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3328)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3328)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3328) )
| ( 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.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__43858] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__43858)
& ? [Vvar__1__Qden__43859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__43859)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__43858,Vvar__1__Qden__43859)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__43859 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qdiv',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.Qinv',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ( ( cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__25634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25634)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25634)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__25634) )
| ? [Vvar__0___24Anonymous__25635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25635)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25635)
& cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)),Vvar__0___24Anonymous__25635) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qle_bool',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQle__bool___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))) ).
fof('$_def_Coq.QArith.QArith_base.Qminus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V1__y)) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__43853] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__43853)
& ? [Vvar__1__Qden__43854] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__43854)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__43853,Vvar__1__Qden__43854)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__43853 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qopp',axiom,
! [V0__x] : cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V0__x) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)) ).
fof('$_def_Coq.QArith.QArith_base.Qplus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x)))),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qpower',axiom,
! [V0__q,V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ( V1__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__25639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25639)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25639)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__25639) )
| ? [Vvar__0___24Anonymous__25640] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25640)
& V1__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25640)
& cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V0__q,V1__z) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V0__q,Vvar__0___24Anonymous__25640)) ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qpower_positive',axiom,
cCoq_2eQArith_2eQArith__base_2eQpower__positive = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_def_Coq.QArith.Qreals.Q2R',axiom,
! [V0__x] : cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x)),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ).
fof('$_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('$_def_Coq.Reals.RIneq.neg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V0__n)
=> ? [Vvar__0__neg__59198] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__59198)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__59198,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& V0__n = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__59198)
& cCoq_2eReals_2eRIneq_2eneg___24a1(V0__n) = Vvar__0__neg__59198 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonneg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__n)
=> ? [Vvar__0__nonneg__50078] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__50078)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__50078))
& V0__n = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__50078)
& cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__n) = Vvar__0__nonneg__50078 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonpos',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V0__n)
=> ? [Vvar__0__nonpos__50083] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__50083)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__50083,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& V0__n = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__50083)
& cCoq_2eReals_2eRIneq_2enonpos___24a1(V0__n) = Vvar__0__nonpos__50083 ) ) ).
fof('$_def_Coq.Reals.RIneq.nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> ? [Vvar__0__nonzero__43871] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__43871)
& Vvar__0__nonzero__43871 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V0__n = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__43871)
& cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) = Vvar__0__nonzero__43871 ) ) ).
fof('$_def_Coq.Reals.RIneq.pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> ? [Vvar__0__pos__59193] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__59193)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__59193))
& V0__p = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__59193)
& cCoq_2eReals_2eRIneq_2epos___24a1(V0__p) = Vvar__0__pos__59193 ) ) ).
fof('$_def_Coq.Reals.R_Ifp.Int_part',axiom,
! [V0__r] : cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.Reals.R_Ifp.frac_part',axiom,
! [V0__r] : cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V0__r))) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__20750] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20750)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20750)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20750)
& ( ( Vvar__0___24Anonymous__20750 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__20753] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20753)
& Vvar__0___24Anonymous__20750 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20753)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__20750),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rabs',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) )
| ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V0__r) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmax',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__43941___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V1__y )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__43942___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ) ).
fof('$_def_Coq.Reals.Rbasic_fun.Rmin',axiom,
! [V0__x,V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__43893___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x )
| ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y),c_24__prop__43894___24a2(V0__x,V1__y))
& cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IPR',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__32505] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32505)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32505)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eR1,cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__32505)) )
| ? [Vvar__0___24Anonymous__32506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32506)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32506)
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(Vvar__0___24Anonymous__32506) )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) = cCoq_2eReals_2eRdefinitions_2eR1 ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__20763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20763)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20763)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__20763) )
| ? [Vvar__0___24Anonymous__20764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20764)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20764)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__20764)) ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
<=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
<=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2 ) ) ).
fof('$_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('$_def_Coq.Reals.Rfunctions.R_dist',axiom,
! [V0__x,V1__y] : cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__x,V1__y)) ).
fof('$_def_Coq.Reals.Rfunctions.infinite_sum',axiom,
! [V0__s,V1__l] :
( cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V0__s,V1__l)
<=> ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__eps,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V0__s,V5__n),V1__l),V2__eps)) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.powerRZ',axiom,
! [V0__x,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__32534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32534)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32534)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__32534)) )
| ? [Vvar__0___24Anonymous__32535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32535)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32535)
& cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__32535))) ) ) ) ).
fof('$_def_Coq.Reals.Rfunctions.sum_f_R0',axiom,
! [V1__f,V2__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__N)
=> ( ( V2__N = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__20784] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20784)
& V2__N = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20784)
& cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,V2__N) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V1__f,Vvar__0___24Anonymous__20784),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20784))) ) ) ) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__20817] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20817)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20817)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__20817)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__408___24a1(V0__A) ).
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('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__20057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20057)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20057)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20057) )
| ? [Vvar__0___24Anonymous__20058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20058)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20058)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20058) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__20059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20059)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20059)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20059) )
| ? [Vvar__0___24Anonymous__20060] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20060)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20060)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20060) ) ) ) ).
fof('$_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__3350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3350)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3350)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__3354] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3354)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3354)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__3350,Vvar__0___24Anonymous__3354)) )
| ? [Vvar__0___24Anonymous__3355] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3355)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3355)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__3350,Vvar__0___24Anonymous__3355) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3356] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3356)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3356)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__3360] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3360)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3360)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__3360,Vvar__0___24Anonymous__3356) )
| ? [Vvar__0___24Anonymous__3361] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3361)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3361)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__3356,Vvar__0___24Anonymous__3361)) ) ) ) ) ) ) ) ).
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__3383] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3383)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3383)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3384] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3384)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3384)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__3385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3385)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3385)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__3389] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3389)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3389)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__3385,Vvar__0___24Anonymous__3389) )
| ? [Vvar__0___24Anonymous__3390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3390)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3390)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__3391] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3391)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3391)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3395] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3395)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3395)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3396)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3396)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__3391,Vvar__0___24Anonymous__3396)) ) ) ) ) ) ) ) ).
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__46222] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__46222)
& ? [Vvar__3___24Anonymous__46223] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__46223)
& 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__46222,Vvar__3___24Anonymous__46223)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__46222 ) ) ) ) ).
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__46261] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46261)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46261)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46261)
& ( ? [Vvar__0___24Anonymous__46265] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46265)
& Vvar__0___24Anonymous__46261 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__46265)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__46265)) )
| ? [Vvar__0___24Anonymous__46266] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46266)
& Vvar__0___24Anonymous__46261 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__46266)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__46266)) )
| ( Vvar__0___24Anonymous__46261 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__46267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46267)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46267)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__47978] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__47978)
& ? [Vvar__3___24Anonymous__47979] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__47979)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__47978,Vvar__3___24Anonymous__47979)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__47979 ) ) ) ) ).
fof('$_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__3370] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3370)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3370)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3374] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3374)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3374)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3370,Vvar__0___24Anonymous__3374)) )
| ? [Vvar__0___24Anonymous__3375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3375)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3375)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3370,Vvar__0___24Anonymous__3375)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3376] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3376)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3376)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3380)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3380)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3376,Vvar__0___24Anonymous__3380)) )
| ? [Vvar__0___24Anonymous__3381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3381)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3381)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3376,Vvar__0___24Anonymous__3381)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__21064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21064)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21064)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21064) ) ) ) ).
fof('$_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__3400] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3400)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3400)
& 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__3400)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3365] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3365)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3365)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3365) )
| ? [Vvar__0___24Anonymous__3366] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3366)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3366)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3366) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__43751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43751)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43751)
& ( ? [Vvar__0___24Anonymous__43755] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43755)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43755)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__43751,Vvar__0___24Anonymous__43755)) )
| ? [Vvar__0___24Anonymous__43756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43756)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43756)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__43751,Vvar__0___24Anonymous__43756)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43751)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__43757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43757)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43757)
& ( ? [Vvar__0___24Anonymous__43761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43761)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43761)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__43757,Vvar__0___24Anonymous__43761)) )
| ? [Vvar__0___24Anonymous__43762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43762)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43762)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__43757,Vvar__0___24Anonymous__43762)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__43757)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__43763] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43763)
& V2__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43763)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43763)) )
| ? [Vvar__0___24Anonymous__43764] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43764)
& V2__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43764)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__43764)) )
| ( V2__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__44239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44239)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44239)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__44239) )
| ? [Vvar__0___24Anonymous__44240] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44240)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__44240)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow_pos',axiom,
! [V0__z] : cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(V0__z),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
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.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__21067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21067)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21067)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__21077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21077)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21067)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21077)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21077)
& ? [Vvar__2___24Anonymous__21085] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21085)
& ? [Vvar__3___24Anonymous__21086] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21086)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21067,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21077)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21085,Vvar__3___24Anonymous__21086)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21085),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21086)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21088] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21088)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21067)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21088)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21088)
& ? [Vvar__2___24Anonymous__21096] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21096)
& ? [Vvar__3___24Anonymous__21097] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21097)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21067,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21088)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21096,Vvar__3___24Anonymous__21097)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21096)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21097)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21099)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21099)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__21109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21109)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21099)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21109)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21109)
& ? [Vvar__2___24Anonymous__21117] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21117)
& ? [Vvar__3___24Anonymous__21118] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21118)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21099,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21109)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21117,Vvar__3___24Anonymous__21118)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21117)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21118))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21120] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21120)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21099)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21120)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21120)
& ? [Vvar__2___24Anonymous__21128] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21128)
& ? [Vvar__3___24Anonymous__21129] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21129)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21099,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21120)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21128,Vvar__3___24Anonymous__21129)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21128),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21129))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__46199] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46199)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46199)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__46200] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46200)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46200)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_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__46268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46268)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__46268)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__46268)) )
| ? [Vvar__0___24Anonymous__46269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__46269)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__46269)
& 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('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.ZArith.Zpower.Zpower_nat',axiom,
! [V0__z] : cCoq_2eZArith_2eZpower_2eZpower__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__20870,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),c_24__lam__20872___24a1(V0__z)) ).
fof('$_def_Coq.micromega.EnvRing.Pphi',axiom,
! [V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P] :
( cType___24t(V0__R)
=> ( cType___24t(V3__C)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,V7__P)
=> ( ? [Vvar__1___24Anonymous__32962] :
( t(Vvar__1___24Anonymous__32962,V3__C)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V3__C,Vvar__1___24Anonymous__32962)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = happ(V4__phi,Vvar__1___24Anonymous__32962) )
| ? [Vvar__1___24Anonymous__32964] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__32964)
& ? [Vvar__2___24Anonymous__32965] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__2___24Anonymous__32965)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V3__C,Vvar__1___24Anonymous__32964,Vvar__2___24Anonymous__32965)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,cCoq_2emicromega_2eEnv_2ejump___24a3(V0__R,Vvar__1___24Anonymous__32964,V6__l),Vvar__2___24Anonymous__32965) ) )
| ? [Vvar__1___24Anonymous__32968] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__1___24Anonymous__32968)
& ? [Vvar__2___24Anonymous__32969] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__32969)
& ? [Vvar__3___24Anonymous__32970] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,Vvar__3___24Anonymous__32970)
& V7__P = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V3__C,Vvar__1___24Anonymous__32968,Vvar__2___24Anonymous__32969,Vvar__3___24Anonymous__32970)
& cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,V7__P) = happ(happ(V1__radd,happ(happ(V2__rmul,cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__l,Vvar__1___24Anonymous__32968)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,cCoq_2emicromega_2eEnv_2ehd___24a2(V0__R,V6__l),Vvar__2___24Anonymous__32969))),cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,cCoq_2emicromega_2eEnv_2etail___24a2(V0__R,V6__l),Vvar__3___24Anonymous__32970)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.QMicromega.QWitness',axiom,
! [Vvar__35298] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(Vvar__35298)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vvar__35298) ) ).
fof('$_def_Coq.micromega.RMicromega.INZ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__59203] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59203)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__59203)
& cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__59203)) ) ) ) ).
fof('$_def_Coq.micromega.RMicromega.Qeval_nformula',axiom,
cCoq_2emicromega_2eRMicromega_2eQeval__nformula = cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a9(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eReals_2eRdefinitions_2eRle,cCoq_2eReals_2eRdefinitions_2eRlt,cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQreals_2eQ2R) ).
fof('$_def_Coq.micromega.RMicromega.Reval_op2',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR) )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = c_24__lam__43879 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRle )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRge )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRlt )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V0__o) = cCoq_2eReals_2eRdefinitions_2eRgt ) ) ) ).
fof('$_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__7402] :
( t(Vvar__1___24Anonymous__7402,V1__A)
& ? [Vvar__2___24Anonymous__7403] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__7403)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__7403)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__7402,Vvar__2___24Anonymous__7403)
& ( ( Vvar__2___24Anonymous__7403 = 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__7402)) ) )
| ? [Vvar__1___24Anonymous__7414] :
( t(Vvar__1___24Anonymous__7414,V1__A)
& ? [Vvar__2___24Anonymous__7415] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__7415)
& Vvar__2___24Anonymous__7403 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__7414,Vvar__2___24Anonymous__7415)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__7402))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__7403) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__35542] :
( t(Vvar__1___24Anonymous__35542,V1__A)
& ? [Vvar__2___24Anonymous__35543] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__35543)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__35542,Vvar__2___24Anonymous__35543)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__35542))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__35543,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.eval_nformula',axiom,
! [V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V7__C,V10__f)
=> ? [Vvar__2___24Anonymous__41301] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V7__C,Vvar__2___24Anonymous__41301)
& ? [Vvar__3___24Anonymous__41302] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vvar__3___24Anonymous__41302)
& V10__f = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V7__C),cCoq_2emicromega_2eRingMicromega_2eOp1,Vvar__2___24Anonymous__41301,Vvar__3___24Anonymous__41302)
& ( cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f)
<=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V0__R,V1__rO,V4__req,V5__rle,V6__rlt,Vvar__3___24Anonymous__41302,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V2__rplus,V3__rtimes,V7__C,V8__phi,V9__env,Vvar__2___24Anonymous__41301)) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__41219___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__41227___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__41235___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__41243___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_pol',axiom,
! [V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi] : cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V0__R,V1__rplus,V2__rtimes,V3__C,V4__phi) ).
fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__41474] :
( t(Vvar__1___24Anonymous__41474,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__41474)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__41474) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
=> ( ? [Vvar__1___24Anonymous__41492] :
( t(Vvar__1___24Anonymous__41492,V0__A)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
=> ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__41492)
& ( ? [Vvar__1___24Anonymous__41497] :
( t(Vvar__1___24Anonymous__41497,V1__B)
& V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__41497)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__41492),Vvar__1___24Anonymous__41497) )
| ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
| ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.BFormula',axiom,
! [V0__A] : cCoq_2emicromega_2eTauto_2eBFormula___24a1(V0__A) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__A,cProp,cCoq_2eInit_2eDatatypes_2eunit,cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_def_Coq.micromega.VarMap.find',axiom,
! [V0__A,V1__default,V3__vm,V4__p] :
( cType___24t(V0__A)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,V3__vm)
=> ( ( V3__vm = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V0__A)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = V1__default )
| ? [Vvar__1___24Anonymous__43176] :
( t(Vvar__1___24Anonymous__43176,V0__A)
& V3__vm = cCoq_2emicromega_2eVarMap_2eElt___24a2(V0__A,Vvar__1___24Anonymous__43176)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__1___24Anonymous__43176 )
| ? [Vvar__1___24Anonymous__43178] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__1___24Anonymous__43178)
& ? [Vvar__2___24Anonymous__43179] :
( t(Vvar__2___24Anonymous__43179,V0__A)
& ? [Vvar__3___24Anonymous__43180] :
( cCoq_2emicromega_2eVarMap_2et___24t(V0__A,Vvar__3___24Anonymous__43180)
& ( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> ( V3__vm = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V0__A,Vvar__1___24Anonymous__43178,Vvar__2___24Anonymous__43179,Vvar__3___24Anonymous__43180)
& ( ? [Vvar__0___24Anonymous__43193] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43193)
& V4__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43193)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__3___24Anonymous__43180,Vvar__0___24Anonymous__43193) )
| ? [Vvar__0___24Anonymous__43194] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43194)
& V4__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43194)
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,Vvar__1___24Anonymous__43178,Vvar__0___24Anonymous__43194) )
| ( V4__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2emicromega_2eVarMap_2efind___24a4(V0__A,V1__default,V3__vm,V4__p) = Vvar__2___24Anonymous__43179 ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__2372] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__2372)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2372) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__24134] :
( t(Vvar__1___24Anonymous__24134,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__24134)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__24134) )
| ? [Vvar__1___24Anonymous__24136] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24136)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__24136)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__24136,V15__l) )
| ? [Vvar__1___24Anonymous__24138] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24138)
& ? [Vvar__2___24Anonymous__24139] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24139)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__24138,Vvar__2___24Anonymous__24139)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24138)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24139)) ) )
| ? [Vvar__1___24Anonymous__24142] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24142)
& ? [Vvar__2___24Anonymous__24143] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24143)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__24142,Vvar__2___24Anonymous__24143)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24142)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24143)) ) )
| ? [Vvar__1___24Anonymous__24146] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24146)
& ? [Vvar__2___24Anonymous__24147] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24147)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__24146,Vvar__2___24Anonymous__24147)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24146)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24147)) ) )
| ? [Vvar__1___24Anonymous__24150] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24150)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__24150)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24150)) )
| ? [Vvar__1___24Anonymous__24152] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24152)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__24152)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24152)) )
| ? [Vvar__1___24Anonymous__24154] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24154)
& ? [Vvar__2___24Anonymous__24155] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__24155)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__24154,Vvar__2___24Anonymous__24155)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24154)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__24155)) ) )
| ? [Vvar__1___24Anonymous__24158] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__24158)
& ? [Vvar__2___24Anonymous__24159] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__24159)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__24158,Vvar__2___24Anonymous__24159)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__24158)),happ(V12__Cp__phi,Vvar__2___24Anonymous__24159)) ) ) ) ) ) ) ) ).
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__33851] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__33851)
& ? [Vvar__2___24Anonymous__33852] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__33852)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__33851,Vvar__2___24Anonymous__33852)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__33851),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__33852,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fnorm',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,V9__e)
=> ( ( V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ( V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__24628] :
( t(Vvar__1___24Anonymous__24628,V0__C)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V0__C,Vvar__1___24Anonymous__24628)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__24628),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__24630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24630)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V0__C,Vvar__1___24Anonymous__24630)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__24630),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V2__cI),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__24632] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24632)
& ? [Vvar__2___24Anonymous__24633] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__24633)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V0__C,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V0__C,V1__cO,V3__cadd,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__24635__24638__24708___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__24636__24639__24709___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633)))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633)),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__24637__24640__24710___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632,Vvar__2___24Anonymous__24633)))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__24635__24638__24708___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24632)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__24636__24639__24709___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24633)))) ) )
| ? [Vvar__1___24Anonymous__24645] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24645)
& ? [Vvar__2___24Anonymous__24646] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__24646)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V0__C,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V0__C,V1__cO,V5__csub,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__24648__24651__24714___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__24649__24652__24715___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646)))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646)),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646)),cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,c_24__let__var__var__14__s__24650__24653__24716___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645,Vvar__2___24Anonymous__24646)))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__24648__24651__24714___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24645)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__24649__24652__24715___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24646)))) ) )
| ? [Vvar__1___24Anonymous__24658] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24658)
& ? [Vvar__2___24Anonymous__24659] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__24659)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V0__C,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s1__24663__24667__24725___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659)),cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__24664__24668__24726___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__24664__24668__24726___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__24663__24667__24725___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658,Vvar__2___24Anonymous__24659))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__24661__24665__24723___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24658)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__24662__24666__24724___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24659)))) ) )
| ? [Vvar__1___24Anonymous__24676] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24676)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V0__C,Vvar__1___24Anonymous__24676)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V0__C,V6__copp,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__24677__24727___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676))),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__24677__24727___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__24677__24727___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24676))) )
| ? [Vvar__1___24Anonymous__24679] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24679)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V0__C,Vvar__1___24Anonymous__24679)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__11__x__24680__24728___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679)),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__24680__24728___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679)),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__11__x__24680__24728___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__11__x__24680__24728___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24679)))) )
| ? [Vvar__1___24Anonymous__24682] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24682)
& ? [Vvar__2___24Anonymous__24683] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__2___24Anonymous__24683)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V0__C,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__14__s1__24687__24691__24737___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__15__s2__24688__24692__24738___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683))),cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,c_24__let__var__var__15__s2__24688__24692__24738___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683)),cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,c_24__let__var__var__14__s1__24687__24691__24737___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682,Vvar__2___24Anonymous__24683))),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__13__y__24686__24690__24736___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683)),cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__24685__24689__24735___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24682)),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__13__y__24686__24690__24736___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__2___24Anonymous__24683))))) ) )
| ? [Vvar__1___24Anonymous__24700] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V0__C,Vvar__1___24Anonymous__24700)
& ? [Vvar__2___24Anonymous__24701] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__24701)
& V9__e = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V0__C,Vvar__1___24Anonymous__24700,Vvar__2___24Anonymous__24701)
& cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,c_24__let__var__var__12__x__24702__24704__24739___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700)),Vvar__2___24Anonymous__24701),cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V4__cmul,V7__ceqb,cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,c_24__let__var__var__12__x__24702__24704__24739___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700)),Vvar__2___24Anonymous__24701),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,c_24__let__var__var__12__x__24702__24704__24739___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,Vvar__1___24Anonymous__24700))) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__4028] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__4028)
& ? [Vvar__2___24Anonymous__4029] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__4029)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__4029)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__4028,Vvar__2___24Anonymous__4029)
& ( ( Vvar__2___24Anonymous__4029 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__4028)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__4040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__4040)
& ? [Vvar__2___24Anonymous__4041] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__4041)
& Vvar__2___24Anonymous__4029 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__4040,Vvar__2___24Anonymous__4041)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__4028)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__4029) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__20697] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20697)
& ? [Vvar__2__denum__20698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20698)
& ? [Vvar__3__condition__20699] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20699)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20697,Vvar__2__denum__20698,Vvar__3__condition__20699)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__20699 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20688] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20688)
& ? [Vvar__2__denum__20689] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20689)
& ? [Vvar__3__condition__20690] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20690)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20688,Vvar__2__denum__20689,Vvar__3__condition__20690)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__20689 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den] : cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__C,V9__cO,V10__cI,V11__ceqb,V12__phi,V13__Cpow,V14__Cp__phi,V15__rpow,V16__get__sign,V17__l,V18__num,V19__den) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__20677] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__20677)
& ? [Vvar__2__denum__20678] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__20678)
& ? [Vvar__3__condition__20679] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__20679)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__20677,Vvar__2__denum__20678,Vvar__3__condition__20679)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__20677 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__24449] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__24449)
& ? [Vvar__2__rsplit__common__24450] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__24450)
& ? [Vvar__3__rsplit__right__24451] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__24451)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__24449,Vvar__2__rsplit__common__24450,Vvar__3__rsplit__right__24451)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__24449 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__24469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__24469)
& ? [Vvar__2__rsplit__common__24470] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__24470)
& ? [Vvar__3__rsplit__right__24471] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__24471)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__24469,Vvar__2__rsplit__common__24470,Vvar__3__rsplit__right__24471)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__24471 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.split',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2] : cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,cCoq_2eNumbers_2eBinNums_2exH,V6__e2) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__48756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48756)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48756)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__48756))) )
| ? [Vvar__0___24Anonymous__48757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48757)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__48757)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__48757)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__25405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25405)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25405)
& 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__25405) )
| ? [Vvar__0___24Anonymous__25406] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25406)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25406)
& 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__25406)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.get_signZ',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__25458] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25458)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25458)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ? [Vvar__0___24Anonymous__25459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25459)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25459)
& cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25459)) ) ) ) ).
fof('$_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__607___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_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__871] :
( t(Vvar__1___24Anonymous__871,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__871)
& 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__871) )
| ? [Vvar__1___24Anonymous__873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__873)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__873)
& 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__873,V13__l) )
| ? [Vvar__1___24Anonymous__875] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__875)
& ? [Vvar__2___24Anonymous__876] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__876)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__875,Vvar__2___24Anonymous__876)
& 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__875)),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__876)) ) )
| ? [Vvar__1___24Anonymous__879] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__879)
& ? [Vvar__2___24Anonymous__880] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__880)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__879,Vvar__2___24Anonymous__880)
& 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__879)),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__880)) ) )
| ? [Vvar__1___24Anonymous__883] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__883)
& ? [Vvar__2___24Anonymous__884] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__884)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__883,Vvar__2___24Anonymous__884)
& 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__883)),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__884)) ) )
| ? [Vvar__1___24Anonymous__887] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__887)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__887)
& 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__887)) )
| ? [Vvar__1___24Anonymous__889] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__889)
& ? [Vvar__2___24Anonymous__890] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__890)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__889,Vvar__2___24Anonymous__890)
& 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__889)),happ(V10__Cp__phi,Vvar__2___24Anonymous__890)) ) ) ) ) ) ) ) ).
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__492] :
( t(Vvar__1___24Anonymous__492,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__492)
& ( ? [Vvar__1___24Anonymous__502] :
( t(Vvar__1___24Anonymous__502,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__502)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__492),Vvar__1___24Anonymous__502) )
| ? [Vvar__1___24Anonymous__504] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__504)
& ? [Vvar__2___24Anonymous__505] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__505)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__504,Vvar__2___24Anonymous__505)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__508] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__508)
& ? [Vvar__2___24Anonymous__509] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__509)
& ? [Vvar__3___24Anonymous__510] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__510)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__508,Vvar__2___24Anonymous__509,Vvar__3___24Anonymous__510)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__515] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__515)
& ? [Vvar__2___24Anonymous__516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__516)
& ( 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__515,Vvar__2___24Anonymous__516)
& ( ? [Vvar__1___24Anonymous__536] :
( t(Vvar__1___24Anonymous__536,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__536)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__538] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__538)
& ? [Vvar__2___24Anonymous__539] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__539)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__515)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__538)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__538,Vvar__2___24Anonymous__539)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__515,Vvar__1___24Anonymous__538) = 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__516,Vvar__2___24Anonymous__539) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__515,Vvar__1___24Anonymous__538) = 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__515,Vvar__1___24Anonymous__538) = 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__544] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__544)
& ? [Vvar__2___24Anonymous__545] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__545)
& ? [Vvar__3___24Anonymous__546] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__546)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__544,Vvar__2___24Anonymous__545,Vvar__3___24Anonymous__546)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__551] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__551)
& ? [Vvar__2___24Anonymous__552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__552)
& ? [Vvar__3___24Anonymous__553] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__553)
& ( 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__551,Vvar__2___24Anonymous__552,Vvar__3___24Anonymous__553)
& ( ? [Vvar__1___24Anonymous__586] :
( t(Vvar__1___24Anonymous__586,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__586)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__588] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__588)
& ? [Vvar__2___24Anonymous__589] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__589)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__588,Vvar__2___24Anonymous__589)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__592)
& ? [Vvar__2___24Anonymous__593] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__593)
& ? [Vvar__3___24Anonymous__594] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__594)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__552)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__593)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__592,Vvar__2___24Anonymous__593,Vvar__3___24Anonymous__594)
& ( ( cType___24t(V0__C)
=> ( c_24__type__607___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__551)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__592)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__552,Vvar__2___24Anonymous__593) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__551,Vvar__1___24Anonymous__592) = 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__553,Vvar__3___24Anonymous__594) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__551,Vvar__1___24Anonymous__592) = 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__552,Vvar__2___24Anonymous__593) = 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__552,Vvar__2___24Anonymous__593) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__25884___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__25885___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__25886___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__1321] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__1321)
& ? [Vvar__2___24Anonymous__1322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__1322)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__1321)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__1321,Vvar__2___24Anonymous__1322)
& ? [Vvar__2___24Anonymous__1340] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__1340)
& ? [Vvar__3___24Anonymous__1341] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__1341)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__1322)
=> ( Vvar__1___24Anonymous__1321 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__1340,Vvar__3___24Anonymous__1341)
& ( ( Vvar__2___24Anonymous__1322 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__1340)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__1341))) ) )
| ? [Vvar__1___24Anonymous__1352] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__1352)
& ? [Vvar__2___24Anonymous__1353] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__1353)
& Vvar__2___24Anonymous__1322 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__1352,Vvar__2___24Anonymous__1353)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__1340)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__1341)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__1322) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__1584] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__1584)
& ? [Vvar__2___24Anonymous__1585] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__1585)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__1584)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__1584,Vvar__2___24Anonymous__1585)
& ? [Vvar__2___24Anonymous__1601] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1601)
& ? [Vvar__3___24Anonymous__1602] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__1602)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__1062___24t(V0__C,V3__cadd)
=> ( c_24__type__1062___24t(V0__C,V4__cmul)
=> ( c_24__type__1062___24t(V0__C,V5__csub)
=> ( c_24__type__1071___24t(V0__C,V6__copp)
=> ( c_24__type__607___24t(V0__C,V7__ceqb)
=> ( c_24__type__1315___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1601)
=> ( Vvar__1___24Anonymous__1584 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__1601,Vvar__3___24Anonymous__1602)
& ( ? [Vvar__1___24Anonymous__1610] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__1610)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__1601)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__1610)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__1610,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__1602)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__1585)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__1601)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__1585) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__1165___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
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('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__1820] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1820)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1820)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__1820) ) ) ) ) ).
fof('$_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__43997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43997)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__43997)
& 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__43998__44001___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43997)),c_24__let__var__6__p__43998__44001___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43997))) )
| ? [Vvar__0___24Anonymous__43999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__43999)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__43999)
& 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__44000__44002___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43999)),c_24__let__var__6__p__44000__44002___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__43999)) )
| ( 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('$_def_QuicksortComplexity.list_utils.add',axiom,
cQuicksortComplexity_2elist__utils_2eadd = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_QuicksortComplexity.list_utils.concat',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2econcat___24a1(V0__T) = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) ).
fof('$_def_QuicksortComplexity.list_utils.count',axiom,
! [V0__X,V1__p,V3__l] :
( cType___24t(V0__X)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X)
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__13046] :
( t(Vvar__1___24Anonymous__13046,V0__X)
& ? [Vvar__2___24Anonymous__13047] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,Vvar__2___24Anonymous__13047)
& ( cType___24t(V0__X)
=> ( c_24__type__6478___24t(V0__X,V1__p)
=> ( t(Vvar__1___24Anonymous__13046,V0__X)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,Vvar__1___24Anonymous__13046,Vvar__2___24Anonymous__13047)
& ( ( happ(V1__p,Vvar__1___24Anonymous__13046) = cCoq_2eInit_2eDatatypes_2etrue
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__13047)) )
| ( happ(V1__p,Vvar__1___24Anonymous__13046) = cCoq_2eInit_2eDatatypes_2efalse
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__13047) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__13388] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__13388)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__13388)
& 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__13388,V3__x)) ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_below.nb_val',axiom,
! [V0__n,V1__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__nb)
=> ? [Vvar__0__v__2879] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__2879)
& ? [Vvar__1__p__2880] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__2880)
& V1__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__2879,Vvar__1__p__2880)
& cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__nb) = Vvar__0__v__2879 ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_seqs.nats',axiom,
! [V1__b,V2__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__w)
=> ( ( V2__w = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V2__w) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__316] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__316)
& V2__w = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__316)
& cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V2__w) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__b,cQuicksortComplexity_2enat__seqs_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__b),Vvar__0___24Anonymous__316)) ) ) ) ).
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.vec.from_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__30849] :
( t(Vvar__1___24Anonymous__30849,V1__A)
& ? [Vvar__2___24Anonymous__30850] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__30850)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__30849,Vvar__2___24Anonymous__30850)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__30849,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__30850),cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,Vvar__2___24Anonymous__30850)) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.head',axiom,
! [V0__A,V1__n,V2__v] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> ( ( V2__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v) = cCoq_2eInit_2eLogic_2eI )
| ? [Vvar__1__h__19280] :
( t(Vvar__1__h__19280,V0__A)
& ? [Vvar__2__n__19281] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__19281)
& ? [Vvar__3___24Anonymous__19282] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__19281,Vvar__3___24Anonymous__19282)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__19280,Vvar__2__n__19281,Vvar__3___24Anonymous__19282)
& cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v) = Vvar__1__h__19280 ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.tail',axiom,
! [V0__n,V1__A,V2__v] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cType___24t(V1__A)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V2__v)
=> ( ( V2__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
& cQuicksortComplexity_2evec_2etail___24a3(V0__n,V1__A,V2__v) = cCoq_2eInit_2eLogic_2eI )
| ? [Vvar__1__h__2900] :
( t(Vvar__1__h__2900,V1__A)
& ? [Vvar__2__n__2901] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__2901)
& ? [Vvar__3___24Anonymous__2902] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__2901,Vvar__3___24Anonymous__2902)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__2900,Vvar__2__n__2901,Vvar__3___24Anonymous__2902)
& cQuicksortComplexity_2evec_2etail___24a3(V0__n,V1__A,V2__v) = Vvar__3___24Anonymous__2902 ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.to_list',axiom,
! [V1__X,V2__n,V3__v] :
( cType___24t(V1__X)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,V2__n,V3__v)
=> ( ( V3__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__X)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__X) )
| ? [Vvar__1__h__19296] :
( t(Vvar__1__h__19296,V1__X)
& ? [Vvar__2__n__19297] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__19297)
& ? [Vvar__3___24Anonymous__19298] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__19297,Vvar__3___24Anonymous__19298)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__19296,Vvar__2__n__19297,Vvar__3___24Anonymous__19298)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__X,Vvar__1__h__19296,cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,Vvar__2__n__19297,Vvar__3___24Anonymous__19298)) ) ) ) ) ) ) ) ).
fof('$_def_sums_and_averages.Ravg',axiom,
! [V0__l] : csums__and__averages_2eRavg___24a1(V0__l) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(csums__and__averages_2eRsum___24a1(V0__l),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V0__l))) ).
fof('$_def_sums_and_averages.Rsum',axiom,
csums__and__averages_2eRsum = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) ).
fof('$_def_sums_and_averages.RsumOver',axiom,
! [V0__X,V1__l,V2__f] : csums__and__averages_2eRsumOver___24a3(V0__X,V1__l,V2__f) = csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V2__f,V1__l)) ).
fof('$_def_sums_and_averages.sum',axiom,
! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& csums__and__averages_2esum___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__1923] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__1923)
& ? [Vvar__2___24Anonymous__1924] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__1924)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__1923,Vvar__2___24Anonymous__1924)
& csums__and__averages_2esum___24a1(V1__l) = cCoq_2eInit_2eNat_2eadd___24a2(Vvar__1___24Anonymous__1923,csums__and__averages_2esum___24a1(Vvar__2___24Anonymous__1924)) ) ) ) ) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3493,Vvar__1___24Anonymous__3494,Vvar__0__A__3495] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3493,Vvar__1___24Anonymous__3494) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3495) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__3515,Vvar__1__B__3516,Vvar__2___24Anonymous__3517,Vvar__0__A__3518,Vvar__1__B__3519,Vvar__2___24Anonymous__3520] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__3515,Vvar__1__B__3516,Vvar__2___24Anonymous__3517) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__3518,Vvar__1__B__3519,Vvar__2___24Anonymous__3520) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__21,Vvar__0__A__22,Vvar__1___24Anonymous__23,Vvar__2___24Anonymous__24] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__21) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22,Vvar__1___24Anonymous__23,Vvar__2___24Anonymous__24) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__10908,Vvar__1__B__10909,Vvar__2___24Anonymous__10910,Vvar__0__A__10911,Vvar__1__B__10912,Vvar__2___24Anonymous__10913] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10908,Vvar__1__B__10909,Vvar__2___24Anonymous__10910) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10911,Vvar__1__B__10912) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2348,Vvar__1__B__2349,Vvar__2___24Anonymous__2350,Vvar__0__A__2351,Vvar__1__B__2352,Vvar__2___24Anonymous__2353] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2348,Vvar__1__B__2349) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2351,Vvar__1__B__2352) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1943] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1943) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1952] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1952) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1935,Vvar__0___24Anonymous__1936] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1935) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1936) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__35630,Vvar__1___24Anonymous__35631,Vvar__0__x__35632,Vvar__1__n__35633,Vvar__2___24Anonymous__35634] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__35630) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__35632,Vvar__1__n__35633) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__2775,Vvar__0__A__2776,Vvar__1__h__2777,Vvar__2__n__2778,Vvar__3___24Anonymous__2779] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2775) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2776,Vvar__1__h__2777,Vvar__2__n__2778,Vvar__3___24Anonymous__2779) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__20286,Vvar__1___24Anonymous__20287,Vvar__0__C__20288,Vvar__1___24Anonymous__20289] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__20286,Vvar__1___24Anonymous__20287) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__20288,Vvar__1___24Anonymous__20289) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__379,Vvar__1___24Anonymous__380,Vvar__0__C__381,Vvar__1___24Anonymous__382,Vvar__2___24Anonymous__383] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__379,Vvar__1___24Anonymous__380) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__381,Vvar__1___24Anonymous__382,Vvar__2___24Anonymous__383) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__195,Vvar__1___24Anonymous__196,Vvar__0__C__197,Vvar__1___24Anonymous__198] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__195,Vvar__1___24Anonymous__196) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__197,Vvar__1___24Anonymous__198) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__11309,Vvar__1__TX__11310,Vvar__2__AA__11311,Vvar__3__AF__11312,Vvar__0__TA__11313,Vvar__1__TX__11314,Vvar__2__AA__11315,Vvar__3__AF__11316] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11309,Vvar__1__TX__11310,Vvar__2__AA__11311,Vvar__3__AF__11312) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11313,Vvar__1__TX__11314,Vvar__2__AA__11315,Vvar__3__AF__11316) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__43144,Vvar__0__A__43145,Vvar__1___24Anonymous__43146] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__43144) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__43145,Vvar__1___24Anonymous__43146) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__2400,Vvar__1___24Anonymous__2401] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__2400,Vvar__1___24Anonymous__2401) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20609,Vvar__0__C__20610] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20609) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20610) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__824,Vvar__0__C__825] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__824) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__825) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__466,Vvar__1___24Anonymous__467,Vvar__0__C__468,Vvar__1___24Anonymous__469,Vvar__2___24Anonymous__470] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__466,Vvar__1___24Anonymous__467) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__468,Vvar__1___24Anonymous__469,Vvar__2___24Anonymous__470) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__634,Vvar__1___24Anonymous__635] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__634,Vvar__1___24Anonymous__635) ).
fof('$_fix_19747_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__19762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19762)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19762)
& ( ? [Vvar__0___24Anonymous__19766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19766)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19766)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__19747__1__add__carry___24a2(Vvar__0___24Anonymous__19762,Vvar__0___24Anonymous__19766)) )
| ? [Vvar__0___24Anonymous__19767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19767)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19767)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__19747__1__add__carry___24a2(Vvar__0___24Anonymous__19762,Vvar__0___24Anonymous__19767)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19762)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__19768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19768)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19768)
& ( ? [Vvar__0___24Anonymous__19772] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19772)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19772)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__19747__1__add__carry___24a2(Vvar__0___24Anonymous__19768,Vvar__0___24Anonymous__19772)) )
| ? [Vvar__0___24Anonymous__19773] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19773)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19773)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__19768,Vvar__0___24Anonymous__19773)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19768)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__19774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19774)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19774)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19774)) )
| ? [Vvar__0___24Anonymous__19775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19775)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19775)
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__19775)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__19747__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_2869_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__2869__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__2870] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2870)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2870)
& c_24__fix__2869__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__2869__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__2870,Vv__CANONICAL__2)) ) ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3500,Vvar__0__A__3501] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3500) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3501)
=> Vvar__0__A__3500 = Vvar__0__A__3501 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__5,Vvar__0___24Anonymous__6] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6)
=> Vvar__0___24Anonymous__5 = Vvar__0___24Anonymous__6 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__3496,Vvar__0__A__3497,Vvar__1___24Anonymous__3498,Vvar__1___24Anonymous__3499] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3496,Vvar__1___24Anonymous__3498) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3497,Vvar__1___24Anonymous__3499)
=> ( Vvar__1___24Anonymous__3498 = Vvar__1___24Anonymous__3499
& Vvar__0__A__3496 = Vvar__0__A__3497 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__27,Vvar__0__A__28,Vvar__1___24Anonymous__29,Vvar__1___24Anonymous__30,Vvar__2___24Anonymous__31,Vvar__2___24Anonymous__32] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27,Vvar__1___24Anonymous__29,Vvar__2___24Anonymous__31) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28,Vvar__1___24Anonymous__30,Vvar__2___24Anonymous__32)
=> ( Vvar__2___24Anonymous__31 = Vvar__2___24Anonymous__32
& Vvar__1___24Anonymous__29 = Vvar__1___24Anonymous__30
& Vvar__0__A__27 = Vvar__0__A__28 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__3521,Vvar__0__A__3522,Vvar__1__B__3523,Vvar__1__B__3524,Vvar__2___24Anonymous__3525,Vvar__2___24Anonymous__3526] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__3521,Vvar__1__B__3523,Vvar__2___24Anonymous__3525) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__3522,Vvar__1__B__3524,Vvar__2___24Anonymous__3526)
=> ( Vvar__2___24Anonymous__3525 = Vvar__2___24Anonymous__3526
& Vvar__1__B__3523 = Vvar__1__B__3524
& Vvar__0__A__3521 = Vvar__0__A__3522 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__3527,Vvar__0__A__3528,Vvar__1__B__3529,Vvar__1__B__3530,Vvar__2___24Anonymous__3531,Vvar__2___24Anonymous__3532] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__3527,Vvar__1__B__3529,Vvar__2___24Anonymous__3531) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__3528,Vvar__1__B__3530,Vvar__2___24Anonymous__3532)
=> ( Vvar__2___24Anonymous__3531 = Vvar__2___24Anonymous__3532
& Vvar__1__B__3529 = Vvar__1__B__3530
& Vvar__0__A__3527 = Vvar__0__A__3528 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__25,Vvar__0__A__26] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__25) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26)
=> Vvar__0__A__25 = Vvar__0__A__26 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__339,Vvar__0__A__340,Vvar__1__B__341,Vvar__1__B__342,Vvar__2___24Anonymous__343,Vvar__2___24Anonymous__344,Vvar__3___24Anonymous__345,Vvar__3___24Anonymous__346] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__339,Vvar__1__B__341,Vvar__2___24Anonymous__343,Vvar__3___24Anonymous__345) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__340,Vvar__1__B__342,Vvar__2___24Anonymous__344,Vvar__3___24Anonymous__346)
=> ( Vvar__3___24Anonymous__345 = Vvar__3___24Anonymous__346
& Vvar__2___24Anonymous__343 = Vvar__2___24Anonymous__344
& Vvar__1__B__341 = Vvar__1__B__342
& Vvar__0__A__339 = Vvar__0__A__340 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__2723,Vvar__0__A__2724,Vvar__1__P__2725,Vvar__1__P__2726,Vvar__2__x__2727,Vvar__2__x__2728,Vvar__3___24Anonymous__2729,Vvar__3___24Anonymous__2730] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2723,Vvar__1__P__2725,Vvar__2__x__2727) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2724,Vvar__1__P__2726,Vvar__2__x__2728)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__2727 = Vvar__2__x__2728
& Vvar__1__P__2725 = Vvar__1__P__2726
& Vvar__0__A__2723 = Vvar__0__A__2724 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__10824,Vvar__0__A__10825,Vvar__1__P__10826,Vvar__1__P__10827,Vvar__2__x__10828,Vvar__2__x__10829,Vvar__3___24Anonymous__10830,Vvar__3___24Anonymous__10831] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10824,Vvar__1__P__10826,Vvar__2__x__10828,Vvar__3___24Anonymous__10830) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10825,Vvar__1__P__10827,Vvar__2__x__10829,Vvar__3___24Anonymous__10831)
=> ( Vvar__3___24Anonymous__10830 = Vvar__3___24Anonymous__10831
& Vvar__2__x__10828 = Vvar__2__x__10829
& Vvar__1__P__10826 = Vvar__1__P__10827
& Vvar__0__A__10824 = Vvar__0__A__10825 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__10914,Vvar__0__A__10915,Vvar__1__B__10916,Vvar__1__B__10917,Vvar__2___24Anonymous__10918,Vvar__2___24Anonymous__10919] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10914,Vvar__1__B__10916,Vvar__2___24Anonymous__10918) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10915,Vvar__1__B__10917,Vvar__2___24Anonymous__10919)
=> ( Vvar__2___24Anonymous__10918 = Vvar__2___24Anonymous__10919
& Vvar__1__B__10916 = Vvar__1__B__10917
& Vvar__0__A__10914 = Vvar__0__A__10915 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__10920,Vvar__0__A__10921,Vvar__1__B__10922,Vvar__1__B__10923,Vvar__2___24Anonymous__10924,Vvar__2___24Anonymous__10925] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10920,Vvar__1__B__10922) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10921,Vvar__1__B__10923)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__10922 = Vvar__1__B__10923
& Vvar__0__A__10920 = Vvar__0__A__10921 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__2354,Vvar__0__A__2355,Vvar__1__B__2356,Vvar__1__B__2357,Vvar__2___24Anonymous__2358,Vvar__2___24Anonymous__2359] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2354,Vvar__1__B__2356) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2355,Vvar__1__B__2357)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2356 = Vvar__1__B__2357
& Vvar__0__A__2354 = Vvar__0__A__2355 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2360,Vvar__0__A__2361,Vvar__1__B__2362,Vvar__1__B__2363,Vvar__2___24Anonymous__2364,Vvar__2___24Anonymous__2365] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2360,Vvar__1__B__2362) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2361,Vvar__1__B__2363)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2362 = Vvar__1__B__2363
& Vvar__0__A__2360 = Vvar__0__A__2361 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1944,Vvar__0___24Anonymous__1945] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1944) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1945)
=> Vvar__0___24Anonymous__1944 = Vvar__0___24Anonymous__1945 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1955,Vvar__0___24Anonymous__1956] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1955) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1956)
=> Vvar__0___24Anonymous__1955 = Vvar__0___24Anonymous__1956 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1953,Vvar__0___24Anonymous__1954] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1953) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1954)
=> Vvar__0___24Anonymous__1953 = Vvar__0___24Anonymous__1954 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1937,Vvar__0___24Anonymous__1938] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1937) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1938)
=> Vvar__0___24Anonymous__1937 = Vvar__0___24Anonymous__1938 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1939,Vvar__0___24Anonymous__1940] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1939) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1940)
=> Vvar__0___24Anonymous__1939 = Vvar__0___24Anonymous__1940 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__25614,Vvar__0__Qnum__25615,Vvar__1__Qden__25616,Vvar__1__Qden__25617] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__25614,Vvar__1__Qden__25616) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__25615,Vvar__1__Qden__25617)
=> ( Vvar__1__Qden__25616 = Vvar__1__Qden__25617
& Vvar__0__Qnum__25614 = Vvar__0__Qnum__25615 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__49774,Vvar__0__neg__49775,Vvar__1__cond__neg__49776,Vvar__1__cond__neg__49777] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__49774) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__49775)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__49774 = Vvar__0__neg__49775 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__49753,Vvar__0__nonneg__49754,Vvar__1__cond__nonneg__49755,Vvar__1__cond__nonneg__49756] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__49753) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__49754)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__49753 = Vvar__0__nonneg__49754 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__49767,Vvar__0__nonpos__49768,Vvar__1__cond__nonpos__49769,Vvar__1__cond__nonpos__49770] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__49767) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__49768)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__49767 = Vvar__0__nonpos__49768 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__35334,Vvar__0__nonzero__35335,Vvar__1__cond__nonzero__35336,Vvar__1__cond__nonzero__35337] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__35334) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__35335)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__35334 = Vvar__0__nonzero__35335 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__49760,Vvar__0__pos__49761,Vvar__1__cond__pos__49762,Vvar__1__cond__pos__49763] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__49760) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__49761)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__49760 = Vvar__0__pos__49761 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__35645,Vvar__0__x__35646,Vvar__1__n__35647,Vvar__1__n__35648,Vvar__2___24Anonymous__35649,Vvar__2___24Anonymous__35650] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__35645,Vvar__1__n__35647) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__35646,Vvar__1__n__35648)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__35647 = Vvar__1__n__35648
& Vvar__0__x__35645 = Vvar__0__x__35646 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__35635,Vvar__0__x__35636,Vvar__1___24Anonymous__35637,Vvar__1___24Anonymous__35638] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__35635) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__35636)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__35635 = Vvar__0__x__35636 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__35639,Vvar__0__x__35640,Vvar__1__n__35641,Vvar__1__n__35642,Vvar__2___24Anonymous__35643,Vvar__2___24Anonymous__35644] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__35639,Vvar__1__n__35641) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__35640,Vvar__1__n__35642)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__35641 = Vvar__1__n__35642
& Vvar__0__x__35639 = Vvar__0__x__35640 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__2782,Vvar__0__A__2783,Vvar__1__h__2784,Vvar__1__h__2785,Vvar__2__n__2786,Vvar__2__n__2787,Vvar__3___24Anonymous__2788,Vvar__3___24Anonymous__2789] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2782,Vvar__1__h__2784,Vvar__2__n__2786,Vvar__3___24Anonymous__2788) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2783,Vvar__1__h__2785,Vvar__2__n__2787,Vvar__3___24Anonymous__2789)
=> ( Vvar__3___24Anonymous__2788 = Vvar__3___24Anonymous__2789
& Vvar__2__n__2786 = Vvar__2__n__2787
& Vvar__1__h__2784 = Vvar__1__h__2785
& Vvar__0__A__2782 = Vvar__0__A__2783 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__2780,Vvar__0__A__2781] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2780) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2781)
=> Vvar__0__A__2780 = Vvar__0__A__2781 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__20294,Vvar__0__C__20295,Vvar__1___24Anonymous__20296,Vvar__1___24Anonymous__20297] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__20294,Vvar__1___24Anonymous__20296) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__20295,Vvar__1___24Anonymous__20297)
=> ( Vvar__1___24Anonymous__20296 = Vvar__1___24Anonymous__20297
& Vvar__0__C__20294 = Vvar__0__C__20295 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__20298,Vvar__0__C__20299,Vvar__1___24Anonymous__20300,Vvar__1___24Anonymous__20301,Vvar__2___24Anonymous__20302,Vvar__2___24Anonymous__20303] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__20298,Vvar__1___24Anonymous__20300,Vvar__2___24Anonymous__20302) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__20299,Vvar__1___24Anonymous__20301,Vvar__2___24Anonymous__20303)
=> ( Vvar__2___24Anonymous__20302 = Vvar__2___24Anonymous__20303
& Vvar__1___24Anonymous__20300 = Vvar__1___24Anonymous__20301
& Vvar__0__C__20298 = Vvar__0__C__20299 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__20290,Vvar__0__C__20291,Vvar__1___24Anonymous__20292,Vvar__1___24Anonymous__20293] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__20290,Vvar__1___24Anonymous__20292) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__20291,Vvar__1___24Anonymous__20293)
=> ( Vvar__1___24Anonymous__20292 = Vvar__1___24Anonymous__20293
& Vvar__0__C__20290 = Vvar__0__C__20291 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__20310,Vvar__0__C__20311,Vvar__1___24Anonymous__20312,Vvar__1___24Anonymous__20313,Vvar__2___24Anonymous__20314,Vvar__2___24Anonymous__20315] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__20310,Vvar__1___24Anonymous__20312,Vvar__2___24Anonymous__20314) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__20311,Vvar__1___24Anonymous__20313,Vvar__2___24Anonymous__20315)
=> ( Vvar__2___24Anonymous__20314 = Vvar__2___24Anonymous__20315
& Vvar__1___24Anonymous__20312 = Vvar__1___24Anonymous__20313
& Vvar__0__C__20310 = Vvar__0__C__20311 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__20316,Vvar__0__C__20317,Vvar__1___24Anonymous__20318,Vvar__1___24Anonymous__20319] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__20316,Vvar__1___24Anonymous__20318) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__20317,Vvar__1___24Anonymous__20319)
=> ( Vvar__1___24Anonymous__20318 = Vvar__1___24Anonymous__20319
& Vvar__0__C__20316 = Vvar__0__C__20317 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__20320,Vvar__0__C__20321,Vvar__1___24Anonymous__20322,Vvar__1___24Anonymous__20323,Vvar__2___24Anonymous__20324,Vvar__2___24Anonymous__20325] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__20320,Vvar__1___24Anonymous__20322,Vvar__2___24Anonymous__20324) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__20321,Vvar__1___24Anonymous__20323,Vvar__2___24Anonymous__20325)
=> ( Vvar__2___24Anonymous__20324 = Vvar__2___24Anonymous__20325
& Vvar__1___24Anonymous__20322 = Vvar__1___24Anonymous__20323
& Vvar__0__C__20320 = Vvar__0__C__20321 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__20304,Vvar__0__C__20305,Vvar__1___24Anonymous__20306,Vvar__1___24Anonymous__20307,Vvar__2___24Anonymous__20308,Vvar__2___24Anonymous__20309] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__20304,Vvar__1___24Anonymous__20306,Vvar__2___24Anonymous__20308) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__20305,Vvar__1___24Anonymous__20307,Vvar__2___24Anonymous__20309)
=> ( Vvar__2___24Anonymous__20308 = Vvar__2___24Anonymous__20309
& Vvar__1___24Anonymous__20306 = Vvar__1___24Anonymous__20307
& Vvar__0__C__20304 = Vvar__0__C__20305 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__394,Vvar__0__C__395,Vvar__1___24Anonymous__396,Vvar__1___24Anonymous__397,Vvar__2___24Anonymous__398,Vvar__2___24Anonymous__399,Vvar__3___24Anonymous__400,Vvar__3___24Anonymous__401] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__394,Vvar__1___24Anonymous__396,Vvar__2___24Anonymous__398,Vvar__3___24Anonymous__400) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__395,Vvar__1___24Anonymous__397,Vvar__2___24Anonymous__399,Vvar__3___24Anonymous__401)
=> ( Vvar__3___24Anonymous__400 = Vvar__3___24Anonymous__401
& Vvar__2___24Anonymous__398 = Vvar__2___24Anonymous__399
& Vvar__1___24Anonymous__396 = Vvar__1___24Anonymous__397
& Vvar__0__C__394 = Vvar__0__C__395 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__384,Vvar__0__C__385,Vvar__1___24Anonymous__386,Vvar__1___24Anonymous__387] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__384,Vvar__1___24Anonymous__386) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__385,Vvar__1___24Anonymous__387)
=> ( Vvar__1___24Anonymous__386 = Vvar__1___24Anonymous__387
& Vvar__0__C__384 = Vvar__0__C__385 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__388,Vvar__0__C__389,Vvar__1___24Anonymous__390,Vvar__1___24Anonymous__391,Vvar__2___24Anonymous__392,Vvar__2___24Anonymous__393] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__388,Vvar__1___24Anonymous__390,Vvar__2___24Anonymous__392) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__389,Vvar__1___24Anonymous__391,Vvar__2___24Anonymous__393)
=> ( Vvar__2___24Anonymous__392 = Vvar__2___24Anonymous__393
& Vvar__1___24Anonymous__390 = Vvar__1___24Anonymous__391
& Vvar__0__C__388 = Vvar__0__C__389 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__35482,Vvar__0__r__35483] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35482) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35483)
=> Vvar__0__r__35482 = Vvar__0__r__35483 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__35470,Vvar__0__r1__35471,Vvar__1__r2__35472,Vvar__1__r2__35473] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35470,Vvar__1__r2__35472) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35471,Vvar__1__r2__35473)
=> ( Vvar__1__r2__35472 = Vvar__1__r2__35473
& Vvar__0__r1__35470 = Vvar__0__r1__35471 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__35474,Vvar__0__r1__35475,Vvar__1__r2__35476,Vvar__1__r2__35477] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35474,Vvar__1__r2__35476) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35475,Vvar__1__r2__35477)
=> ( Vvar__1__r2__35476 = Vvar__1__r2__35477
& Vvar__0__r1__35474 = Vvar__0__r1__35475 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__35484,Vvar__0__r__35485] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35484) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35485)
=> Vvar__0__r__35484 = Vvar__0__r__35485 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__35466,Vvar__0__r1__35467,Vvar__1__r2__35468,Vvar__1__r2__35469] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35466,Vvar__1__r2__35468) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35467,Vvar__1__r2__35469)
=> ( Vvar__1__r2__35468 = Vvar__1__r2__35469
& Vvar__0__r1__35466 = Vvar__0__r1__35467 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__35478,Vvar__0__r1__35479,Vvar__1__z__35480,Vvar__1__z__35481] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35478,Vvar__1__z__35480) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35479,Vvar__1__z__35481)
=> ( Vvar__1__z__35480 = Vvar__1__z__35481
& Vvar__0__r1__35478 = Vvar__0__r1__35479 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__35462,Vvar__0__r__35463] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35462) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35463)
=> Vvar__0__r__35462 = Vvar__0__r__35463 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__35464,Vvar__0__r__35465] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35464) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35465)
=> Vvar__0__r__35464 = Vvar__0__r__35465 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__20805,Vvar__0__T__20806,Vvar__1__Flhs__20807,Vvar__1__Flhs__20808,Vvar__2__Fop__20809,Vvar__2__Fop__20810,Vvar__3__Frhs__20811,Vvar__3__Frhs__20812] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20805,Vvar__1__Flhs__20807,Vvar__2__Fop__20809,Vvar__3__Frhs__20811) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20806,Vvar__1__Flhs__20808,Vvar__2__Fop__20810,Vvar__3__Frhs__20812)
=> ( Vvar__3__Frhs__20811 = Vvar__3__Frhs__20812
& Vvar__2__Fop__20809 = Vvar__2__Fop__20810
& Vvar__1__Flhs__20807 = Vvar__1__Flhs__20808
& Vvar__0__T__20805 = Vvar__0__T__20806 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__219,Vvar__0__C__220,Vvar__1___24Anonymous__221,Vvar__1___24Anonymous__222,Vvar__2___24Anonymous__223,Vvar__2___24Anonymous__224] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__219,Vvar__1___24Anonymous__221,Vvar__2___24Anonymous__223) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__220,Vvar__1___24Anonymous__222,Vvar__2___24Anonymous__224)
=> ( Vvar__2___24Anonymous__223 = Vvar__2___24Anonymous__224
& Vvar__1___24Anonymous__221 = Vvar__1___24Anonymous__222
& Vvar__0__C__219 = Vvar__0__C__220 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__225,Vvar__0__C__226,Vvar__1___24Anonymous__227,Vvar__1___24Anonymous__228] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__225,Vvar__1___24Anonymous__227) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__226,Vvar__1___24Anonymous__228)
=> ( Vvar__1___24Anonymous__227 = Vvar__1___24Anonymous__228
& Vvar__0__C__225 = Vvar__0__C__226 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__199,Vvar__0__C__200,Vvar__1___24Anonymous__201,Vvar__1___24Anonymous__202] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__199,Vvar__1___24Anonymous__201) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__200,Vvar__1___24Anonymous__202)
=> ( Vvar__1___24Anonymous__201 = Vvar__1___24Anonymous__202
& Vvar__0__C__199 = Vvar__0__C__200 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__207,Vvar__0__C__208,Vvar__1___24Anonymous__209,Vvar__1___24Anonymous__210,Vvar__2___24Anonymous__211,Vvar__2___24Anonymous__212] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__207,Vvar__1___24Anonymous__209,Vvar__2___24Anonymous__211) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__208,Vvar__1___24Anonymous__210,Vvar__2___24Anonymous__212)
=> ( Vvar__2___24Anonymous__211 = Vvar__2___24Anonymous__212
& Vvar__1___24Anonymous__209 = Vvar__1___24Anonymous__210
& Vvar__0__C__207 = Vvar__0__C__208 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__213,Vvar__0__C__214,Vvar__1___24Anonymous__215,Vvar__1___24Anonymous__216,Vvar__2___24Anonymous__217,Vvar__2___24Anonymous__218] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__213,Vvar__1___24Anonymous__215,Vvar__2___24Anonymous__217) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__214,Vvar__1___24Anonymous__216,Vvar__2___24Anonymous__218)
=> ( Vvar__2___24Anonymous__217 = Vvar__2___24Anonymous__218
& Vvar__1___24Anonymous__215 = Vvar__1___24Anonymous__216
& Vvar__0__C__213 = Vvar__0__C__214 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__203,Vvar__0__C__204,Vvar__1___24Anonymous__205,Vvar__1___24Anonymous__206] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__203,Vvar__1___24Anonymous__205) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__204,Vvar__1___24Anonymous__206)
=> ( Vvar__1___24Anonymous__205 = Vvar__1___24Anonymous__206
& Vvar__0__C__203 = Vvar__0__C__204 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__229,Vvar__0__C__230] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__229) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__230)
=> Vvar__0__C__229 = Vvar__0__C__230 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__11343,Vvar__0__TA__11344,Vvar__1__TX__11345,Vvar__1__TX__11346,Vvar__2__AA__11347,Vvar__2__AA__11348,Vvar__3__AF__11349,Vvar__3__AF__11350,Vvar__4___24Anonymous__11351,Vvar__4___24Anonymous__11352,Vvar__5___24Anonymous__11353,Vvar__5___24Anonymous__11354] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__11343,Vvar__1__TX__11345,Vvar__2__AA__11347,Vvar__3__AF__11349,Vvar__4___24Anonymous__11351,Vvar__5___24Anonymous__11353) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__11344,Vvar__1__TX__11346,Vvar__2__AA__11348,Vvar__3__AF__11350,Vvar__4___24Anonymous__11352,Vvar__5___24Anonymous__11354)
=> ( Vvar__5___24Anonymous__11353 = Vvar__5___24Anonymous__11354
& Vvar__4___24Anonymous__11351 = Vvar__4___24Anonymous__11352
& Vvar__3__AF__11349 = Vvar__3__AF__11350
& Vvar__2__AA__11347 = Vvar__2__AA__11348
& Vvar__1__TX__11345 = Vvar__1__TX__11346
& Vvar__0__TA__11343 = Vvar__0__TA__11344 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__11355,Vvar__0__TA__11356,Vvar__1__TX__11357,Vvar__1__TX__11358,Vvar__2__AA__11359,Vvar__2__AA__11360,Vvar__3__AF__11361,Vvar__3__AF__11362,Vvar__4___24Anonymous__11363,Vvar__4___24Anonymous__11364,Vvar__5___24Anonymous__11365,Vvar__5___24Anonymous__11366] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__11355,Vvar__1__TX__11357,Vvar__2__AA__11359,Vvar__3__AF__11361,Vvar__4___24Anonymous__11363,Vvar__5___24Anonymous__11365) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__11356,Vvar__1__TX__11358,Vvar__2__AA__11360,Vvar__3__AF__11362,Vvar__4___24Anonymous__11364,Vvar__5___24Anonymous__11366)
=> ( Vvar__5___24Anonymous__11365 = Vvar__5___24Anonymous__11366
& Vvar__4___24Anonymous__11363 = Vvar__4___24Anonymous__11364
& Vvar__3__AF__11361 = Vvar__3__AF__11362
& Vvar__2__AA__11359 = Vvar__2__AA__11360
& Vvar__1__TX__11357 = Vvar__1__TX__11358
& Vvar__0__TA__11355 = Vvar__0__TA__11356 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__11367,Vvar__0__TA__11368,Vvar__1__TX__11369,Vvar__1__TX__11370,Vvar__2__AA__11371,Vvar__2__AA__11372,Vvar__3__AF__11373,Vvar__3__AF__11374,Vvar__4___24Anonymous__11375,Vvar__4___24Anonymous__11376,Vvar__5___24Anonymous__11377,Vvar__5___24Anonymous__11378] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__11367,Vvar__1__TX__11369,Vvar__2__AA__11371,Vvar__3__AF__11373,Vvar__4___24Anonymous__11375,Vvar__5___24Anonymous__11377) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__11368,Vvar__1__TX__11370,Vvar__2__AA__11372,Vvar__3__AF__11374,Vvar__4___24Anonymous__11376,Vvar__5___24Anonymous__11378)
=> ( Vvar__5___24Anonymous__11377 = Vvar__5___24Anonymous__11378
& Vvar__4___24Anonymous__11375 = Vvar__4___24Anonymous__11376
& Vvar__3__AF__11373 = Vvar__3__AF__11374
& Vvar__2__AA__11371 = Vvar__2__AA__11372
& Vvar__1__TX__11369 = Vvar__1__TX__11370
& Vvar__0__TA__11367 = Vvar__0__TA__11368 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__11325,Vvar__0__TA__11326,Vvar__1__TX__11327,Vvar__1__TX__11328,Vvar__2__AA__11329,Vvar__2__AA__11330,Vvar__3__AF__11331,Vvar__3__AF__11332] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11325,Vvar__1__TX__11327,Vvar__2__AA__11329,Vvar__3__AF__11331) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11326,Vvar__1__TX__11328,Vvar__2__AA__11330,Vvar__3__AF__11332)
=> ( Vvar__3__AF__11331 = Vvar__3__AF__11332
& Vvar__2__AA__11329 = Vvar__2__AA__11330
& Vvar__1__TX__11327 = Vvar__1__TX__11328
& Vvar__0__TA__11325 = Vvar__0__TA__11326 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__11389,Vvar__0__TA__11390,Vvar__1__TX__11391,Vvar__1__TX__11392,Vvar__2__AA__11393,Vvar__2__AA__11394,Vvar__3__AF__11395,Vvar__3__AF__11396,Vvar__4___24Anonymous__11397,Vvar__4___24Anonymous__11398,Vvar__5___24Anonymous__11399,Vvar__5___24Anonymous__11400,Vvar__6___24Anonymous__11401,Vvar__6___24Anonymous__11402] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__11389,Vvar__1__TX__11391,Vvar__2__AA__11393,Vvar__3__AF__11395,Vvar__4___24Anonymous__11397,Vvar__5___24Anonymous__11399,Vvar__6___24Anonymous__11401) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__11390,Vvar__1__TX__11392,Vvar__2__AA__11394,Vvar__3__AF__11396,Vvar__4___24Anonymous__11398,Vvar__5___24Anonymous__11400,Vvar__6___24Anonymous__11402)
=> ( Vvar__6___24Anonymous__11401 = Vvar__6___24Anonymous__11402
& Vvar__5___24Anonymous__11399 = Vvar__5___24Anonymous__11400
& Vvar__4___24Anonymous__11397 = Vvar__4___24Anonymous__11398
& Vvar__3__AF__11395 = Vvar__3__AF__11396
& Vvar__2__AA__11393 = Vvar__2__AA__11394
& Vvar__1__TX__11391 = Vvar__1__TX__11392
& Vvar__0__TA__11389 = Vvar__0__TA__11390 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__11379,Vvar__0__TA__11380,Vvar__1__TX__11381,Vvar__1__TX__11382,Vvar__2__AA__11383,Vvar__2__AA__11384,Vvar__3__AF__11385,Vvar__3__AF__11386,Vvar__4___24Anonymous__11387,Vvar__4___24Anonymous__11388] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__11379,Vvar__1__TX__11381,Vvar__2__AA__11383,Vvar__3__AF__11385,Vvar__4___24Anonymous__11387) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__11380,Vvar__1__TX__11382,Vvar__2__AA__11384,Vvar__3__AF__11386,Vvar__4___24Anonymous__11388)
=> ( Vvar__4___24Anonymous__11387 = Vvar__4___24Anonymous__11388
& Vvar__3__AF__11385 = Vvar__3__AF__11386
& Vvar__2__AA__11383 = Vvar__2__AA__11384
& Vvar__1__TX__11381 = Vvar__1__TX__11382
& Vvar__0__TA__11379 = Vvar__0__TA__11380 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__11317,Vvar__0__TA__11318,Vvar__1__TX__11319,Vvar__1__TX__11320,Vvar__2__AA__11321,Vvar__2__AA__11322,Vvar__3__AF__11323,Vvar__3__AF__11324] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11317,Vvar__1__TX__11319,Vvar__2__AA__11321,Vvar__3__AF__11323) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11318,Vvar__1__TX__11320,Vvar__2__AA__11322,Vvar__3__AF__11324)
=> ( Vvar__3__AF__11323 = Vvar__3__AF__11324
& Vvar__2__AA__11321 = Vvar__2__AA__11322
& Vvar__1__TX__11319 = Vvar__1__TX__11320
& Vvar__0__TA__11317 = Vvar__0__TA__11318 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__11333,Vvar__0__TA__11334,Vvar__1__TX__11335,Vvar__1__TX__11336,Vvar__2__AA__11337,Vvar__2__AA__11338,Vvar__3__AF__11339,Vvar__3__AF__11340,Vvar__4___24Anonymous__11341,Vvar__4___24Anonymous__11342] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__11333,Vvar__1__TX__11335,Vvar__2__AA__11337,Vvar__3__AF__11339,Vvar__4___24Anonymous__11341) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__11334,Vvar__1__TX__11336,Vvar__2__AA__11338,Vvar__3__AF__11340,Vvar__4___24Anonymous__11342)
=> ( Vvar__4___24Anonymous__11341 = Vvar__4___24Anonymous__11342
& Vvar__3__AF__11339 = Vvar__3__AF__11340
& Vvar__2__AA__11337 = Vvar__2__AA__11338
& Vvar__1__TX__11335 = Vvar__1__TX__11336
& Vvar__0__TA__11333 = Vvar__0__TA__11334 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__43153,Vvar__0__A__43154,Vvar__1___24Anonymous__43155,Vvar__1___24Anonymous__43156,Vvar__2___24Anonymous__43157,Vvar__2___24Anonymous__43158,Vvar__3___24Anonymous__43159,Vvar__3___24Anonymous__43160] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__43153,Vvar__1___24Anonymous__43155,Vvar__2___24Anonymous__43157,Vvar__3___24Anonymous__43159) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__43154,Vvar__1___24Anonymous__43156,Vvar__2___24Anonymous__43158,Vvar__3___24Anonymous__43160)
=> ( Vvar__3___24Anonymous__43159 = Vvar__3___24Anonymous__43160
& Vvar__2___24Anonymous__43157 = Vvar__2___24Anonymous__43158
& Vvar__1___24Anonymous__43155 = Vvar__1___24Anonymous__43156
& Vvar__0__A__43153 = Vvar__0__A__43154 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__43149,Vvar__0__A__43150,Vvar__1___24Anonymous__43151,Vvar__1___24Anonymous__43152] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__43149,Vvar__1___24Anonymous__43151) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__43150,Vvar__1___24Anonymous__43152)
=> ( Vvar__1___24Anonymous__43151 = Vvar__1___24Anonymous__43152
& Vvar__0__A__43149 = Vvar__0__A__43150 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__43147,Vvar__0__A__43148] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__43147) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__43148)
=> Vvar__0__A__43147 = Vvar__0__A__43148 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__2406,Vvar__0___24Anonymous__2407,Vvar__1___24Anonymous__2408,Vvar__1___24Anonymous__2409] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__2406,Vvar__1___24Anonymous__2408) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__2407,Vvar__1___24Anonymous__2409)
=> ( Vvar__1___24Anonymous__2408 = Vvar__1___24Anonymous__2409
& Vvar__0___24Anonymous__2406 = Vvar__0___24Anonymous__2407 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__2410,Vvar__0___24Anonymous__2411,Vvar__1___24Anonymous__2412,Vvar__1___24Anonymous__2413,Vvar__2___24Anonymous__2414,Vvar__2___24Anonymous__2415] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__2410,Vvar__1___24Anonymous__2412,Vvar__2___24Anonymous__2414) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__2411,Vvar__1___24Anonymous__2413,Vvar__2___24Anonymous__2415)
=> ( Vvar__2___24Anonymous__2414 = Vvar__2___24Anonymous__2415
& Vvar__1___24Anonymous__2412 = Vvar__1___24Anonymous__2413
& Vvar__0___24Anonymous__2410 = Vvar__0___24Anonymous__2411 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__2402,Vvar__0___24Anonymous__2403,Vvar__1___24Anonymous__2404,Vvar__1___24Anonymous__2405] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__2402,Vvar__1___24Anonymous__2404) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__2403,Vvar__1___24Anonymous__2405)
=> ( Vvar__1___24Anonymous__2404 = Vvar__1___24Anonymous__2405
& Vvar__0___24Anonymous__2402 = Vvar__0___24Anonymous__2403 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__20613,Vvar__0__C__20614] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20613) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20614)
=> Vvar__0__C__20613 = Vvar__0__C__20614 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__20611,Vvar__0__C__20612] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20611) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20612)
=> Vvar__0__C__20611 = Vvar__0__C__20612 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__20619,Vvar__0__C__20620,Vvar__1___24Anonymous__20621,Vvar__1___24Anonymous__20622] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20619,Vvar__1___24Anonymous__20621) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20620,Vvar__1___24Anonymous__20622)
=> ( Vvar__1___24Anonymous__20621 = Vvar__1___24Anonymous__20622
& Vvar__0__C__20619 = Vvar__0__C__20620 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__20623,Vvar__0__C__20624,Vvar__1___24Anonymous__20625,Vvar__1___24Anonymous__20626,Vvar__2___24Anonymous__20627,Vvar__2___24Anonymous__20628] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20623,Vvar__1___24Anonymous__20625,Vvar__2___24Anonymous__20627) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20624,Vvar__1___24Anonymous__20626,Vvar__2___24Anonymous__20628)
=> ( Vvar__2___24Anonymous__20627 = Vvar__2___24Anonymous__20628
& Vvar__1___24Anonymous__20625 = Vvar__1___24Anonymous__20626
& Vvar__0__C__20623 = Vvar__0__C__20624 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__20615,Vvar__0__C__20616,Vvar__1___24Anonymous__20617,Vvar__1___24Anonymous__20618] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20615,Vvar__1___24Anonymous__20617) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20616,Vvar__1___24Anonymous__20618)
=> ( Vvar__1___24Anonymous__20617 = Vvar__1___24Anonymous__20618
& Vvar__0__C__20615 = Vvar__0__C__20616 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__20649,Vvar__0__C__20650,Vvar__1___24Anonymous__20651,Vvar__1___24Anonymous__20652,Vvar__2___24Anonymous__20653,Vvar__2___24Anonymous__20654] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20649,Vvar__1___24Anonymous__20651,Vvar__2___24Anonymous__20653) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20650,Vvar__1___24Anonymous__20652,Vvar__2___24Anonymous__20654)
=> ( Vvar__2___24Anonymous__20653 = Vvar__2___24Anonymous__20654
& Vvar__1___24Anonymous__20651 = Vvar__1___24Anonymous__20652
& Vvar__0__C__20649 = Vvar__0__C__20650 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__20645,Vvar__0__C__20646,Vvar__1___24Anonymous__20647,Vvar__1___24Anonymous__20648] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20645,Vvar__1___24Anonymous__20647) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20646,Vvar__1___24Anonymous__20648)
=> ( Vvar__1___24Anonymous__20647 = Vvar__1___24Anonymous__20648
& Vvar__0__C__20645 = Vvar__0__C__20646 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__20635,Vvar__0__C__20636,Vvar__1___24Anonymous__20637,Vvar__1___24Anonymous__20638,Vvar__2___24Anonymous__20639,Vvar__2___24Anonymous__20640] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20635,Vvar__1___24Anonymous__20637,Vvar__2___24Anonymous__20639) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20636,Vvar__1___24Anonymous__20638,Vvar__2___24Anonymous__20640)
=> ( Vvar__2___24Anonymous__20639 = Vvar__2___24Anonymous__20640
& Vvar__1___24Anonymous__20637 = Vvar__1___24Anonymous__20638
& Vvar__0__C__20635 = Vvar__0__C__20636 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__20641,Vvar__0__C__20642,Vvar__1___24Anonymous__20643,Vvar__1___24Anonymous__20644] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20641,Vvar__1___24Anonymous__20643) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20642,Vvar__1___24Anonymous__20644)
=> ( Vvar__1___24Anonymous__20643 = Vvar__1___24Anonymous__20644
& Vvar__0__C__20641 = Vvar__0__C__20642 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__20655,Vvar__0__C__20656,Vvar__1___24Anonymous__20657,Vvar__1___24Anonymous__20658,Vvar__2___24Anonymous__20659,Vvar__2___24Anonymous__20660] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20655,Vvar__1___24Anonymous__20657,Vvar__2___24Anonymous__20659) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20656,Vvar__1___24Anonymous__20658,Vvar__2___24Anonymous__20660)
=> ( Vvar__2___24Anonymous__20659 = Vvar__2___24Anonymous__20660
& Vvar__1___24Anonymous__20657 = Vvar__1___24Anonymous__20658
& Vvar__0__C__20655 = Vvar__0__C__20656 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__20629,Vvar__0__C__20630,Vvar__1___24Anonymous__20631,Vvar__1___24Anonymous__20632,Vvar__2___24Anonymous__20633,Vvar__2___24Anonymous__20634] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20629,Vvar__1___24Anonymous__20631,Vvar__2___24Anonymous__20633) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20630,Vvar__1___24Anonymous__20632,Vvar__2___24Anonymous__20634)
=> ( Vvar__2___24Anonymous__20633 = Vvar__2___24Anonymous__20634
& Vvar__1___24Anonymous__20631 = Vvar__1___24Anonymous__20632
& Vvar__0__C__20629 = Vvar__0__C__20630 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__20667,Vvar__0__C__20668,Vvar__1__num__20669,Vvar__1__num__20670,Vvar__2__denum__20671,Vvar__2__denum__20672,Vvar__3__condition__20673,Vvar__3__condition__20674] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20667,Vvar__1__num__20669,Vvar__2__denum__20671,Vvar__3__condition__20673) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20668,Vvar__1__num__20670,Vvar__2__denum__20672,Vvar__3__condition__20674)
=> ( Vvar__3__condition__20673 = Vvar__3__condition__20674
& Vvar__2__denum__20671 = Vvar__2__denum__20672
& Vvar__1__num__20669 = Vvar__1__num__20670
& Vvar__0__C__20667 = Vvar__0__C__20668 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__20712,Vvar__0__C__20713,Vvar__1__rsplit__left__20714,Vvar__1__rsplit__left__20715,Vvar__2__rsplit__common__20716,Vvar__2__rsplit__common__20717,Vvar__3__rsplit__right__20718,Vvar__3__rsplit__right__20719] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__20712,Vvar__1__rsplit__left__20714,Vvar__2__rsplit__common__20716,Vvar__3__rsplit__right__20718) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__20713,Vvar__1__rsplit__left__20715,Vvar__2__rsplit__common__20717,Vvar__3__rsplit__right__20719)
=> ( Vvar__3__rsplit__right__20718 = Vvar__3__rsplit__right__20719
& Vvar__2__rsplit__common__20716 = Vvar__2__rsplit__common__20717
& Vvar__1__rsplit__left__20714 = Vvar__1__rsplit__left__20715
& Vvar__0__C__20712 = Vvar__0__C__20713 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__828,Vvar__0__C__829] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__828) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__829)
=> Vvar__0__C__828 = Vvar__0__C__829 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__826,Vvar__0__C__827] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__826) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__827)
=> Vvar__0__C__826 = Vvar__0__C__827 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__834,Vvar__0__C__835,Vvar__1___24Anonymous__836,Vvar__1___24Anonymous__837] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__834,Vvar__1___24Anonymous__836) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__835,Vvar__1___24Anonymous__837)
=> ( Vvar__1___24Anonymous__836 = Vvar__1___24Anonymous__837
& Vvar__0__C__834 = Vvar__0__C__835 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__838,Vvar__0__C__839,Vvar__1___24Anonymous__840,Vvar__1___24Anonymous__841,Vvar__2___24Anonymous__842,Vvar__2___24Anonymous__843] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__838,Vvar__1___24Anonymous__840,Vvar__2___24Anonymous__842) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__839,Vvar__1___24Anonymous__841,Vvar__2___24Anonymous__843)
=> ( Vvar__2___24Anonymous__842 = Vvar__2___24Anonymous__843
& Vvar__1___24Anonymous__840 = Vvar__1___24Anonymous__841
& Vvar__0__C__838 = Vvar__0__C__839 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__830,Vvar__0__C__831,Vvar__1___24Anonymous__832,Vvar__1___24Anonymous__833] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__830,Vvar__1___24Anonymous__832) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__831,Vvar__1___24Anonymous__833)
=> ( Vvar__1___24Anonymous__832 = Vvar__1___24Anonymous__833
& Vvar__0__C__830 = Vvar__0__C__831 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__850,Vvar__0__C__851,Vvar__1___24Anonymous__852,Vvar__1___24Anonymous__853,Vvar__2___24Anonymous__854,Vvar__2___24Anonymous__855] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__850,Vvar__1___24Anonymous__852,Vvar__2___24Anonymous__854) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__851,Vvar__1___24Anonymous__853,Vvar__2___24Anonymous__855)
=> ( Vvar__2___24Anonymous__854 = Vvar__2___24Anonymous__855
& Vvar__1___24Anonymous__852 = Vvar__1___24Anonymous__853
& Vvar__0__C__850 = Vvar__0__C__851 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__856,Vvar__0__C__857,Vvar__1___24Anonymous__858,Vvar__1___24Anonymous__859] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__856,Vvar__1___24Anonymous__858) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__857,Vvar__1___24Anonymous__859)
=> ( Vvar__1___24Anonymous__858 = Vvar__1___24Anonymous__859
& Vvar__0__C__856 = Vvar__0__C__857 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__860,Vvar__0__C__861,Vvar__1___24Anonymous__862,Vvar__1___24Anonymous__863,Vvar__2___24Anonymous__864,Vvar__2___24Anonymous__865] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__860,Vvar__1___24Anonymous__862,Vvar__2___24Anonymous__864) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__861,Vvar__1___24Anonymous__863,Vvar__2___24Anonymous__865)
=> ( Vvar__2___24Anonymous__864 = Vvar__2___24Anonymous__865
& Vvar__1___24Anonymous__862 = Vvar__1___24Anonymous__863
& Vvar__0__C__860 = Vvar__0__C__861 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__844,Vvar__0__C__845,Vvar__1___24Anonymous__846,Vvar__1___24Anonymous__847,Vvar__2___24Anonymous__848,Vvar__2___24Anonymous__849] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__844,Vvar__1___24Anonymous__846,Vvar__2___24Anonymous__848) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__845,Vvar__1___24Anonymous__847,Vvar__2___24Anonymous__849)
=> ( Vvar__2___24Anonymous__848 = Vvar__2___24Anonymous__849
& Vvar__1___24Anonymous__846 = Vvar__1___24Anonymous__847
& Vvar__0__C__844 = Vvar__0__C__845 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__481,Vvar__0__C__482,Vvar__1___24Anonymous__483,Vvar__1___24Anonymous__484,Vvar__2___24Anonymous__485,Vvar__2___24Anonymous__486,Vvar__3___24Anonymous__487,Vvar__3___24Anonymous__488] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__481,Vvar__1___24Anonymous__483,Vvar__2___24Anonymous__485,Vvar__3___24Anonymous__487) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__482,Vvar__1___24Anonymous__484,Vvar__2___24Anonymous__486,Vvar__3___24Anonymous__488)
=> ( Vvar__3___24Anonymous__487 = Vvar__3___24Anonymous__488
& Vvar__2___24Anonymous__485 = Vvar__2___24Anonymous__486
& Vvar__1___24Anonymous__483 = Vvar__1___24Anonymous__484
& Vvar__0__C__481 = Vvar__0__C__482 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__471,Vvar__0__C__472,Vvar__1___24Anonymous__473,Vvar__1___24Anonymous__474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__471,Vvar__1___24Anonymous__473) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__472,Vvar__1___24Anonymous__474)
=> ( Vvar__1___24Anonymous__473 = Vvar__1___24Anonymous__474
& Vvar__0__C__471 = Vvar__0__C__472 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__475,Vvar__0__C__476,Vvar__1___24Anonymous__477,Vvar__1___24Anonymous__478,Vvar__2___24Anonymous__479,Vvar__2___24Anonymous__480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__475,Vvar__1___24Anonymous__477,Vvar__2___24Anonymous__479) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__476,Vvar__1___24Anonymous__478,Vvar__2___24Anonymous__480)
=> ( Vvar__2___24Anonymous__479 = Vvar__2___24Anonymous__480
& Vvar__1___24Anonymous__477 = Vvar__1___24Anonymous__478
& Vvar__0__C__475 = Vvar__0__C__476 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__640,Vvar__0___24Anonymous__641,Vvar__1___24Anonymous__642,Vvar__1___24Anonymous__643] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__640,Vvar__1___24Anonymous__642) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__641,Vvar__1___24Anonymous__643)
=> ( Vvar__1___24Anonymous__642 = Vvar__1___24Anonymous__643
& Vvar__0___24Anonymous__640 = Vvar__0___24Anonymous__641 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__636,Vvar__0___24Anonymous__637,Vvar__1___24Anonymous__638,Vvar__1___24Anonymous__639] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__636,Vvar__1___24Anonymous__638) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__637,Vvar__1___24Anonymous__639)
=> ( Vvar__1___24Anonymous__638 = Vvar__1___24Anonymous__639
& Vvar__0___24Anonymous__636 = Vvar__0___24Anonymous__637 ) ) ).
fof('$_inj_QuicksortComplexity.nat_below.mkNatBelow',axiom,
! [Vvar__0__v__2871,Vvar__0__v__2872,Vvar__1__p__2873,Vvar__1__p__2874] :
( cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__2871,Vvar__1__p__2873) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__2872,Vvar__1__p__2874)
=> ( Vvar__1__p__2873 = Vvar__1__p__2874
& Vvar__0__v__2871 = Vvar__0__v__2872 ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__30942,Vvar__1__Q__30943,Vvar__2___24Anonymous__30944] :
( cProp___24t(Vvar__0__P__30942)
=> ( cProp___24t(Vvar__1__Q__30943)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__30944)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__30942,Vvar__1__Q__30943,Vvar__2___24Anonymous__30944)
=> ( ( p(Vvar__0__P__30942)
& Vvar__2___24Anonymous__30944 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__30943)
& Vvar__2___24Anonymous__30944 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__20142,Vvar__1__Plt__20143,Vvar__2__Pgt__20144,Vvar__3___24Anonymous__20145] :
( cProp___24t(Vvar__0__Peq__20142)
=> ( cProp___24t(Vvar__1__Plt__20143)
=> ( cProp___24t(Vvar__2__Pgt__20144)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__20145)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__20142,Vvar__1__Plt__20143,Vvar__2__Pgt__20144,Vvar__3___24Anonymous__20145)
=> ( ( p(Vvar__0__Peq__20142)
& Vvar__3___24Anonymous__20145 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__20143)
& Vvar__3___24Anonymous__20145 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__20144)
& Vvar__3___24Anonymous__20145 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2etrue
| VX1 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX2558] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX2558)
=> ( VX2558 = cCoq_2eInit_2eDatatypes_2eEq
| VX2558 = cCoq_2eInit_2eDatatypes_2eLt
| VX2558 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__13,VX14] :
( cType___24t(Vvar__0__A__13)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13,VX14)
=> ( VX14 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__13)
| ? [Vvar__1___24Anonymous__17] :
( t(Vvar__1___24Anonymous__17,Vvar__0__A__13)
& ? [Vvar__2___24Anonymous__18] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13,Vvar__2___24Anonymous__18)
& VX14 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__13,Vvar__1___24Anonymous__17,Vvar__2___24Anonymous__18) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX2)
=> ( VX2 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3)
& VX2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__3488,VX3489] :
( cType___24t(Vvar__0__A__3488)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__3488,VX3489)
=> ( ? [Vvar__1___24Anonymous__3491] :
( t(Vvar__1___24Anonymous__3491,Vvar__0__A__3488)
& VX3489 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3488,Vvar__1___24Anonymous__3491) )
| VX3489 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3488) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__329,Vvar__1__B__330,VX331] :
( cType___24t(Vvar__0__A__329)
=> ( cType___24t(Vvar__1__B__330)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__329,Vvar__1__B__330,VX331)
=> ? [Vvar__2___24Anonymous__334] :
( t(Vvar__2___24Anonymous__334,Vvar__0__A__329)
& ? [Vvar__3___24Anonymous__335] :
( t(Vvar__3___24Anonymous__335,Vvar__1__B__330)
& VX331 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__329,Vvar__1__B__330,Vvar__2___24Anonymous__334,Vvar__3___24Anonymous__335) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__3505,Vvar__1__B__3506,VX3507] :
( cType___24t(Vvar__0__A__3505)
=> ( cType___24t(Vvar__1__B__3506)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__3505,Vvar__1__B__3506,VX3507)
=> ( ? [Vvar__2___24Anonymous__3510] :
( t(Vvar__2___24Anonymous__3510,Vvar__0__A__3505)
& VX3507 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__3505,Vvar__1__B__3506,Vvar__2___24Anonymous__3510) )
| ? [Vvar__2___24Anonymous__3513] :
( t(Vvar__2___24Anonymous__3513,Vvar__1__B__3506)
& VX3507 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__3505,Vvar__1__B__3506,Vvar__2___24Anonymous__3513) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX2557] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX2557)
=> VX2557 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2054,Vvar__1___24Anonymous__2055] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2054)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2055)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2054,Vvar__1___24Anonymous__2055))
=> ( Vvar__1___24Anonymous__2055 = Vvar__0__n__2054
| ? [Vvar__1__m__2059] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2059)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2054,Vvar__1__m__2059))
& Vvar__1___24Anonymous__2055 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2059) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__2700,Vvar__1__P__2701,VX2704] :
( cType___24t(Vvar__0__A__2700)
=> ( c_24__type__2714___24t(Vvar__0__A__2700,Vvar__1__P__2701,Vvar__1__P__2701)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__2700,Vvar__1__P__2701,VX2704)
=> ? [Vvar__2__x__2709] :
( t(Vvar__2__x__2709,Vvar__0__A__2700)
& p(happ(Vvar__1__P__2701,Vvar__2__x__2709))
& VX2704 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2700,Vvar__1__P__2701,Vvar__2__x__2709) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__10801,Vvar__1__P__10802,VX10805] :
( cType___24t(Vvar__0__A__10801)
=> ( c_24__type__10815___24t(Vvar__0__A__10801,Vvar__1__P__10802,Vvar__1__P__10802)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__10801,Vvar__1__P__10802,VX10805)
=> ? [Vvar__2__x__10810] :
( t(Vvar__2__x__10810,Vvar__0__A__10801)
& ? [Vvar__3___24Anonymous__10811] :
( t(Vvar__3___24Anonymous__10811,happ(Vvar__1__P__10802,Vvar__2__x__10810))
& VX10805 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10801,Vvar__1__P__10802,Vvar__2__x__10810,Vvar__3___24Anonymous__10811) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__2336,Vvar__1__B__2337,VX2338] :
( cProp___24t(Vvar__0__A__2336)
=> ( cProp___24t(Vvar__1__B__2337)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__2336,Vvar__1__B__2337,VX2338)
=> ( ( p(Vvar__0__A__2336)
& VX2338 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2336,Vvar__1__B__2337) )
| ( p(Vvar__1__B__2337)
& VX2338 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2336,Vvar__1__B__2337) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__10896,Vvar__1__B__10897,VX10898] :
( cType___24t(Vvar__0__A__10896)
=> ( cProp___24t(Vvar__1__B__10897)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__10896,Vvar__1__B__10897,VX10898)
=> ( ? [Vvar__2___24Anonymous__10901] :
( t(Vvar__2___24Anonymous__10901,Vvar__0__A__10896)
& VX10898 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10896,Vvar__1__B__10897,Vvar__2___24Anonymous__10901) )
| ( p(Vvar__1__B__10897)
& VX10898 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10896,Vvar__1__B__10897) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__6627,Vvar__1__a__6628,Vvar__2___24Anonymous__6629,Vvar__3___24Anonymous__6630] :
( cType___24t(Vvar__0__A__6627)
=> ( t(Vvar__1__a__6628,Vvar__0__A__6627)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6627,Vvar__2___24Anonymous__6629)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6627,Vvar__3___24Anonymous__6630)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__6627,Vvar__1__a__6628,Vvar__2___24Anonymous__6629,Vvar__3___24Anonymous__6630)
=> ( ? [Vvar__2__l__6634] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6627,Vvar__2__l__6634)
& Vvar__3___24Anonymous__6630 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6627,Vvar__1__a__6628,Vvar__2__l__6634)
& Vvar__2___24Anonymous__6629 = Vvar__2__l__6634 )
| ? [Vvar__2__x__6637] :
( t(Vvar__2__x__6637,Vvar__0__A__6627)
& ? [Vvar__3__l__6638] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6627,Vvar__3__l__6638)
& ? [Vvar__4__l_27__6639] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6627,Vvar__4__l_27__6639)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__6627,Vvar__1__a__6628,Vvar__3__l__6638,Vvar__4__l_27__6639)
& Vvar__3___24Anonymous__6630 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6627,Vvar__2__x__6637,Vvar__4__l_27__6639)
& Vvar__2___24Anonymous__6629 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6627,Vvar__2__x__6637,Vvar__3__l__6638) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__6730,Vvar__1__P__6731,Vvar__2___24Anonymous__6734] :
( cType___24t(Vvar__0__A__6730)
=> ( c_24__type__6754___24t(Vvar__0__A__6730,Vvar__1__P__6731,Vvar__2___24Anonymous__6734,Vvar__1__P__6731)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6730,Vvar__2___24Anonymous__6734)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__6730,Vvar__1__P__6731,Vvar__2___24Anonymous__6734)
=> ( ? [Vvar__2__x__6740] :
( t(Vvar__2__x__6740,Vvar__0__A__6730)
& ? [Vvar__3__l__6741] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6730,Vvar__3__l__6741)
& p(happ(Vvar__1__P__6731,Vvar__2__x__6740))
& Vvar__2___24Anonymous__6734 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6730,Vvar__2__x__6740,Vvar__3__l__6741) ) )
| ? [Vvar__2__x__6747] :
( t(Vvar__2__x__6747,Vvar__0__A__6730)
& ? [Vvar__3__l__6748] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6730,Vvar__3__l__6748)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__6730,Vvar__1__P__6731,Vvar__3__l__6748)
& Vvar__2___24Anonymous__6734 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6730,Vvar__2__x__6747,Vvar__3__l__6748) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__6888,Vvar__1__P__6889,Vvar__2___24Anonymous__6892] :
( cType___24t(Vvar__0__A__6888)
=> ( c_24__type__6910___24t(Vvar__0__A__6888,Vvar__1__P__6889,Vvar__2___24Anonymous__6892,Vvar__1__P__6889)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6888,Vvar__2___24Anonymous__6892)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__6888,Vvar__1__P__6889,Vvar__2___24Anonymous__6892)
=> ( Vvar__2___24Anonymous__6892 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__6888)
| ? [Vvar__2__x__6902] :
( t(Vvar__2__x__6902,Vvar__0__A__6888)
& ? [Vvar__3__l__6903] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6888,Vvar__3__l__6903)
& p(happ(Vvar__1__P__6889,Vvar__2__x__6902))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__6888,Vvar__1__P__6889,Vvar__3__l__6903)
& Vvar__2___24Anonymous__6892 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6888,Vvar__2__x__6902,Vvar__3__l__6903) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__6661,Vvar__1___24Anonymous__6662] :
( cType___24t(Vvar__0__A__6661)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6661,Vvar__1___24Anonymous__6662)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__6661,Vvar__1___24Anonymous__6662)
=> ( Vvar__1___24Anonymous__6662 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__6661)
| ? [Vvar__1__x__6666] :
( t(Vvar__1__x__6666,Vvar__0__A__6661)
& ? [Vvar__2__l__6667] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6661,Vvar__2__l__6667)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__6661,Vvar__1__x__6666,Vvar__2__l__6667))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__6661,Vvar__2__l__6667)
& Vvar__1___24Anonymous__6662 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6661,Vvar__1__x__6666,Vvar__2__l__6667) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__9108,Vvar__1__eqA__9109,Vvar__2__x__9114,Vvar__3___24Anonymous__9115] :
( cType___24t(Vvar__0__A__9108)
=> ( c_24__type__9148___24t(Vvar__0__A__9108,Vvar__1__eqA__9109,Vvar__2__x__9114,Vvar__3___24Anonymous__9115,Vvar__1__eqA__9109)
=> ( t(Vvar__2__x__9114,Vvar__0__A__9108)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9108,Vvar__3___24Anonymous__9115)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__9108,Vvar__1__eqA__9109,Vvar__2__x__9114,Vvar__3___24Anonymous__9115)
=> ( ? [Vvar__3__y__9124] :
( t(Vvar__3__y__9124,Vvar__0__A__9108)
& ? [Vvar__4__l__9125] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9108,Vvar__4__l__9125)
& p(happ(happ(Vvar__1__eqA__9109,Vvar__2__x__9114),Vvar__3__y__9124))
& Vvar__3___24Anonymous__9115 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9108,Vvar__3__y__9124,Vvar__4__l__9125) ) )
| ? [Vvar__3__y__9134] :
( t(Vvar__3__y__9134,Vvar__0__A__9108)
& ? [Vvar__4__l__9135] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9108,Vvar__4__l__9135)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__9108,Vvar__1__eqA__9109,Vvar__2__x__9114,Vvar__4__l__9135)
& Vvar__3___24Anonymous__9115 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9108,Vvar__3__y__9134,Vvar__4__l__9135) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1941] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1941)
=> ( VX1941 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1942] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1942)
& VX1941 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1942) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1946] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1946)
=> ( VX1946 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1947] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1947)
& VX1946 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1947) )
| ? [Vvar__0___24Anonymous__1948] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1948)
& VX1946 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1948) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1930] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1930)
=> ( ? [Vvar__0___24Anonymous__1931] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1931)
& VX1930 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1931) )
| ? [Vvar__0___24Anonymous__1932] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1932)
& VX1930 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1932) )
| VX1930 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX25611] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX25611)
=> ? [Vvar__0__Qnum__25612] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__25612)
& ? [Vvar__1__Qden__25613] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__25613)
& VX25611 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__25612,Vvar__1__Qden__25613) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX49771] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX49771)
=> ? [Vvar__0__neg__49772] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__49772)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__49772,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& VX49771 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__49772) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX49750] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX49750)
=> ? [Vvar__0__nonneg__49751] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__49751)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__49751))
& VX49750 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__49751) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX49764] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX49764)
=> ? [Vvar__0__nonpos__49765] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__49765)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__49765,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& VX49764 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__49765) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX35331] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX35331)
=> ? [Vvar__0__nonzero__35332] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__35332)
& Vvar__0__nonzero__35332 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX35331 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__35332) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX49757] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX49757)
=> ? [Vvar__0__pos__49758] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__49758)
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__49758))
& VX49757 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__49758) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__35562,Vvar__1___24Anonymous__35563,VX35564] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__35562)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__35563)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__35562,Vvar__1___24Anonymous__35563,VX35564)
=> ( ( Vvar__0__x__35562 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__35563 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX35564 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__35562) )
| ? [Vvar__1__n__35568] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__35568)
& Vvar__0__x__35562 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__35568)
& Vvar__1___24Anonymous__35563 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2435588___24a3(Vvar__0__x__35562,Vvar__1___24Anonymous__35563,Vvar__1__n__35568)
& VX35564 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__35562,Vvar__1__n__35568) )
| ? [Vvar__1__n__35573] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__35573)
& Vvar__0__x__35562 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__35573))
& Vvar__1___24Anonymous__35563 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605___24a3(Vvar__0__x__35562,Vvar__1___24Anonymous__35563,Vvar__1__n__35573)
& VX35564 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__35562,Vvar__1__n__35573) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__25649,Vvar__1__R__25650] :
( cType___24t(Vvar__0__A__25649)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__25649,Vvar__1__R__25650)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__25649,Vvar__1__R__25650)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__25649,Vvar__1__R__25650)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__25649,Vvar__1__R__25650)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__2679,Vvar__1___24Anonymous__2680,Vvar__2___24Anonymous__2681] :
( cType___24t(Vvar__0__A__2679)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__1___24Anonymous__2680)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__2___24Anonymous__2681)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2679,Vvar__1___24Anonymous__2680,Vvar__2___24Anonymous__2681)
=> ( ( Vvar__2___24Anonymous__2681 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2679)
& Vvar__1___24Anonymous__2680 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2679) )
| ? [Vvar__1__x__2685] :
( t(Vvar__1__x__2685,Vvar__0__A__2679)
& ? [Vvar__2__l__2686] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__2__l__2686)
& ? [Vvar__3__l_27__2687] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__3__l_27__2687)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2679,Vvar__2__l__2686,Vvar__3__l_27__2687)
& Vvar__2___24Anonymous__2681 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__1__x__2685,Vvar__3__l_27__2687)
& Vvar__1___24Anonymous__2680 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__1__x__2685,Vvar__2__l__2686) ) ) )
| ? [Vvar__1__x__2690] :
( t(Vvar__1__x__2690,Vvar__0__A__2679)
& ? [Vvar__2__y__2691] :
( t(Vvar__2__y__2691,Vvar__0__A__2679)
& ? [Vvar__3__l__2692] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__3__l__2692)
& Vvar__2___24Anonymous__2681 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__1__x__2690,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__2__y__2691,Vvar__3__l__2692))
& Vvar__1___24Anonymous__2680 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__2__y__2691,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2679,Vvar__1__x__2690,Vvar__3__l__2692)) ) ) )
| ? [Vvar__1__l__2694] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__1__l__2694)
& ? [Vvar__2__l_27__2695] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__2__l_27__2695)
& ? [Vvar__3__l_27_27__2696] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2679,Vvar__3__l_27_27__2696)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2679,Vvar__1__l__2694,Vvar__2__l_27__2695)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2679,Vvar__2__l_27__2695,Vvar__3__l_27_27__2696)
& Vvar__2___24Anonymous__2681 = Vvar__3__l_27_27__2696
& Vvar__1___24Anonymous__2680 = Vvar__1__l__2694 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__10394,Vvar__1__R__10395,Vvar__2__a__10400,Vvar__3___24Anonymous__10401] :
( cType___24t(Vvar__0__A__10394)
=> ( c_24__type__10431___24t(Vvar__0__A__10394,Vvar__1__R__10395,Vvar__2__a__10400,Vvar__3___24Anonymous__10401,Vvar__1__R__10395)
=> ( t(Vvar__2__a__10400,Vvar__0__A__10394)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10394,Vvar__3___24Anonymous__10401)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__10394,Vvar__1__R__10395,Vvar__2__a__10400,Vvar__3___24Anonymous__10401)
=> ( Vvar__3___24Anonymous__10401 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10394)
| ? [Vvar__3__b__10417] :
( t(Vvar__3__b__10417,Vvar__0__A__10394)
& ? [Vvar__4__l__10418] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10394,Vvar__4__l__10418)
& p(happ(happ(Vvar__1__R__10395,Vvar__2__a__10400),Vvar__3__b__10417))
& Vvar__3___24Anonymous__10401 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10394,Vvar__3__b__10417,Vvar__4__l__10418) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__2764,Vvar__1___24Anonymous__2765,VX2766] :
( cType___24t(Vvar__0__A__2764)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2765)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2764,Vvar__1___24Anonymous__2765,VX2766)
=> ( ( Vvar__1___24Anonymous__2765 = cCoq_2eInit_2eDatatypes_2eO
& VX2766 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2764) )
| ? [Vvar__1__h__2769] :
( t(Vvar__1__h__2769,Vvar__0__A__2764)
& ? [Vvar__2__n__2770] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__2770)
& ? [Vvar__3___24Anonymous__2771] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2764,Vvar__2__n__2770,Vvar__3___24Anonymous__2771)
& Vvar__1___24Anonymous__2765 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__2770)
& VX2766 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2764,Vvar__1__h__2769,Vvar__2__n__2770,Vvar__3___24Anonymous__2771) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__61435,Vvar__1__b__61436,Vvar__2__g__61437] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__61435)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__61436)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__61437)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__61435,Vvar__1__b__61436,Vvar__2__g__61437)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__61437,Vvar__0__a__61435)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__61437,Vvar__1__b__61436)
& ! [Vvar__var__var__var__var__5__x__61445__61448__61451__61454__61457] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__61445__61448__61451__61454__61457)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__61445__61448__61451__61454__61457,Vvar__0__a__61435)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__61445__61448__61451__61454__61457,Vvar__1__b__61436)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__61445__61448__61451__61454__61457,Vvar__2__g__61437) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__20162,VX20163] :
( cType___24t(Vvar__0__C__20162)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,VX20163)
=> ( ? [Vvar__1___24Anonymous__20165] :
( t(Vvar__1___24Anonymous__20165,Vvar__0__C__20162)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__20162,Vvar__1___24Anonymous__20165) )
| ? [Vvar__1___24Anonymous__20167] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20167)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__20162,Vvar__1___24Anonymous__20167) )
| ? [Vvar__1___24Anonymous__20169] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__1___24Anonymous__20169)
& ? [Vvar__2___24Anonymous__20170] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__2___24Anonymous__20170)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__20162,Vvar__1___24Anonymous__20169,Vvar__2___24Anonymous__20170) ) )
| ? [Vvar__1___24Anonymous__20172] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__1___24Anonymous__20172)
& ? [Vvar__2___24Anonymous__20173] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__2___24Anonymous__20173)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__20162,Vvar__1___24Anonymous__20172,Vvar__2___24Anonymous__20173) ) )
| ? [Vvar__1___24Anonymous__20175] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__1___24Anonymous__20175)
& ? [Vvar__2___24Anonymous__20176] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__2___24Anonymous__20176)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__20162,Vvar__1___24Anonymous__20175,Vvar__2___24Anonymous__20176) ) )
| ? [Vvar__1___24Anonymous__20178] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__1___24Anonymous__20178)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__20162,Vvar__1___24Anonymous__20178) )
| ? [Vvar__1___24Anonymous__20180] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__20162,Vvar__1___24Anonymous__20180)
& ? [Vvar__2___24Anonymous__20181] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20181)
& VX20163 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__20162,Vvar__1___24Anonymous__20180,Vvar__2___24Anonymous__20181) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__355,VX356] :
( cType___24t(Vvar__0__C__355)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__355,VX356)
=> ( ? [Vvar__1___24Anonymous__358] :
( t(Vvar__1___24Anonymous__358,Vvar__0__C__355)
& VX356 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__355,Vvar__1___24Anonymous__358) )
| ? [Vvar__1___24Anonymous__360] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__360)
& ? [Vvar__2___24Anonymous__361] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__355,Vvar__2___24Anonymous__361)
& VX356 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__355,Vvar__1___24Anonymous__360,Vvar__2___24Anonymous__361) ) )
| ? [Vvar__1___24Anonymous__363] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__355,Vvar__1___24Anonymous__363)
& ? [Vvar__2___24Anonymous__364] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__364)
& ? [Vvar__3___24Anonymous__365] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__355,Vvar__3___24Anonymous__365)
& VX356 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__355,Vvar__1___24Anonymous__363,Vvar__2___24Anonymous__364,Vvar__3___24Anonymous__365) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185] :
( cType___24t(Vvar__0__R__34154)
=> ( t(Vvar__1__rO__34155,Vvar__0__R__34154)
=> ( t(Vvar__2__rI__34156,Vvar__0__R__34154)
=> ( c_24__type__34586___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__3__rplus__34157)
=> ( c_24__type__34687___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__4__rtimes__34162)
=> ( c_24__type__34788___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__5__rminus__34167)
=> ( c_24__type__34878___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__6__ropp__34172)
=> ( c_24__type__34979___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__7__req__34175)
=> ( c_24__type__35080___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__8__rle__34180)
=> ( c_24__type__35181___24t(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185,Vvar__9__rlt__34185)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175,Vvar__8__rle__34180,Vvar__9__rlt__34185)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__34154,Vvar__7__req__34175)
& ! [Vvar__var__var__var__var__11__x1__34229__34235__34340__34346__34352] :
( t(Vvar__var__var__var__var__11__x1__34229__34235__34340__34346__34352,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__12__x2__34230__34236__34341__34347__34353] :
( t(Vvar__var__var__var__var__12__x2__34230__34236__34341__34347__34353,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__11__x1__34229__34235__34340__34346__34352),Vvar__var__var__var__var__12__x2__34230__34236__34341__34347__34353))
=> ! [Vvar__var__var__var__var__14__y1__34231__34237__34342__34348__34354] :
( t(Vvar__var__var__var__var__14__y1__34231__34237__34342__34348__34354,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__15__y2__34232__34238__34343__34349__34355] :
( t(Vvar__var__var__var__var__15__y2__34232__34238__34343__34349__34355,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__14__y1__34231__34237__34342__34348__34354),Vvar__var__var__var__var__15__y2__34232__34238__34343__34349__34355))
=> p(happ(happ(Vvar__7__req__34175,happ(happ(Vvar__3__rplus__34157,Vvar__var__var__var__var__11__x1__34229__34235__34340__34346__34352),Vvar__var__var__var__var__14__y1__34231__34237__34342__34348__34354)),happ(happ(Vvar__3__rplus__34157,Vvar__var__var__var__var__12__x2__34230__34236__34341__34347__34353),Vvar__var__var__var__var__15__y2__34232__34238__34343__34349__34355))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__34242__34248__34358__34364__34370] :
( t(Vvar__var__var__var__var__12__x1__34242__34248__34358__34364__34370,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__13__x2__34243__34249__34359__34365__34371] :
( t(Vvar__var__var__var__var__13__x2__34243__34249__34359__34365__34371,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__12__x1__34242__34248__34358__34364__34370),Vvar__var__var__var__var__13__x2__34243__34249__34359__34365__34371))
=> ! [Vvar__var__var__var__var__15__y1__34244__34250__34360__34366__34372] :
( t(Vvar__var__var__var__var__15__y1__34244__34250__34360__34366__34372,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__16__y2__34245__34251__34361__34367__34373] :
( t(Vvar__var__var__var__var__16__y2__34245__34251__34361__34367__34373,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__15__y1__34244__34250__34360__34366__34372),Vvar__var__var__var__var__16__y2__34245__34251__34361__34367__34373))
=> p(happ(happ(Vvar__7__req__34175,happ(happ(Vvar__4__rtimes__34162,Vvar__var__var__var__var__12__x1__34242__34248__34358__34364__34370),Vvar__var__var__var__var__15__y1__34244__34250__34360__34366__34372)),happ(happ(Vvar__4__rtimes__34162,Vvar__var__var__var__var__13__x2__34243__34249__34359__34365__34371),Vvar__var__var__var__var__16__y2__34245__34251__34361__34367__34373))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__34255__34258__34376__34379__34382] :
( t(Vvar__var__var__var__var__13__x1__34255__34258__34376__34379__34382,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__14__x2__34256__34259__34377__34380__34383] :
( t(Vvar__var__var__var__var__14__x2__34256__34259__34377__34380__34383,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__13__x1__34255__34258__34376__34379__34382),Vvar__var__var__var__var__14__x2__34256__34259__34377__34380__34383))
=> p(happ(happ(Vvar__7__req__34175,happ(Vvar__6__ropp__34172,Vvar__var__var__var__var__13__x1__34255__34258__34376__34379__34382)),happ(Vvar__6__ropp__34172,Vvar__var__var__var__var__14__x2__34256__34259__34377__34380__34383))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__34262__34268__34385__34391__34397] :
( t(Vvar__var__var__var__var__14__x1__34262__34268__34385__34391__34397,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__15__x2__34263__34269__34386__34392__34398] :
( t(Vvar__var__var__var__var__15__x2__34263__34269__34386__34392__34398,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__14__x1__34262__34268__34385__34391__34397),Vvar__var__var__var__var__15__x2__34263__34269__34386__34392__34398))
=> ! [Vvar__var__var__var__var__17__y1__34264__34270__34387__34393__34399] :
( t(Vvar__var__var__var__var__17__y1__34264__34270__34387__34393__34399,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__18__y2__34265__34271__34388__34394__34400] :
( t(Vvar__var__var__var__var__18__y2__34265__34271__34388__34394__34400,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__17__y1__34264__34270__34387__34393__34399),Vvar__var__var__var__var__18__y2__34265__34271__34388__34394__34400))
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__14__x1__34262__34268__34385__34391__34397),Vvar__var__var__var__var__17__y1__34264__34270__34387__34393__34399))
<=> p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__15__x2__34263__34269__34386__34392__34398),Vvar__var__var__var__var__18__y2__34265__34271__34388__34394__34400)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__34275__34281__34403__34409__34415] :
( t(Vvar__var__var__var__var__15__x1__34275__34281__34403__34409__34415,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__16__x2__34276__34282__34404__34410__34416] :
( t(Vvar__var__var__var__var__16__x2__34276__34282__34404__34410__34416,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__15__x1__34275__34281__34403__34409__34415),Vvar__var__var__var__var__16__x2__34276__34282__34404__34410__34416))
=> ! [Vvar__var__var__var__var__18__y1__34277__34283__34405__34411__34417] :
( t(Vvar__var__var__var__var__18__y1__34277__34283__34405__34411__34417,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__19__y2__34278__34284__34406__34412__34418] :
( t(Vvar__var__var__var__var__19__y2__34278__34284__34406__34412__34418,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__18__y1__34277__34283__34405__34411__34417),Vvar__var__var__var__var__19__y2__34278__34284__34406__34412__34418))
=> ( p(happ(happ(Vvar__9__rlt__34185,Vvar__var__var__var__var__15__x1__34275__34281__34403__34409__34415),Vvar__var__var__var__var__18__y1__34277__34283__34405__34411__34417))
<=> p(happ(happ(Vvar__9__rlt__34185,Vvar__var__var__var__var__16__x2__34276__34282__34404__34410__34416),Vvar__var__var__var__var__19__y2__34278__34284__34406__34412__34418)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__34154,Vvar__1__rO__34155,Vvar__2__rI__34156,Vvar__3__rplus__34157,Vvar__4__rtimes__34162,Vvar__5__rminus__34167,Vvar__6__ropp__34172,Vvar__7__req__34175)
& ! [Vvar__var__var__var__17__n__34289__34290__34421__34422] :
( t(Vvar__var__var__var__17__n__34289__34290__34421__34422,Vvar__0__R__34154)
=> p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__17__n__34289__34290__34421__34422),Vvar__var__var__var__17__n__34289__34290__34421__34422)) )
& ! [Vvar__var__var__var__var__18__n__34292__34296__34423__34427__34431] :
( t(Vvar__var__var__var__var__18__n__34292__34296__34423__34427__34431,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__19__m__34293__34297__34424__34428__34432] :
( t(Vvar__var__var__var__var__19__m__34293__34297__34424__34428__34432,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__18__n__34292__34296__34423__34427__34431),Vvar__var__var__var__var__19__m__34293__34297__34424__34428__34432))
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__19__m__34293__34297__34424__34428__34432),Vvar__var__var__var__var__18__n__34292__34296__34423__34427__34431))
=> p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__18__n__34292__34296__34423__34427__34431),Vvar__var__var__var__var__19__m__34293__34297__34424__34428__34432)) ) ) ) )
& ! [Vvar__var__var__var__19__n__34301__34306__34435__34440] :
( t(Vvar__var__var__var__19__n__34301__34306__34435__34440,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__20__m__34302__34307__34436__34441] :
( t(Vvar__var__var__var__20__m__34302__34307__34436__34441,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__21__p__34303__34308__34437__34442] :
( t(Vvar__var__var__var__21__p__34303__34308__34437__34442,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__19__n__34301__34306__34435__34440),Vvar__var__var__var__20__m__34302__34307__34436__34441))
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__20__m__34302__34307__34436__34441),Vvar__var__var__var__21__p__34303__34308__34437__34442))
=> p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__19__n__34301__34306__34435__34440),Vvar__var__var__var__21__p__34303__34308__34437__34442)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__34312__34314__34445__34447__34449__34451] :
( t(Vvar__var__var__var__var__var__20__n__34312__34314__34445__34447__34449__34451,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__var__21__m__34313__34315__34446__34448__34450__34452] :
( t(Vvar__var__var__var__var__var__21__m__34313__34315__34446__34448__34450__34452,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__9__rlt__34185,Vvar__var__var__var__var__var__20__n__34312__34314__34445__34447__34449__34451),Vvar__var__var__var__var__var__21__m__34313__34315__34446__34448__34450__34452))
<=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__var__20__n__34312__34314__34445__34447__34449__34451),Vvar__var__var__var__var__var__21__m__34313__34315__34446__34448__34450__34452))
& ~ p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__var__20__n__34312__34314__34445__34447__34449__34451),Vvar__var__var__var__var__var__21__m__34313__34315__34446__34448__34450__34452)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__34317__34319__34453__34455__34457] :
( t(Vvar__var__var__var__var__21__n__34317__34319__34453__34455__34457,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__22__m__34318__34320__34454__34456__34458] :
( t(Vvar__var__var__var__var__22__m__34318__34320__34454__34456__34458,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__9__rlt__34185,Vvar__var__var__var__var__21__n__34317__34319__34453__34455__34457),Vvar__var__var__var__var__22__m__34318__34320__34454__34456__34458))
| p(happ(happ(Vvar__7__req__34175,Vvar__var__var__var__var__21__n__34317__34319__34453__34455__34457),Vvar__var__var__var__var__22__m__34318__34320__34454__34456__34458))
| p(happ(happ(Vvar__9__rlt__34185,Vvar__var__var__var__var__22__m__34318__34320__34454__34456__34458),Vvar__var__var__var__var__21__n__34317__34319__34453__34455__34457)) ) ) )
& ! [Vvar__var__var__var__var__22__n__34322__34326__34459__34463__34467] :
( t(Vvar__var__var__var__var__22__n__34322__34326__34459__34463__34467,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__23__m__34323__34327__34460__34464__34468] :
( t(Vvar__var__var__var__var__23__m__34323__34327__34460__34464__34468,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__24__p__34324__34328__34461__34465__34469] :
( t(Vvar__var__var__var__var__24__p__34324__34328__34461__34465__34469,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__8__rle__34180,Vvar__var__var__var__var__22__n__34322__34326__34459__34463__34467),Vvar__var__var__var__var__23__m__34323__34327__34460__34464__34468))
=> p(happ(happ(Vvar__8__rle__34180,happ(happ(Vvar__3__rplus__34157,Vvar__var__var__var__var__24__p__34324__34328__34461__34465__34469),Vvar__var__var__var__var__22__n__34322__34326__34459__34463__34467)),happ(happ(Vvar__3__rplus__34157,Vvar__var__var__var__var__24__p__34324__34328__34461__34465__34469),Vvar__var__var__var__var__23__m__34323__34327__34460__34464__34468))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__34331__34335__34471__34475__34479__34483] :
( t(Vvar__var__var__var__var__var__23__n__34331__34335__34471__34475__34479__34483,Vvar__0__R__34154)
=> ! [Vvar__var__var__var__var__var__24__m__34332__34336__34472__34476__34480__34484] :
( t(Vvar__var__var__var__var__var__24__m__34332__34336__34472__34476__34480__34484,Vvar__0__R__34154)
=> ( p(happ(happ(Vvar__9__rlt__34185,Vvar__1__rO__34155),Vvar__var__var__var__var__var__23__n__34331__34335__34471__34475__34479__34483))
=> ( p(happ(happ(Vvar__9__rlt__34185,Vvar__1__rO__34155),Vvar__var__var__var__var__var__24__m__34332__34336__34472__34476__34480__34484))
=> p(happ(happ(Vvar__9__rlt__34185,Vvar__1__rO__34155),happ(happ(Vvar__4__rtimes__34162,Vvar__var__var__var__var__var__23__n__34331__34335__34471__34475__34479__34483),Vvar__var__var__var__var__var__24__m__34332__34336__34472__34476__34480__34484))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__34175,Vvar__1__rO__34155),Vvar__2__rI__34156))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX35341] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX35341)
=> ( VX35341 = cCoq_2emicromega_2eRMicromega_2eC0
| VX35341 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__35342] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__35342)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35342) )
| ? [Vvar__0__r__35343] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__35343)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35343) )
| ? [Vvar__0__r1__35344] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35344)
& ? [Vvar__1__r2__35345] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35345)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35344,Vvar__1__r2__35345) ) )
| ? [Vvar__0__r1__35346] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35346)
& ? [Vvar__1__r2__35347] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35347)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35346,Vvar__1__r2__35347) ) )
| ? [Vvar__0__r1__35348] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35348)
& ? [Vvar__1__r2__35349] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35349)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35348,Vvar__1__r2__35349) ) )
| ? [Vvar__0__r1__35350] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35350)
& ? [Vvar__1__z__35351] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__35351)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35350,Vvar__1__z__35351) ) )
| ? [Vvar__0__r__35352] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__35352)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35352) )
| ? [Vvar__0__r__35353] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__35353)
& VX35341 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35353) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__20799,VX20800] :
( cType___24t(Vvar__0__T__20799)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__20799,VX20800)
=> ? [Vvar__1__Flhs__20802] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20799,Vvar__1__Flhs__20802)
& ? [Vvar__2__Fop__20803] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__20803)
& ? [Vvar__3__Frhs__20804] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20799,Vvar__3__Frhs__20804)
& VX20800 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20799,Vvar__1__Flhs__20802,Vvar__2__Fop__20803,Vvar__3__Frhs__20804) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX441] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX441)
=> ( VX441 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX441 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX441 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX441 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX42238] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX42238)
=> ( VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX42238 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__85,VX86] :
( cType___24t(Vvar__0__C__85)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,VX86)
=> ( ? [Vvar__1___24Anonymous__88] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__88)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__85,Vvar__1___24Anonymous__88) )
| ? [Vvar__1___24Anonymous__90] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__85,Vvar__1___24Anonymous__90)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__85,Vvar__1___24Anonymous__90) )
| ? [Vvar__1___24Anonymous__92] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__85,Vvar__1___24Anonymous__92)
& ? [Vvar__2___24Anonymous__93] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,Vvar__2___24Anonymous__93)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__85,Vvar__1___24Anonymous__92,Vvar__2___24Anonymous__93) ) )
| ? [Vvar__1___24Anonymous__95] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,Vvar__1___24Anonymous__95)
& ? [Vvar__2___24Anonymous__96] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,Vvar__2___24Anonymous__96)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__85,Vvar__1___24Anonymous__95,Vvar__2___24Anonymous__96) ) )
| ? [Vvar__1___24Anonymous__98] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,Vvar__1___24Anonymous__98)
& ? [Vvar__2___24Anonymous__99] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85,Vvar__2___24Anonymous__99)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__85,Vvar__1___24Anonymous__98,Vvar__2___24Anonymous__99) ) )
| ? [Vvar__1___24Anonymous__101] :
( t(Vvar__1___24Anonymous__101,Vvar__0__C__85)
& VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__85,Vvar__1___24Anonymous__101) )
| VX86 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__85) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722] :
( cType___24t(Vvar__0__R__35653)
=> ( t(Vvar__1__rO__35654,Vvar__0__R__35653)
=> ( t(Vvar__2__rI__35655,Vvar__0__R__35653)
=> ( c_24__type__36186___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__3__rplus__35656)
=> ( c_24__type__36532___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__4__rtimes__35661)
=> ( c_24__type__36878___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__5__rminus__35666)
=> ( c_24__type__37201___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__6__ropp__35671)
=> ( c_24__type__37547___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__7__req__35674)
=> ( c_24__type__37893___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__8__rle__35679)
=> ( cType___24t(Vvar__9__C__35684)
=> ( t(Vvar__10__cO__35685,Vvar__9__C__35684)
=> ( t(Vvar__11__cI__35686,Vvar__9__C__35684)
=> ( c_24__type__38239___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__12__cplus__35687)
=> ( c_24__type__38585___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__13__ctimes__35692)
=> ( c_24__type__38931___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__14__cminus__35697)
=> ( c_24__type__39254___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__15__copp__35702)
=> ( c_24__type__39600___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__16__ceqb__35705)
=> ( c_24__type__39946___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__17__cleb__35710)
=> ( c_24__type__40269___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__18__phi__35715)
=> ( cType___24t(Vvar__19__E__35718)
=> ( c_24__type__40592___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__20__pow__phi__35719)
=> ( c_24__type__40938___24t(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722,Vvar__21__rpow__35722)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__8__rle__35679,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__17__cleb__35710,Vvar__18__phi__35715,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__35653,Vvar__1__rO__35654,Vvar__2__rI__35655,Vvar__3__rplus__35656,Vvar__4__rtimes__35661,Vvar__5__rminus__35666,Vvar__6__ropp__35671,Vvar__7__req__35674,Vvar__9__C__35684,Vvar__10__cO__35685,Vvar__11__cI__35686,Vvar__12__cplus__35687,Vvar__13__ctimes__35692,Vvar__14__cminus__35697,Vvar__15__copp__35702,Vvar__16__ceqb__35705,Vvar__18__phi__35715)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__35653,Vvar__2__rI__35655,Vvar__4__rtimes__35661,Vvar__7__req__35674,Vvar__19__E__35718,Vvar__20__pow__phi__35719,Vvar__21__rpow__35722)
& ! [Vvar__var__var__var__var__var__24__x__35805__35808__35818__35821__35824__35827] :
( t(Vvar__var__var__var__var__var__24__x__35805__35808__35818__35821__35824__35827,Vvar__9__C__35684)
=> ! [Vvar__var__var__var__var__var__25__y__35806__35809__35819__35822__35825__35828] :
( t(Vvar__var__var__var__var__var__25__y__35806__35809__35819__35822__35825__35828,Vvar__9__C__35684)
=> ( happ(happ(Vvar__16__ceqb__35705,Vvar__var__var__var__var__var__24__x__35805__35808__35818__35821__35824__35827),Vvar__var__var__var__var__var__25__y__35806__35809__35819__35822__35825__35828) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__35674,happ(Vvar__18__phi__35715,Vvar__var__var__var__var__var__24__x__35805__35808__35818__35821__35824__35827)),happ(Vvar__18__phi__35715,Vvar__var__var__var__var__var__25__y__35806__35809__35819__35822__35825__35828))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__35812__35815__35830__35833__35836__35839] :
( t(Vvar__var__var__var__var__var__25__x__35812__35815__35830__35833__35836__35839,Vvar__9__C__35684)
=> ! [Vvar__var__var__var__var__var__26__y__35813__35816__35831__35834__35837__35840] :
( t(Vvar__var__var__var__var__var__26__y__35813__35816__35831__35834__35837__35840,Vvar__9__C__35684)
=> ( happ(happ(Vvar__17__cleb__35710,Vvar__var__var__var__var__var__25__x__35812__35815__35830__35833__35836__35839),Vvar__var__var__var__var__var__26__y__35813__35816__35831__35834__35837__35840) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__35679,happ(Vvar__18__phi__35715,Vvar__var__var__var__var__var__25__x__35812__35815__35830__35833__35836__35839)),happ(Vvar__18__phi__35715,Vvar__var__var__var__var__var__26__y__35813__35816__35831__35834__35837__35840))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,VX10964] :
( cType___24t(Vvar__0__TA__10960)
=> ( cType___24t(Vvar__1__TX__10961)
=> ( cType___24t(Vvar__2__AA__10962)
=> ( cType___24t(Vvar__3__AF__10963)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,VX10964)
=> ( VX10964 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963)
| VX10964 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963)
| ? [Vvar__4___24Anonymous__10977] :
( t(Vvar__4___24Anonymous__10977,Vvar__1__TX__10961)
& VX10964 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10977) )
| ? [Vvar__4___24Anonymous__10982] :
( t(Vvar__4___24Anonymous__10982,Vvar__0__TA__10960)
& ? [Vvar__5___24Anonymous__10983] :
( t(Vvar__5___24Anonymous__10983,Vvar__2__AA__10962)
& VX10964 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10982,Vvar__5___24Anonymous__10983) ) )
| ? [Vvar__4___24Anonymous__10988] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10988)
& ? [Vvar__5___24Anonymous__10989] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__5___24Anonymous__10989)
& VX10964 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10988,Vvar__5___24Anonymous__10989) ) )
| ? [Vvar__4___24Anonymous__10994] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10994)
& ? [Vvar__5___24Anonymous__10995] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__5___24Anonymous__10995)
& VX10964 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__10994,Vvar__5___24Anonymous__10995) ) )
| ? [Vvar__4___24Anonymous__11000] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__11000)
& VX10964 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__11000) )
| ? [Vvar__4___24Anonymous__11005] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__11005)
& ? [Vvar__5___24Anonymous__11006] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__10963,Vvar__5___24Anonymous__11006)
& ? [Vvar__6___24Anonymous__11007] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__6___24Anonymous__11007)
& VX10964 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__10960,Vvar__1__TX__10961,Vvar__2__AA__10962,Vvar__3__AF__10963,Vvar__4___24Anonymous__11005,Vvar__5___24Anonymous__11006,Vvar__6___24Anonymous__11007) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__43124,VX43125] :
( cType___24t(Vvar__0__A__43124)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__43124,VX43125)
=> ( VX43125 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__43124)
| ? [Vvar__1___24Anonymous__43128] :
( t(Vvar__1___24Anonymous__43128,Vvar__0__A__43124)
& VX43125 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__43124,Vvar__1___24Anonymous__43128) )
| ? [Vvar__1___24Anonymous__43130] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__43124,Vvar__1___24Anonymous__43130)
& ? [Vvar__2___24Anonymous__43131] :
( t(Vvar__2___24Anonymous__43131,Vvar__0__A__43124)
& ? [Vvar__3___24Anonymous__43132] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__43124,Vvar__3___24Anonymous__43132)
& VX43125 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__43124,Vvar__1___24Anonymous__43130,Vvar__2___24Anonymous__43131,Vvar__3___24Anonymous__43132) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX2373] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX2373)
=> ( VX2373 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__2374] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__2374)
& ? [Vvar__1___24Anonymous__2375] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__2375)
& VX2373 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__2374,Vvar__1___24Anonymous__2375) ) )
| ? [Vvar__0___24Anonymous__2376] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__2376)
& ? [Vvar__1___24Anonymous__2377] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__2377)
& VX2373 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__2376,Vvar__1___24Anonymous__2377) ) )
| ? [Vvar__0___24Anonymous__2378] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__2378)
& ? [Vvar__1___24Anonymous__2379] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__2379)
& ? [Vvar__2___24Anonymous__2380] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__2380)
& VX2373 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__2378,Vvar__1___24Anonymous__2379,Vvar__2___24Anonymous__2380) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__20334,VX20335] :
( cType___24t(Vvar__0__C__20334)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,VX20335)
=> ( VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__20334)
| VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__20334)
| ? [Vvar__1___24Anonymous__20339] :
( t(Vvar__1___24Anonymous__20339,Vvar__0__C__20334)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__20334,Vvar__1___24Anonymous__20339) )
| ? [Vvar__1___24Anonymous__20341] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20341)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__20334,Vvar__1___24Anonymous__20341) )
| ? [Vvar__1___24Anonymous__20343] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20343)
& ? [Vvar__2___24Anonymous__20344] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__2___24Anonymous__20344)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__20334,Vvar__1___24Anonymous__20343,Vvar__2___24Anonymous__20344) ) )
| ? [Vvar__1___24Anonymous__20346] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20346)
& ? [Vvar__2___24Anonymous__20347] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__2___24Anonymous__20347)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__20334,Vvar__1___24Anonymous__20346,Vvar__2___24Anonymous__20347) ) )
| ? [Vvar__1___24Anonymous__20349] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20349)
& ? [Vvar__2___24Anonymous__20350] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__2___24Anonymous__20350)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__20334,Vvar__1___24Anonymous__20349,Vvar__2___24Anonymous__20350) ) )
| ? [Vvar__1___24Anonymous__20352] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20352)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__20334,Vvar__1___24Anonymous__20352) )
| ? [Vvar__1___24Anonymous__20354] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20354)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__20334,Vvar__1___24Anonymous__20354) )
| ? [Vvar__1___24Anonymous__20356] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20356)
& ? [Vvar__2___24Anonymous__20357] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__2___24Anonymous__20357)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__20334,Vvar__1___24Anonymous__20356,Vvar__2___24Anonymous__20357) ) )
| ? [Vvar__1___24Anonymous__20359] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__20334,Vvar__1___24Anonymous__20359)
& ? [Vvar__2___24Anonymous__20360] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20360)
& VX20335 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__20334,Vvar__1___24Anonymous__20359,Vvar__2___24Anonymous__20360) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027] :
( cType___24t(Vvar__0__R__47998)
=> ( t(Vvar__1__rO__47999,Vvar__0__R__47998)
=> ( t(Vvar__2__rI__48000,Vvar__0__R__47998)
=> ( c_24__type__48192___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__3__radd__48001)
=> ( c_24__type__48285___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__4__rmul__48006)
=> ( c_24__type__48378___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__5__rsub__48011)
=> ( c_24__type__48460___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__6__ropp__48016)
=> ( c_24__type__48553___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__7__rdiv__48019)
=> ( c_24__type__48635___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__8__rinv__48024)
=> ( c_24__type__48728___24t(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027,Vvar__9__req__48027)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__7__rdiv__48019,Vvar__8__rinv__48024,Vvar__9__req__48027)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__47998,Vvar__1__rO__47999,Vvar__2__rI__48000,Vvar__3__radd__48001,Vvar__4__rmul__48006,Vvar__5__rsub__48011,Vvar__6__ropp__48016,Vvar__9__req__48027)
& ~ p(happ(happ(Vvar__9__req__48027,Vvar__2__rI__48000),Vvar__1__rO__47999))
& ! [Vvar__var__var__var__var__var__var__12__p__48070__48072__48079__48081__48083__48085__48087] :
( t(Vvar__var__var__var__var__var__var__12__p__48070__48072__48079__48081__48083__48085__48087,Vvar__0__R__47998)
=> ! [Vvar__var__var__var__var__var__var__13__q__48071__48073__48080__48082__48084__48086__48088] :
( t(Vvar__var__var__var__var__var__var__13__q__48071__48073__48080__48082__48084__48086__48088,Vvar__0__R__47998)
=> p(happ(happ(Vvar__9__req__48027,happ(happ(Vvar__7__rdiv__48019,Vvar__var__var__var__var__var__var__12__p__48070__48072__48079__48081__48083__48085__48087),Vvar__var__var__var__var__var__var__13__q__48071__48073__48080__48082__48084__48086__48088)),happ(happ(Vvar__4__rmul__48006,Vvar__var__var__var__var__var__var__12__p__48070__48072__48079__48081__48083__48085__48087),happ(Vvar__8__rinv__48024,Vvar__var__var__var__var__var__var__13__q__48071__48073__48080__48082__48084__48086__48088)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__48075__48077__48089__48091__48093__48095__48097__48099] :
( t(Vvar__var__var__var__var__var__var__var__13__p__48075__48077__48089__48091__48093__48095__48097__48099,Vvar__0__R__47998)
=> ( ~ p(happ(happ(Vvar__9__req__48027,Vvar__var__var__var__var__var__var__var__13__p__48075__48077__48089__48091__48093__48095__48097__48099),Vvar__1__rO__47999))
=> p(happ(happ(Vvar__9__req__48027,happ(happ(Vvar__4__rmul__48006,happ(Vvar__8__rinv__48024,Vvar__var__var__var__var__var__var__var__13__p__48075__48077__48089__48091__48093__48095__48097__48099)),Vvar__var__var__var__var__var__var__var__13__p__48075__48077__48089__48091__48093__48095__48097__48099)),Vvar__2__rI__48000)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__20661,VX20662] :
( cType___24t(Vvar__0__C__20661)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__20661,VX20662)
=> ? [Vvar__1__num__20664] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20661,Vvar__1__num__20664)
& ? [Vvar__2__denum__20665] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20661,Vvar__2__denum__20665)
& ? [Vvar__3__condition__20666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__20661),Vvar__3__condition__20666)
& VX20662 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__20661,Vvar__1__num__20664,Vvar__2__denum__20665,Vvar__3__condition__20666) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__20706,VX20707] :
( cType___24t(Vvar__0__C__20706)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__20706,VX20707)
=> ? [Vvar__1__rsplit__left__20709] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20706,Vvar__1__rsplit__left__20709)
& ? [Vvar__2__rsplit__common__20710] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20706,Vvar__2__rsplit__common__20710)
& ? [Vvar__3__rsplit__right__20711] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__20706,Vvar__3__rsplit__right__20711)
& VX20707 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__20706,Vvar__1__rsplit__left__20709,Vvar__2__rsplit__common__20710,Vvar__3__rsplit__right__20711) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX623] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX623)
=> ( VX623 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__624)
& ? [Vvar__1___24Anonymous__625] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__625)
& VX623 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__624,Vvar__1___24Anonymous__625) ) )
| ? [Vvar__0___24Anonymous__626] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__626)
& ? [Vvar__1___24Anonymous__627] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__627)
& VX623 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__626,Vvar__1___24Anonymous__627) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__644,VX645] :
( cType___24t(Vvar__0__C__644)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,VX645)
=> ( VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__644)
| VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__644)
| ? [Vvar__1___24Anonymous__649] :
( t(Vvar__1___24Anonymous__649,Vvar__0__C__644)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__644,Vvar__1___24Anonymous__649) )
| ? [Vvar__1___24Anonymous__651] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__651)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__644,Vvar__1___24Anonymous__651) )
| ? [Vvar__1___24Anonymous__653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__1___24Anonymous__653)
& ? [Vvar__2___24Anonymous__654] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__2___24Anonymous__654)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__644,Vvar__1___24Anonymous__653,Vvar__2___24Anonymous__654) ) )
| ? [Vvar__1___24Anonymous__656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__1___24Anonymous__656)
& ? [Vvar__2___24Anonymous__657] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__2___24Anonymous__657)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__644,Vvar__1___24Anonymous__656,Vvar__2___24Anonymous__657) ) )
| ? [Vvar__1___24Anonymous__659] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__1___24Anonymous__659)
& ? [Vvar__2___24Anonymous__660] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__2___24Anonymous__660)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__644,Vvar__1___24Anonymous__659,Vvar__2___24Anonymous__660) ) )
| ? [Vvar__1___24Anonymous__662] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__1___24Anonymous__662)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__644,Vvar__1___24Anonymous__662) )
| ? [Vvar__1___24Anonymous__664] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__644,Vvar__1___24Anonymous__664)
& ? [Vvar__2___24Anonymous__665] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__665)
& VX645 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__644,Vvar__1___24Anonymous__664,Vvar__2___24Anonymous__665) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__442,VX443] :
( cType___24t(Vvar__0__C__442)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__442,VX443)
=> ( ? [Vvar__1___24Anonymous__445] :
( t(Vvar__1___24Anonymous__445,Vvar__0__C__442)
& VX443 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__442,Vvar__1___24Anonymous__445) )
| ? [Vvar__1___24Anonymous__447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__447)
& ? [Vvar__2___24Anonymous__448] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__442,Vvar__2___24Anonymous__448)
& VX443 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__442,Vvar__1___24Anonymous__447,Vvar__2___24Anonymous__448) ) )
| ? [Vvar__1___24Anonymous__450] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__442,Vvar__1___24Anonymous__450)
& ? [Vvar__2___24Anonymous__451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__451)
& ? [Vvar__3___24Anonymous__452] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__442,Vvar__3___24Anonymous__452)
& VX443 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__442,Vvar__1___24Anonymous__450,Vvar__2___24Anonymous__451,Vvar__3___24Anonymous__452) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228] :
( cType___24t(Vvar__0__R__8207)
=> ( t(Vvar__1__rO__8208,Vvar__0__R__8207)
=> ( t(Vvar__2__rI__8209,Vvar__0__R__8207)
=> ( c_24__type__8456___24t(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228,Vvar__3__radd__8210)
=> ( c_24__type__8519___24t(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228,Vvar__4__rmul__8215)
=> ( c_24__type__8582___24t(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228,Vvar__5__rsub__8220)
=> ( c_24__type__8636___24t(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228,Vvar__6__ropp__8225)
=> ( c_24__type__8699___24t(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228,Vvar__7__req__8228)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__8207,Vvar__1__rO__8208,Vvar__2__rI__8209,Vvar__3__radd__8210,Vvar__4__rmul__8215,Vvar__5__rsub__8220,Vvar__6__ropp__8225,Vvar__7__req__8228)
=> ( ! [Vvar__var__var__var__var__var__8__x__8261__8262__8315__8316__8317__8318] :
( t(Vvar__var__var__var__var__var__8__x__8261__8262__8315__8316__8317__8318,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__3__radd__8210,Vvar__1__rO__8208),Vvar__var__var__var__var__var__8__x__8261__8262__8315__8316__8317__8318)),Vvar__var__var__var__var__var__8__x__8261__8262__8315__8316__8317__8318)) )
& ! [Vvar__var__var__var__var__9__x__8264__8266__8319__8321__8323] :
( t(Vvar__var__var__var__var__9__x__8264__8266__8319__8321__8323,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__10__y__8265__8267__8320__8322__8324] :
( t(Vvar__var__var__var__var__10__y__8265__8267__8320__8322__8324,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__9__x__8264__8266__8319__8321__8323),Vvar__var__var__var__var__10__y__8265__8267__8320__8322__8324)),happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__10__y__8265__8267__8320__8322__8324),Vvar__var__var__var__var__9__x__8264__8266__8319__8321__8323))) ) )
& ! [Vvar__var__var__var__var__10__x__8269__8272__8325__8328__8331] :
( t(Vvar__var__var__var__var__10__x__8269__8272__8325__8328__8331,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__11__y__8270__8273__8326__8329__8332] :
( t(Vvar__var__var__var__var__11__y__8270__8273__8326__8329__8332,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__12__z__8271__8274__8327__8330__8333] :
( t(Vvar__var__var__var__var__12__z__8271__8274__8327__8330__8333,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__10__x__8269__8272__8325__8328__8331),happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__11__y__8270__8273__8326__8329__8332),Vvar__var__var__var__var__12__z__8271__8274__8327__8330__8333))),happ(happ(Vvar__3__radd__8210,happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__10__x__8269__8272__8325__8328__8331),Vvar__var__var__var__var__11__y__8270__8273__8326__8329__8332)),Vvar__var__var__var__var__12__z__8271__8274__8327__8330__8333))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__8276__8277__8334__8335__8336__8337] :
( t(Vvar__var__var__var__var__var__11__x__8276__8277__8334__8335__8336__8337,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__4__rmul__8215,Vvar__2__rI__8209),Vvar__var__var__var__var__var__11__x__8276__8277__8334__8335__8336__8337)),Vvar__var__var__var__var__var__11__x__8276__8277__8334__8335__8336__8337)) )
& ! [Vvar__var__var__var__var__var__12__x__8279__8280__8338__8339__8340__8341] :
( t(Vvar__var__var__var__var__var__12__x__8279__8280__8338__8339__8340__8341,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__4__rmul__8215,Vvar__1__rO__8208),Vvar__var__var__var__var__var__12__x__8279__8280__8338__8339__8340__8341)),Vvar__1__rO__8208)) )
& ! [Vvar__var__var__var__var__13__x__8282__8284__8342__8344__8346] :
( t(Vvar__var__var__var__var__13__x__8282__8284__8342__8344__8346,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__14__y__8283__8285__8343__8345__8347] :
( t(Vvar__var__var__var__var__14__y__8283__8285__8343__8345__8347,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__13__x__8282__8284__8342__8344__8346),Vvar__var__var__var__var__14__y__8283__8285__8343__8345__8347)),happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__14__y__8283__8285__8343__8345__8347),Vvar__var__var__var__var__13__x__8282__8284__8342__8344__8346))) ) )
& ! [Vvar__var__var__var__var__14__x__8287__8290__8348__8351__8354] :
( t(Vvar__var__var__var__var__14__x__8287__8290__8348__8351__8354,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__15__y__8288__8291__8349__8352__8355] :
( t(Vvar__var__var__var__var__15__y__8288__8291__8349__8352__8355,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__16__z__8289__8292__8350__8353__8356] :
( t(Vvar__var__var__var__var__16__z__8289__8292__8350__8353__8356,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__14__x__8287__8290__8348__8351__8354),happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__15__y__8288__8291__8349__8352__8355),Vvar__var__var__var__var__16__z__8289__8292__8350__8353__8356))),happ(happ(Vvar__4__rmul__8215,happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__14__x__8287__8290__8348__8351__8354),Vvar__var__var__var__var__15__y__8288__8291__8349__8352__8355)),Vvar__var__var__var__var__16__z__8289__8292__8350__8353__8356))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__8294__8297__8357__8360__8363__8366] :
( t(Vvar__var__var__var__var__var__15__x__8294__8297__8357__8360__8363__8366,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__var__16__y__8295__8298__8358__8361__8364__8367] :
( t(Vvar__var__var__var__var__var__16__y__8295__8298__8358__8361__8364__8367,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__var__17__z__8296__8299__8359__8362__8365__8368] :
( t(Vvar__var__var__var__var__var__17__z__8296__8299__8359__8362__8365__8368,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__4__rmul__8215,happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__var__15__x__8294__8297__8357__8360__8363__8366),Vvar__var__var__var__var__var__16__y__8295__8298__8358__8361__8364__8367)),Vvar__var__var__var__var__var__17__z__8296__8299__8359__8362__8365__8368)),happ(happ(Vvar__3__radd__8210,happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__var__15__x__8294__8297__8357__8360__8363__8366),Vvar__var__var__var__var__var__17__z__8296__8299__8359__8362__8365__8368)),happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__var__16__y__8295__8298__8358__8361__8364__8367),Vvar__var__var__var__var__var__17__z__8296__8299__8359__8362__8365__8368)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__8301__8303__8369__8371__8373__8375] :
( t(Vvar__var__var__var__var__var__16__x__8301__8303__8369__8371__8373__8375,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__var__17__y__8302__8304__8370__8372__8374__8376] :
( t(Vvar__var__var__var__var__var__17__y__8302__8304__8370__8372__8374__8376,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(Vvar__6__ropp__8225,happ(happ(Vvar__4__rmul__8215,Vvar__var__var__var__var__var__16__x__8301__8303__8369__8371__8373__8375),Vvar__var__var__var__var__var__17__y__8302__8304__8370__8372__8374__8376))),happ(happ(Vvar__4__rmul__8215,happ(Vvar__6__ropp__8225,Vvar__var__var__var__var__var__16__x__8301__8303__8369__8371__8373__8375)),Vvar__var__var__var__var__var__17__y__8302__8304__8370__8372__8374__8376))) ) )
& ! [Vvar__var__var__var__var__var__17__x__8306__8308__8377__8379__8381__8383] :
( t(Vvar__var__var__var__var__var__17__x__8306__8308__8377__8379__8381__8383,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__var__18__y__8307__8309__8378__8380__8382__8384] :
( t(Vvar__var__var__var__var__var__18__y__8307__8309__8378__8380__8382__8384,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(Vvar__6__ropp__8225,happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__var__17__x__8306__8308__8377__8379__8381__8383),Vvar__var__var__var__var__var__18__y__8307__8309__8378__8380__8382__8384))),happ(happ(Vvar__3__radd__8210,happ(Vvar__6__ropp__8225,Vvar__var__var__var__var__var__17__x__8306__8308__8377__8379__8381__8383)),happ(Vvar__6__ropp__8225,Vvar__var__var__var__var__var__18__y__8307__8309__8378__8380__8382__8384)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__8311__8313__8385__8387__8389__8391__8393] :
( t(Vvar__var__var__var__var__var__var__18__x__8311__8313__8385__8387__8389__8391__8393,Vvar__0__R__8207)
=> ! [Vvar__var__var__var__var__var__var__19__y__8312__8314__8386__8388__8390__8392__8394] :
( t(Vvar__var__var__var__var__var__var__19__y__8312__8314__8386__8388__8390__8392__8394,Vvar__0__R__8207)
=> p(happ(happ(Vvar__7__req__8228,happ(happ(Vvar__5__rsub__8220,Vvar__var__var__var__var__var__var__18__x__8311__8313__8385__8387__8389__8391__8393),Vvar__var__var__var__var__var__var__19__y__8312__8314__8386__8388__8390__8392__8394)),happ(happ(Vvar__3__radd__8210,Vvar__var__var__var__var__var__var__18__x__8311__8313__8385__8387__8389__8391__8393),happ(Vvar__6__ropp__8225,Vvar__var__var__var__var__var__var__19__y__8312__8314__8386__8388__8390__8392__8394)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536] :
( cType___24t(Vvar__0__R__29520)
=> ( t(Vvar__1__rI__29521,Vvar__0__R__29520)
=> ( c_24__type__29622___24t(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536,Vvar__2__rmul__29522)
=> ( c_24__type__29666___24t(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536,Vvar__3__req__29527)
=> ( cType___24t(Vvar__4__Cpow__29532)
=> ( c_24__type__29702___24t(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536,Vvar__5__Cp__phi__29533)
=> ( c_24__type__29746___24t(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536,Vvar__6__rpow__29536)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__3__req__29527,Vvar__4__Cpow__29532,Vvar__5__Cp__phi__29533,Vvar__6__rpow__29536)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__29564__29566__29568__29570__29572__29574__29576__29578] :
( t(Vvar__var__var__var__var__var__var__var__7__r__29564__29566__29568__29570__29572__29574__29576__29578,Vvar__0__R__29520)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__29565__29567__29569__29571__29573__29575__29577__29579] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__29565__29567__29569__29571__29573__29575__29577__29579)
=> p(happ(happ(Vvar__3__req__29527,happ(happ(Vvar__6__rpow__29536,Vvar__var__var__var__var__var__var__var__7__r__29564__29566__29568__29570__29572__29574__29576__29578),happ(Vvar__5__Cp__phi__29533,Vvar__var__var__var__var__var__var__var__8__n__29565__29567__29569__29571__29573__29575__29577__29579))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__29520,Vvar__1__rI__29521,Vvar__2__rmul__29522,Vvar__var__var__var__var__var__var__var__7__r__29564__29566__29568__29570__29572__29574__29576__29578,Vvar__var__var__var__var__var__var__var__8__n__29565__29567__29569__29571__29573__29575__29577__29579))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763] :
( cType___24t(Vvar__0__R__8749)
=> ( c_24__type__8854___24t(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763,Vvar__1__radd__8750)
=> ( c_24__type__8884___24t(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763,Vvar__2__rmul__8755)
=> ( c_24__type__8908___24t(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763,Vvar__3__ropp__8760)
=> ( c_24__type__8938___24t(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763,Vvar__4__req__8763)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8968___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8749,c_24__type__8992___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763),Vvar__4__req__8763,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8749,Vvar__0__R__8749,Vvar__4__req__8763,Vvar__4__req__8763)),Vvar__1__radd__8750)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9025___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8749,c_24__type__9049___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763),Vvar__4__req__8763,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8749,Vvar__0__R__8749,Vvar__4__req__8763,Vvar__4__req__8763)),Vvar__2__rmul__8755)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9076___24a5(Vvar__0__R__8749,Vvar__1__radd__8750,Vvar__2__rmul__8755,Vvar__3__ropp__8760,Vvar__4__req__8763),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__8749,Vvar__0__R__8749,Vvar__4__req__8763,Vvar__4__req__8763),Vvar__3__ropp__8760)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485] :
( cType___24t(Vvar__0__R__26433)
=> ( t(Vvar__1__rO__26434,Vvar__0__R__26433)
=> ( t(Vvar__2__rI__26435,Vvar__0__R__26433)
=> ( c_24__type__26829___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__3__radd__26436)
=> ( c_24__type__27042___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__4__rmul__26441)
=> ( c_24__type__27255___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__5__rsub__26446)
=> ( c_24__type__27450___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__6__ropp__26451)
=> ( c_24__type__27663___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__7__req__26454)
=> ( cType___24t(Vvar__8__C__26459)
=> ( t(Vvar__9__cO__26460,Vvar__8__C__26459)
=> ( t(Vvar__10__cI__26461,Vvar__8__C__26459)
=> ( c_24__type__27876___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__11__cadd__26462)
=> ( c_24__type__28089___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__12__cmul__26467)
=> ( c_24__type__28302___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__13__csub__26472)
=> ( c_24__type__28497___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__14__copp__26477)
=> ( c_24__type__28710___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__15__ceqb__26480)
=> ( c_24__type__28905___24t(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485,Vvar__16__phi__26485)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__26433,Vvar__1__rO__26434,Vvar__2__rI__26435,Vvar__3__radd__26436,Vvar__4__rmul__26441,Vvar__5__rsub__26446,Vvar__6__ropp__26451,Vvar__7__req__26454,Vvar__8__C__26459,Vvar__9__cO__26460,Vvar__10__cI__26461,Vvar__11__cadd__26462,Vvar__12__cmul__26467,Vvar__13__csub__26472,Vvar__14__copp__26477,Vvar__15__ceqb__26480,Vvar__16__phi__26485)
=> ( p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,Vvar__9__cO__26460)),Vvar__1__rO__26434))
& p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,Vvar__10__cI__26461)),Vvar__2__rI__26435))
& ! [Vvar__var__var__var__var__var__var__19__x__26547__26549__26571__26573__26575__26577__26579] :
( t(Vvar__var__var__var__var__var__var__19__x__26547__26549__26571__26573__26575__26577__26579,Vvar__8__C__26459)
=> ! [Vvar__var__var__var__var__var__var__20__y__26548__26550__26572__26574__26576__26578__26580] :
( t(Vvar__var__var__var__var__var__var__20__y__26548__26550__26572__26574__26576__26578__26580,Vvar__8__C__26459)
=> p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,happ(happ(Vvar__11__cadd__26462,Vvar__var__var__var__var__var__var__19__x__26547__26549__26571__26573__26575__26577__26579),Vvar__var__var__var__var__var__var__20__y__26548__26550__26572__26574__26576__26578__26580))),happ(happ(Vvar__3__radd__26436,happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__19__x__26547__26549__26571__26573__26575__26577__26579)),happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__20__y__26548__26550__26572__26574__26576__26578__26580)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__26552__26554__26581__26583__26585__26587__26589] :
( t(Vvar__var__var__var__var__var__var__20__x__26552__26554__26581__26583__26585__26587__26589,Vvar__8__C__26459)
=> ! [Vvar__var__var__var__var__var__var__21__y__26553__26555__26582__26584__26586__26588__26590] :
( t(Vvar__var__var__var__var__var__var__21__y__26553__26555__26582__26584__26586__26588__26590,Vvar__8__C__26459)
=> p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,happ(happ(Vvar__13__csub__26472,Vvar__var__var__var__var__var__var__20__x__26552__26554__26581__26583__26585__26587__26589),Vvar__var__var__var__var__var__var__21__y__26553__26555__26582__26584__26586__26588__26590))),happ(happ(Vvar__5__rsub__26446,happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__20__x__26552__26554__26581__26583__26585__26587__26589)),happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__21__y__26553__26555__26582__26584__26586__26588__26590)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__26557__26559__26591__26593__26595__26597__26599] :
( t(Vvar__var__var__var__var__var__var__21__x__26557__26559__26591__26593__26595__26597__26599,Vvar__8__C__26459)
=> ! [Vvar__var__var__var__var__var__var__22__y__26558__26560__26592__26594__26596__26598__26600] :
( t(Vvar__var__var__var__var__var__var__22__y__26558__26560__26592__26594__26596__26598__26600,Vvar__8__C__26459)
=> p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,happ(happ(Vvar__12__cmul__26467,Vvar__var__var__var__var__var__var__21__x__26557__26559__26591__26593__26595__26597__26599),Vvar__var__var__var__var__var__var__22__y__26558__26560__26592__26594__26596__26598__26600))),happ(happ(Vvar__4__rmul__26441,happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__21__x__26557__26559__26591__26593__26595__26597__26599)),happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__22__y__26558__26560__26592__26594__26596__26598__26600)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__26562__26563__26601__26602__26603__26604__26605] :
( t(Vvar__var__var__var__var__var__var__22__x__26562__26563__26601__26602__26603__26604__26605,Vvar__8__C__26459)
=> p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,happ(Vvar__14__copp__26477,Vvar__var__var__var__var__var__var__22__x__26562__26563__26601__26602__26603__26604__26605))),happ(Vvar__6__ropp__26451,happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__var__22__x__26562__26563__26601__26602__26603__26604__26605)))) )
& ! [Vvar__var__var__var__var__var__23__x__26565__26568__26606__26609__26612__26615] :
( t(Vvar__var__var__var__var__var__23__x__26565__26568__26606__26609__26612__26615,Vvar__8__C__26459)
=> ! [Vvar__var__var__var__var__var__24__y__26566__26569__26607__26610__26613__26616] :
( t(Vvar__var__var__var__var__var__24__y__26566__26569__26607__26610__26613__26616,Vvar__8__C__26459)
=> ( happ(happ(Vvar__15__ceqb__26480,Vvar__var__var__var__var__var__23__x__26565__26568__26606__26609__26612__26615),Vvar__var__var__var__var__var__24__y__26566__26569__26607__26610__26613__26616) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__26454,happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__23__x__26565__26568__26606__26609__26612__26615)),happ(Vvar__16__phi__26485,Vvar__var__var__var__var__var__24__y__26566__26569__26607__26610__26613__26616))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098] :
( cType___24t(Vvar__0__R__47077)
=> ( t(Vvar__1__rO__47078,Vvar__0__R__47077)
=> ( t(Vvar__2__rI__47079,Vvar__0__R__47077)
=> ( c_24__type__47301___24t(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098,Vvar__3__radd__47080)
=> ( c_24__type__47364___24t(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098,Vvar__4__rmul__47085)
=> ( c_24__type__47427___24t(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098,Vvar__5__rsub__47090)
=> ( c_24__type__47481___24t(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098,Vvar__6__ropp__47095)
=> ( c_24__type__47544___24t(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098,Vvar__7__req__47098)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__47077,Vvar__1__rO__47078,Vvar__2__rI__47079,Vvar__3__radd__47080,Vvar__4__rmul__47085,Vvar__5__rsub__47090,Vvar__6__ropp__47095,Vvar__7__req__47098)
=> ( ! [Vvar__var__var__var__var__var__8__x__47131__47132__47175__47176__47177__47178] :
( t(Vvar__var__var__var__var__var__8__x__47131__47132__47175__47176__47177__47178,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__3__radd__47080,Vvar__1__rO__47078),Vvar__var__var__var__var__var__8__x__47131__47132__47175__47176__47177__47178)),Vvar__var__var__var__var__var__8__x__47131__47132__47175__47176__47177__47178)) )
& ! [Vvar__var__var__var__var__9__x__47134__47136__47179__47181__47183] :
( t(Vvar__var__var__var__var__9__x__47134__47136__47179__47181__47183,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__10__y__47135__47137__47180__47182__47184] :
( t(Vvar__var__var__var__var__10__y__47135__47137__47180__47182__47184,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__9__x__47134__47136__47179__47181__47183),Vvar__var__var__var__var__10__y__47135__47137__47180__47182__47184)),happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__10__y__47135__47137__47180__47182__47184),Vvar__var__var__var__var__9__x__47134__47136__47179__47181__47183))) ) )
& ! [Vvar__var__var__var__var__10__x__47139__47142__47185__47188__47191] :
( t(Vvar__var__var__var__var__10__x__47139__47142__47185__47188__47191,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__11__y__47140__47143__47186__47189__47192] :
( t(Vvar__var__var__var__var__11__y__47140__47143__47186__47189__47192,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__12__z__47141__47144__47187__47190__47193] :
( t(Vvar__var__var__var__var__12__z__47141__47144__47187__47190__47193,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__10__x__47139__47142__47185__47188__47191),happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__11__y__47140__47143__47186__47189__47192),Vvar__var__var__var__var__12__z__47141__47144__47187__47190__47193))),happ(happ(Vvar__3__radd__47080,happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__10__x__47139__47142__47185__47188__47191),Vvar__var__var__var__var__11__y__47140__47143__47186__47189__47192)),Vvar__var__var__var__var__12__z__47141__47144__47187__47190__47193))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__47146__47147__47194__47195__47196__47197] :
( t(Vvar__var__var__var__var__var__11__x__47146__47147__47194__47195__47196__47197,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__4__rmul__47085,Vvar__2__rI__47079),Vvar__var__var__var__var__var__11__x__47146__47147__47194__47195__47196__47197)),Vvar__var__var__var__var__var__11__x__47146__47147__47194__47195__47196__47197)) )
& ! [Vvar__var__var__var__var__12__x__47149__47151__47198__47200__47202] :
( t(Vvar__var__var__var__var__12__x__47149__47151__47198__47200__47202,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__13__y__47150__47152__47199__47201__47203] :
( t(Vvar__var__var__var__var__13__y__47150__47152__47199__47201__47203,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__12__x__47149__47151__47198__47200__47202),Vvar__var__var__var__var__13__y__47150__47152__47199__47201__47203)),happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__13__y__47150__47152__47199__47201__47203),Vvar__var__var__var__var__12__x__47149__47151__47198__47200__47202))) ) )
& ! [Vvar__var__var__var__var__13__x__47154__47157__47204__47207__47210] :
( t(Vvar__var__var__var__var__13__x__47154__47157__47204__47207__47210,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__14__y__47155__47158__47205__47208__47211] :
( t(Vvar__var__var__var__var__14__y__47155__47158__47205__47208__47211,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__15__z__47156__47159__47206__47209__47212] :
( t(Vvar__var__var__var__var__15__z__47156__47159__47206__47209__47212,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__13__x__47154__47157__47204__47207__47210),happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__14__y__47155__47158__47205__47208__47211),Vvar__var__var__var__var__15__z__47156__47159__47206__47209__47212))),happ(happ(Vvar__4__rmul__47085,happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__13__x__47154__47157__47204__47207__47210),Vvar__var__var__var__var__14__y__47155__47158__47205__47208__47211)),Vvar__var__var__var__var__15__z__47156__47159__47206__47209__47212))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__47161__47164__47213__47216__47219__47222] :
( t(Vvar__var__var__var__var__var__14__x__47161__47164__47213__47216__47219__47222,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__var__15__y__47162__47165__47214__47217__47220__47223] :
( t(Vvar__var__var__var__var__var__15__y__47162__47165__47214__47217__47220__47223,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__var__16__z__47163__47166__47215__47218__47221__47224] :
( t(Vvar__var__var__var__var__var__16__z__47163__47166__47215__47218__47221__47224,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__4__rmul__47085,happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__var__14__x__47161__47164__47213__47216__47219__47222),Vvar__var__var__var__var__var__15__y__47162__47165__47214__47217__47220__47223)),Vvar__var__var__var__var__var__16__z__47163__47166__47215__47218__47221__47224)),happ(happ(Vvar__3__radd__47080,happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__var__14__x__47161__47164__47213__47216__47219__47222),Vvar__var__var__var__var__var__16__z__47163__47166__47215__47218__47221__47224)),happ(happ(Vvar__4__rmul__47085,Vvar__var__var__var__var__var__15__y__47162__47165__47214__47217__47220__47223),Vvar__var__var__var__var__var__16__z__47163__47166__47215__47218__47221__47224)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__47168__47170__47225__47227__47229__47231__47233] :
( t(Vvar__var__var__var__var__var__var__15__x__47168__47170__47225__47227__47229__47231__47233,Vvar__0__R__47077)
=> ! [Vvar__var__var__var__var__var__var__16__y__47169__47171__47226__47228__47230__47232__47234] :
( t(Vvar__var__var__var__var__var__var__16__y__47169__47171__47226__47228__47230__47232__47234,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__5__rsub__47090,Vvar__var__var__var__var__var__var__15__x__47168__47170__47225__47227__47229__47231__47233),Vvar__var__var__var__var__var__var__16__y__47169__47171__47226__47228__47230__47232__47234)),happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__var__var__15__x__47168__47170__47225__47227__47229__47231__47233),happ(Vvar__6__ropp__47095,Vvar__var__var__var__var__var__var__16__y__47169__47171__47226__47228__47230__47232__47234)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__47173__47174__47235__47236__47237__47238__47239] :
( t(Vvar__var__var__var__var__var__var__16__x__47173__47174__47235__47236__47237__47238__47239,Vvar__0__R__47077)
=> p(happ(happ(Vvar__7__req__47098,happ(happ(Vvar__3__radd__47080,Vvar__var__var__var__var__var__var__16__x__47173__47174__47235__47236__47237__47238__47239),happ(Vvar__6__ropp__47095,Vvar__var__var__var__var__var__var__16__x__47173__47174__47235__47236__47237__47238__47239))),Vvar__1__rO__47078)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.InP',axiom,
! [Vvar__0__X__13063,Vvar__1__P__13064,Vvar__2___24Anonymous__13067] :
( cType___24t(Vvar__0__X__13063)
=> ( c_24__type__13087___24t(Vvar__0__X__13063,Vvar__1__P__13064,Vvar__2___24Anonymous__13067,Vvar__1__P__13064)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__13063,Vvar__2___24Anonymous__13067)
=> ( cQuicksortComplexity_2elist__utils_2eInP___24a3(Vvar__0__X__13063,Vvar__1__P__13064,Vvar__2___24Anonymous__13067)
=> ( ? [Vvar__2__x__13073] :
( t(Vvar__2__x__13073,Vvar__0__X__13063)
& ? [Vvar__3__t__13074] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__13063,Vvar__3__t__13074)
& p(happ(Vvar__1__P__13064,Vvar__2__x__13073))
& Vvar__2___24Anonymous__13067 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__X__13063,Vvar__2__x__13073,Vvar__3__t__13074) ) )
| ? [Vvar__2__x__13080] :
( t(Vvar__2__x__13080,Vvar__0__X__13063)
& ? [Vvar__3__t__13081] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__13063,Vvar__3__t__13081)
& cQuicksortComplexity_2elist__utils_2eInP___24a3(Vvar__0__X__13063,Vvar__1__P__13064,Vvar__3__t__13081)
& Vvar__2___24Anonymous__13067 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__X__13063,Vvar__2__x__13080,Vvar__3__t__13081) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.NoDupL',axiom,
! [Vvar__0__A__13100,Vvar__1___24Anonymous__13101] :
( cType___24t(Vvar__0__A__13100)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__13100),Vvar__1___24Anonymous__13101)
=> ( cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(Vvar__0__A__13100,Vvar__1___24Anonymous__13101)
=> ( Vvar__1___24Anonymous__13101 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__13100))
| ? [Vvar__1__l__13105] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__13100,Vvar__1__l__13105)
& ? [Vvar__2__ll__13106] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__13100),Vvar__2__ll__13106)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__13100,Vvar__1__l__13105)
& ! [Vvar__var__var__4__x__13109__13111__13114] :
( t(Vvar__var__var__4__x__13109__13111__13114,Vvar__0__A__13100)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__13100,Vvar__var__var__4__x__13109__13111__13114,Vvar__1__l__13105))
=> ~ cQuicksortComplexity_2elist__utils_2eInP___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__13100),cCoq_2eLists_2eList_2eIn___24a2(Vvar__0__A__13100,Vvar__var__var__4__x__13109__13111__13114),Vvar__2__ll__13106) ) )
& cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(Vvar__0__A__13100,Vvar__2__ll__13106)
& Vvar__1___24Anonymous__13101 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__13100),Vvar__1__l__13105,Vvar__2__ll__13106) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.elemsR',axiom,
! [Vvar__0__A__2438,Vvar__1__B__2439,Vvar__2__R__2440,Vvar__3___24Anonymous__2445,Vvar__4___24Anonymous__2446] :
( cType___24t(Vvar__0__A__2438)
=> ( cType___24t(Vvar__1__B__2439)
=> ( c_24__type__2483___24t(Vvar__0__A__2438,Vvar__1__B__2439,Vvar__2__R__2440,Vvar__3___24Anonymous__2445,Vvar__4___24Anonymous__2446,Vvar__2__R__2440)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2438,Vvar__3___24Anonymous__2445)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__2439,Vvar__4___24Anonymous__2446)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__2438,Vvar__1__B__2439,Vvar__2__R__2440,Vvar__3___24Anonymous__2445,Vvar__4___24Anonymous__2446)
=> ( ( Vvar__4___24Anonymous__2446 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__2439)
& Vvar__3___24Anonymous__2445 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2438) )
| ? [Vvar__3__a__2462] :
( t(Vvar__3__a__2462,Vvar__0__A__2438)
& ? [Vvar__4__b__2463] :
( t(Vvar__4__b__2463,Vvar__1__B__2439)
& p(happ(happ(Vvar__2__R__2440,Vvar__3__a__2462),Vvar__4__b__2463))
& ? [Vvar__6__l__2465] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2438,Vvar__6__l__2465)
& ? [Vvar__7__l_27__2466] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__2439,Vvar__7__l_27__2466)
& cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__2438,Vvar__1__B__2439,Vvar__2__R__2440,Vvar__6__l__2465,Vvar__7__l_27__2466)
& Vvar__4___24Anonymous__2446 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__2439,Vvar__4__b__2463,Vvar__7__l_27__2466)
& Vvar__3___24Anonymous__2445 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2438,Vvar__3__a__2462,Vvar__6__l__2465) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.nat_below.natBelow',axiom,
! [Vvar__0___24Anonymous__2800,VX2801] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2800)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vvar__0___24Anonymous__2800,VX2801)
=> ? [Vvar__0__v__2802] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__2802)
& ? [Vvar__1__p__2803] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__2803)
& Vvar__0___24Anonymous__2800 = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_242850___24a3(Vvar__0___24Anonymous__2800,Vvar__0__v__2802,Vvar__1__p__2803))
& VX2801 = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__2802,Vvar__1__p__2803) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.vec.sorted',axiom,
! [Vvar__0__X__30855,Vvar__1__Xle__30856,Vvar__2__n__30861,Vvar__3___24Anonymous__30862] :
( cType___24t(Vvar__0__X__30855)
=> ( c_24__type__30900___24t(Vvar__0__X__30855,Vvar__1__Xle__30856,Vvar__2__n__30861,Vvar__3___24Anonymous__30862,Vvar__1__Xle__30856)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30861)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__X__30855,Vvar__2__n__30861,Vvar__3___24Anonymous__30862)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(Vvar__0__X__30855,Vvar__1__Xle__30856,Vvar__2__n__30861,Vvar__3___24Anonymous__30862)
=> ( ( Vvar__3___24Anonymous__30862 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__X__30855)
& Vvar__2__n__30861 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__x__30876] :
( t(Vvar__2__x__30876,Vvar__0__X__30855)
& Vvar__3___24Anonymous__30862 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__30855,Vvar__2__x__30876,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__X__30855))
& Vvar__2__n__30861 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__2__a__30883] :
( t(Vvar__2__a__30883,Vvar__0__X__30855)
& ? [Vvar__3__b__30884] :
( t(Vvar__3__b__30884,Vvar__0__X__30855)
& ? [Vvar__4__n__30885] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__n__30885)
& ? [Vvar__5__t__30886] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__X__30855,Vvar__4__n__30885,Vvar__5__t__30886)
& p(happ(happ(Vvar__1__Xle__30856,Vvar__2__a__30883),Vvar__3__b__30884))
& cQuicksortComplexity_2evec_2esorted___24a4(Vvar__0__X__30855,Vvar__1__Xle__30856,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__30885),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__30855,Vvar__3__b__30884,Vvar__4__n__30885,Vvar__5__t__30886))
& Vvar__3___24Anonymous__30862 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__30855,Vvar__2__a__30883,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__30885),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__30855,Vvar__3__b__30884,Vvar__4__n__30885,Vvar__5__t__30886))
& Vvar__2__n__30861 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__30885)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_1165',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__1165___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__1093___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___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__11)) ).
fof('$_lam_20870',axiom,
! [Vv__CANONICAL__0] : c_24__lam__20870___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ ).
fof('$_lam_20872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__20872___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(Vv__CANONICAL__0) ).
fof('$_lam_41219',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__41219___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_41227',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__41227___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_41235',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__41235___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_41243',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__41243___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_43879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__43879___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_lam_50211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__50211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_6433',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__6433___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_prop_20161',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__20161___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_30978',axiom,
! [V0__A,V1__x,V2__y] :
( p(c_24__prop__30978___24a3(V0__A,V1__x,V2__y))
<=> V1__x = V2__y ) ).
fof('$_prop_32477',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__32477___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_34028',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__34028___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> cCoq_2eLists_2eList_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ).
fof('$_prop_35327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__35327___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_35521',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__35521___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_43321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43321___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_43322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_43728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43728___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_43729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43729___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_43771',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__43771___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_43869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43869___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_43893',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__43893___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_43894',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__43894___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_43941',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__43941___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_43942',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__43942___24a2(V0__x,V1__y))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ).
fof('$_prop_49745',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__49745___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_5375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__5375___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_5376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__5376___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_5377',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__5377___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ).
fof('$_prop_5424',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__5404] :
( p(c_24__prop__5424___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
<=> V3__x = Vvar__1___24Anonymous__5404 ) ).
fof('$_prop_5425',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__5404] :
( p(c_24__prop__5425___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
<=> V3__x != Vvar__1___24Anonymous__5404 ) ).
fof('$_prop_5426',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__5404] :
( p(c_24__prop__5426___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
<=> V3__x = Vvar__1___24Anonymous__5404 ) ).
fof('$_prop_5427',axiom,
! [V0__A,V3__x,Vvar__1___24Anonymous__5404] :
( p(c_24__prop__5427___24a3(V0__A,V3__x,Vvar__1___24Anonymous__5404))
<=> V3__x != Vvar__1___24Anonymous__5404 ) ).
fof('$_prop_5559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__5559___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_5560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__5560___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_5561',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__5561___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_5562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__5562___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_6706',axiom,
! [V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687] :
( p(c_24__prop__6706___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687)) ) ).
fof('$_prop_6718',axiom,
! [V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687] :
( p(c_24__prop__6718___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,Vvar__1___24Anonymous__6686,Vvar__2___24Anonymous__6687)) ) ).
fof('$_type_10431',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10432] :
( c_24__type__10431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10432)
<=> ! [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__10432,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_1057',axiom,
! [Vvar__1058] :
( c_24__type__1057___24t(Vvar__1058)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1058,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1062',axiom,
! [Vv__CANONICAL__0,Vvar__1063] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vvar__1063)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1063,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1071',axiom,
! [Vv__CANONICAL__0,Vvar__1072] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vvar__1072)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1072,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1075',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1076] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1076)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1076,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1080',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1081] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1081)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__1081,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_10815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10816] :
( c_24__type__10815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10816)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10816,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10819',axiom,
! [Vvar__10820] :
( c_24__type__10819___24t(Vvar__10820)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10820,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10822',axiom,
! [Vv__CANONICAL__0,Vvar__10823] :
( c_24__type__10822___24t(Vv__CANONICAL__0,Vvar__10823)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10823,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10845',axiom,
! [Vvar__10846] :
( c_24__type__10845___24t(Vvar__10846)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__10846,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_10850',axiom,
! [Vvar__10851] :
( c_24__type__10850___24t(Vvar__10851)
<=> ! [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__10851,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_10876',axiom,
! [Vvar__10877] :
( c_24__type__10876___24t(Vvar__10877)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__10880___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__10887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__10894___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__10877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_10880',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10881] :
( c_24__type__10880___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10881)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__10881,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10888] :
( c_24__type__10887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10888)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__10888,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eleft___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_1089',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1090] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1090)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__1090,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10894',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10895] :
( c_24__type__10894___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__10895)
<=> ( p(Vv__CANONICAL__1)
=> t(Vvar__10895,happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eright___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ) ).
fof('$_type_10906',axiom,
! [Vvar__10907] :
( c_24__type__10906___24t(Vvar__10907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10907,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11014',axiom,
! [Vvar__11015] :
( c_24__type__11014___24t(Vvar__11015)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__11015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12191',axiom,
! [Vvar__12192] :
( c_24__type__12191___24t(Vvar__12192)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__12192,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12264',axiom,
! [Vvar__12265] :
( c_24__type__12264___24t(Vvar__12265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__12265,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12270',axiom,
! [Vvar__12271] :
( c_24__type__12270___24t(Vvar__12271)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12271,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12427',axiom,
! [Vv__CANONICAL__0,Vvar__12428] :
( c_24__type__12427___24t(Vv__CANONICAL__0,Vvar__12428)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__12428,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1297',axiom,
! [Vvar__1298] :
( c_24__type__1297___24t(Vvar__1298)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1315___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_13040',axiom,
! [Vvar__13041] :
( c_24__type__13040___24t(Vvar__13041)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__13041,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13056',axiom,
! [Vvar__13057] :
( c_24__type__13056___24t(Vvar__13057)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6478___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__13057,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_13087',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13088] :
( c_24__type__13087___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13088)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__13088,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1315',axiom,
! [Vv__CANONICAL__0,Vvar__1316] :
( c_24__type__1315___24t(Vv__CANONICAL__0,Vvar__1316)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__1316,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_13392',axiom,
! [Vvar__13393] :
( c_24__type__13392___24t(Vvar__13393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__13393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1553',axiom,
! [Vvar__1554] :
( c_24__type__1553___24t(Vvar__1554)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1554,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1738',axiom,
! [Vvar__1739] :
( c_24__type__1738___24t(Vvar__1739)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1315___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1739,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1774',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1775] :
( c_24__type__1774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1775)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__1775,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_1788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1789] :
( c_24__type__1788___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1789)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__1789,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_1795',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1796] :
( c_24__type__1795___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1796)
<=> ! [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__1796,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1817] :
( c_24__type__1816___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1817)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__1817,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1836',axiom,
! [Vvar__1837] :
( c_24__type__1836___24t(Vvar__1837)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1062___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__1837,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_1841',axiom,
! [Vvar__1842] :
( c_24__type__1841___24t(Vvar__1842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1842,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1856',axiom,
! [Vvar__1857] :
( c_24__type__1856___24t(Vvar__1857)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1857,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19',axiom,
! [Vvar__20] :
( c_24__type__19___24t(Vvar__20)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__20,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1926',axiom,
! [Vvar__1927] :
( c_24__type__1926___24t(Vvar__1927)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1927,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19289',axiom,
! [Vvar__19290] :
( c_24__type__19289___24t(Vvar__19290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__19290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_1958',axiom,
! [Vv__CANONICAL__0,Vvar__1959] :
( c_24__type__1958___24t(Vv__CANONICAL__0,Vvar__1959)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__1959,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19679',axiom,
! [Vvar__19680] :
( c_24__type__19679___24t(Vvar__19680)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__19680,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1971',axiom,
! [Vvar__1972] :
( c_24__type__1971___24t(Vvar__1972)
<=> ! [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__1972,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19777',axiom,
! [Vvar__19778] :
( c_24__type__19777___24t(Vvar__19778)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__19778,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19814',axiom,
! [Vvar__19815] :
( c_24__type__19814___24t(Vvar__19815)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__19815,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19816',axiom,
! [Vvar__19817] :
( c_24__type__19816___24t(Vvar__19817)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__19817,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1983',axiom,
! [Vvar__1984] :
( c_24__type__1983___24t(Vvar__1984)
<=> ! [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__1984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_19854',axiom,
! [Vvar__19855] :
( c_24__type__19854___24t(Vvar__19855)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__19855,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20055',axiom,
! [Vvar__20056] :
( c_24__type__20055___24t(Vvar__20056)
<=> ! [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__20056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20061',axiom,
! [Vvar__20062] :
( c_24__type__20061___24t(Vvar__20062)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__20062,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20111',axiom,
! [Vv__CANONICAL__0,Vvar__20112] :
( c_24__type__20111___24t(Vv__CANONICAL__0,Vvar__20112)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__20112,Vv__CANONICAL__1)) ) ) ).
fof('$_type_20124',axiom,
! [Vvar__20125] :
( c_24__type__20124___24t(Vvar__20125)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__2565___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__20129___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__20125,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_20129',axiom,
! [Vv__CANONICAL__0,Vvar__20130] :
( c_24__type__20129___24t(Vv__CANONICAL__0,Vvar__20130)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__20130,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_2014',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2015] :
( c_24__type__2014___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2015)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__2015,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20159',axiom,
! [Vvar__20160] :
( c_24__type__20159___24t(Vvar__20160)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__20160,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2038',axiom,
! [Vvar__2039] :
( c_24__type__2038___24t(Vvar__2039)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__2039,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_2045',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2046] :
( c_24__type__2045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2046)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2046,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2047',axiom,
! [Vvar__2048] :
( c_24__type__2047___24t(Vvar__2048)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2048,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2052',axiom,
! [Vv__CANONICAL__0,Vvar__2053] :
( c_24__type__2052___24t(Vv__CANONICAL__0,Vvar__2053)
<=> ! [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__2053,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2062',axiom,
! [Vvar__2063] :
( c_24__type__2062___24t(Vvar__2063)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2063,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20684',axiom,
! [Vvar__20685] :
( c_24__type__20684___24t(Vvar__20685)
<=> ! [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__20685,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20704',axiom,
! [Vvar__20705] :
( c_24__type__20704___24t(Vvar__20705)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__20705,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20754',axiom,
! [Vvar__20755] :
( c_24__type__20754___24t(Vvar__20755)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__20755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20757',axiom,
! [Vvar__20758] :
( c_24__type__20757___24t(Vvar__20758)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__20758,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20760',axiom,
! [Vvar__20761] :
( c_24__type__20760___24t(Vvar__20761)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__20761,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20765',axiom,
! [Vvar__20766] :
( c_24__type__20765___24t(Vvar__20766)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__20766,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20786',axiom,
! [Vvar__20787] :
( c_24__type__20786___24t(Vvar__20787)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__20754___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__20787,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20819',axiom,
! [Vvar__20820] :
( c_24__type__20819___24t(Vvar__20820)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__20820,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20840',axiom,
! [Vv__CANONICAL__0,Vvar__20841] :
( c_24__type__20840___24t(Vv__CANONICAL__0,Vvar__20841)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__20841,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20874',axiom,
! [Vvar__20875] :
( c_24__type__20874___24t(Vvar__20875)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__20875,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20895',axiom,
! [Vvar__20896] :
( c_24__type__20895___24t(Vvar__20896)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__71___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__71___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__20896,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21062',axiom,
! [Vvar__21063] :
( c_24__type__21062___24t(Vvar__21063)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21063,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21065',axiom,
! [Vvar__21066] :
( c_24__type__21065___24t(Vvar__21066)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__21066,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21132',axiom,
! [Vvar__21133] :
( c_24__type__21132___24t(Vvar__21133)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__21133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21146',axiom,
! [Vvar__21147] :
( c_24__type__21146___24t(Vvar__21147)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6478___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__21147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2328] :
( c_24__type__2327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2328)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__2328,Vv__CANONICAL__3)) ) ) ).
fof('$_type_2330',axiom,
! [Vvar__2331] :
( c_24__type__2330___24t(Vvar__2331)
<=> ! [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__2331,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2346',axiom,
! [Vvar__2347] :
( c_24__type__2346___24t(Vvar__2347)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2347,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2368',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2369] :
( c_24__type__2368___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2369)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2369,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24386',axiom,
! [Vvar__24387] :
( c_24__type__24386___24t(Vvar__24387)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__24387,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_24420',axiom,
! [Vvar__24421] :
( c_24__type__24420___24t(Vvar__24421)
<=> ! [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__24421,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24456',axiom,
! [Vvar__24457] :
( c_24__type__24456___24t(Vvar__24457)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24457,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24513',axiom,
! [Vvar__24514] :
( c_24__type__24513___24t(Vvar__24514)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__24514,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_24824',axiom,
! [Vvar__24825] :
( c_24__type__24824___24t(Vvar__24825)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__24825,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2483',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2484] :
( c_24__type__2483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__2484)
<=> ! [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__2484,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_2490',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2491] :
( c_24__type__2490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2491)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2491,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2523',axiom,
! [Vvar__2524] :
( c_24__type__2523___24t(Vvar__2524)
<=> ! [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__2524,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2537',axiom,
! [Vvar__2538] :
( c_24__type__2537___24t(Vvar__2538)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2538,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2544',axiom,
! [Vvar__2545] :
( c_24__type__2544___24t(Vvar__2545)
<=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__2545,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25449',axiom,
! [Vvar__25450] :
( c_24__type__25449___24t(Vvar__25450)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__25450,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_25460',axiom,
! [Vvar__25461] :
( c_24__type__25460___24t(Vvar__25461)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__25461,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2547',axiom,
! [Vvar__2548] :
( c_24__type__2547___24t(Vvar__2548)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2548,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2550',axiom,
! [Vvar__2551] :
( c_24__type__2550___24t(Vvar__2551)
<=> ! [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__2551,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25501',axiom,
! [Vvar__25502] :
( c_24__type__25501___24t(Vvar__25502)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__25502,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_2552',axiom,
! [Vvar__2553] :
( c_24__type__2552___24t(Vvar__2553)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2553,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25547',axiom,
! [Vv__CANONICAL__0,Vvar__25548] :
( c_24__type__25547___24t(Vv__CANONICAL__0,Vvar__25548)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__25548,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_25619',axiom,
! [Vvar__25620] :
( c_24__type__25619___24t(Vvar__25620)
<=> ! [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__25620,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25622',axiom,
! [Vvar__25623] :
( c_24__type__25622___24t(Vvar__25623)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__25623,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25625',axiom,
! [Vvar__25626] :
( c_24__type__25625___24t(Vvar__25626)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__25626,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25628',axiom,
! [Vvar__25629] :
( c_24__type__25628___24t(Vvar__25629)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__25629,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25631',axiom,
! [Vvar__25632] :
( c_24__type__25631___24t(Vvar__25632)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(Vvar__25632,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25642',axiom,
! [Vvar__25643] :
( c_24__type__25642___24t(Vvar__25643)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__25643,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2565',axiom,
! [Vvar__2566] :
( c_24__type__2565___24t(Vvar__2566)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2566,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26164',axiom,
! [Vvar__26165] :
( c_24__type__26164___24t(Vvar__26165)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__1795___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__2327___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__26165,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_2659',axiom,
! [Vvar__2660] :
( c_24__type__2659___24t(Vvar__2660)
<=> ! [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)
=> cProp___24t(happ(happ(happ(Vvar__2660,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_26829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26830] :
( c_24__type__26829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__26830)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26830,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27043] :
( c_24__type__27042___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__27043)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27043,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2715] :
( c_24__type__2714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2715)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2715,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2718',axiom,
! [Vvar__2719] :
( c_24__type__2718___24t(Vvar__2719)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2719,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2721',axiom,
! [Vv__CANONICAL__0,Vvar__2722] :
( c_24__type__2721___24t(Vv__CANONICAL__0,Vvar__2722)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2722,Vv__CANONICAL__1)) ) ) ).
fof('$_type_27255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27256] :
( c_24__type__27255___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__27256)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27256,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2738',axiom,
! [Vvar__2739] :
( c_24__type__2738___24t(Vvar__2739)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2739,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_27450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27451] :
( c_24__type__27450___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__27451)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__27451,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_27663',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27664] :
( c_24__type__27663___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27664)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27664,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2773',axiom,
! [Vvar__2774] :
( c_24__type__2773___24t(Vvar__2774)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2774,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27876',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27877] :
( c_24__type__27876___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__27877)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__27877,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2796',axiom,
! [Vvar__2797] :
( c_24__type__2796___24t(Vvar__2797)
<=> ! [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__2797,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28089',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28090] :
( c_24__type__28089___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28090)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__28090,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_28302',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28303] :
( c_24__type__28302___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__28303)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__28303,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_28497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28498] :
( c_24__type__28497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28498)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__28498,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_28710',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__28711] :
( c_24__type__28710___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__28711)
<=> ! [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__28711,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_2876',axiom,
! [Vvar__2877] :
( c_24__type__2876___24t(Vvar__2877)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),happ(happ(Vvar__2877,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2885',axiom,
! [Vvar__2886] :
( c_24__type__2885___24t(Vvar__2886)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__2886,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28906] :
( c_24__type__28905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__28906)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__28906,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2909',axiom,
! [Vvar__2910] :
( c_24__type__2909___24t(Vvar__2910)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,happ(happ(happ(Vvar__2910,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29623] :
( c_24__type__29622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29623)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29623,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29667] :
( c_24__type__29666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29667)
<=> ! [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__29667,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_29702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29703] :
( c_24__type__29702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29703)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__29703,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_29746',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29747] :
( c_24__type__29746___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__29747)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__29747,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29758',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29759] :
( c_24__type__29758___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29759)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__29759,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_30853',axiom,
! [Vvar__30854] :
( c_24__type__30853___24t(Vvar__30854)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__30854,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30900',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30901] :
( c_24__type__30900___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30901)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30901,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_30979',axiom,
! [Vvar__30980] :
( c_24__type__30979___24t(Vvar__30980)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30980,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31016',axiom,
! [Vvar__31017] :
( c_24__type__31016___24t(Vvar__31017)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31017,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_313',axiom,
! [Vvar__314] :
( c_24__type__313___24t(Vvar__314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32507',axiom,
! [Vvar__32508] :
( c_24__type__32507___24t(Vvar__32508)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__32508,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32529',axiom,
! [Vvar__32530] :
( c_24__type__32529___24t(Vvar__32530)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__32530,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32537',axiom,
! [Vvar__32538] :
( c_24__type__32537___24t(Vvar__32538)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__32538,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_327',axiom,
! [Vvar__328] :
( c_24__type__327___24t(Vvar__328)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__328,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32865',axiom,
! [Vvar__32866] :
( c_24__type__32865___24t(Vvar__32866)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__32866,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33',axiom,
! [Vvar__34] :
( c_24__type__33___24t(Vvar__34)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__34,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33007',axiom,
! [Vvar__33008] :
( c_24__type__33007___24t(Vvar__33008)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__33008,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_33055',axiom,
! [Vvar__33056] :
( c_24__type__33055___24t(Vvar__33056)
<=> ! [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__33056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33058',axiom,
! [Vvar__33059] :
( c_24__type__33058___24t(Vvar__33059)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__33059,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33063',axiom,
! [Vvar__33064] :
( c_24__type__33063___24t(Vvar__33064)
<=> ! [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__33064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33066',axiom,
! [Vvar__33067] :
( c_24__type__33066___24t(Vvar__33067)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__33067,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3329',axiom,
! [Vvar__3330] :
( c_24__type__3329___24t(Vvar__3330)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__3330,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33413] :
( c_24__type__33412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33413)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__33413,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_3348',axiom,
! [Vvar__3349] :
( c_24__type__3348___24t(Vvar__3349)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__3349,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3363',axiom,
! [Vvar__3364] :
( c_24__type__3363___24t(Vvar__3364)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__3364,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3367',axiom,
! [Vvar__3368] :
( c_24__type__3367___24t(Vvar__3368)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3368,Vv__CANONICAL__0)) ) ) ).
fof('$_type_337',axiom,
! [Vvar__338] :
( c_24__type__337___24t(Vvar__338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__338,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33748',axiom,
! [Vvar__33749] :
( c_24__type__33748___24t(Vvar__33749)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1795___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cType___24t(Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__2327___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__17)
=> ! [Vv__CANONICAL__18] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__18)
=> ! [Vv__CANONICAL__19] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__8,Vv__CANONICAL__19)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__33749,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_33863',axiom,
! [Vvar__33864] :
( c_24__type__33863___24t(Vvar__33864)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__33868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__33864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33868',axiom,
! [Vv__CANONICAL__0,Vvar__33869] :
( c_24__type__33868___24t(Vv__CANONICAL__0,Vvar__33869)
<=> ! [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__33869,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3398',axiom,
! [Vvar__3399] :
( c_24__type__3398___24t(Vvar__3399)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__3399,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34009',axiom,
! [Vvar__34010] :
( c_24__type__34009___24t(Vvar__34010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34010,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3401',axiom,
! [Vvar__3402] :
( c_24__type__3401___24t(Vvar__3402)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3402,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34026',axiom,
! [Vvar__34027] :
( c_24__type__34026___24t(Vvar__34027)
<=> ! [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)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,cCoq_2eLists_2eList_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__2),c_24__prop__34028___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__34027,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34102',axiom,
! [Vvar__34103] :
( c_24__type__34102___24t(Vvar__34103)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6478___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__34103,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34586',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__34587] :
( c_24__type__34586___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__34587)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34587,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34687',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__34688] :
( c_24__type__34687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__34688)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34688,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__34789] :
( c_24__type__34788___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__34789)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34789,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3482',axiom,
! [Vvar__3483] :
( c_24__type__3482___24t(Vvar__3483)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3483,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3486',axiom,
! [Vvar__3487] :
( c_24__type__3486___24t(Vvar__3487)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3487,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34878',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__34879] :
( c_24__type__34878___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__34879)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__34879,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_34979',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__34980] :
( c_24__type__34979___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__34980)
<=> ! [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__34980,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_3503',axiom,
! [Vvar__3504] :
( c_24__type__3503___24t(Vvar__3504)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__3504,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35080',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__35081] :
( c_24__type__35080___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__35081)
<=> ! [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__35081,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_35181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35182] :
( c_24__type__35181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35182)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35182,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_353',axiom,
! [Vvar__354] :
( c_24__type__353___24t(Vvar__354)
<=> ! [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__354,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35320',axiom,
! [Vvar__35321] :
( c_24__type__35320___24t(Vvar__35321)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(Vvar__35321,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35325',axiom,
! [Vvar__35326] :
( c_24__type__35325___24t(Vvar__35326)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__35327___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__35326,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_35329',axiom,
! [Vv__CANONICAL__0,Vvar__35330] :
( c_24__type__35329___24t(Vv__CANONICAL__0,Vvar__35330)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__35330,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_35339',axiom,
! [Vvar__35340] :
( c_24__type__35339___24t(Vvar__35340)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRIneq_2enonzeroreal___24t(happ(Vvar__35340,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_3536',axiom,
! [Vvar__3537] :
( c_24__type__3536___24t(Vvar__3537)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__3537,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3541',axiom,
! [Vvar__3542] :
( c_24__type__3541___24t(Vvar__3542)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__3542,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3545',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3546] :
( c_24__type__3545___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3546)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__3546,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35519',axiom,
! [Vvar__35520] :
( c_24__type__35519___24t(Vvar__35520)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__35521___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eReals_2eRdefinitions_2eRgt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__35520,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35522',axiom,
! [Vvar__35523] :
( c_24__type__35522___24t(Vvar__35523)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),cCoq_2eReals_2eRdefinitions_2eRge___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)),happ(Vvar__35523,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35533',axiom,
! [Vvar__35534] :
( c_24__type__35533___24t(Vvar__35534)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35534,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35554',axiom,
! [Vvar__35555] :
( c_24__type__35554___24t(Vvar__35555)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__35555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3559',axiom,
! [Vvar__3560] :
( c_24__type__3559___24t(Vvar__3560)
<=> ! [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__3560,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_35617',axiom,
! [Vvar__35618] :
( c_24__type__35617___24t(Vvar__35618)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35618,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35651',axiom,
! [Vvar__35652] :
( c_24__type__35651___24t(Vvar__35652)
<=> ! [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__35652,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3571',axiom,
! [Vvar__3572] :
( c_24__type__3571___24t(Vvar__3572)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__3572,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_3583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3584] :
( c_24__type__3583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3584)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__3584,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3608',axiom,
! [Vvar__3609] :
( c_24__type__3608___24t(Vvar__3609)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3611___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__3623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__3609,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_3611',axiom,
! [Vv__CANONICAL__0,Vvar__3612] :
( c_24__type__3611___24t(Vv__CANONICAL__0,Vvar__3612)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__3612,Vv__CANONICAL__1)) ) ) ).
fof('$_type_36186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__36187] :
( c_24__type__36186___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__36187)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36187,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3624] :
( c_24__type__3623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3624)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__3624,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_36532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__36533] :
( c_24__type__36532___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__36533)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36533,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36878',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__36879] :
( c_24__type__36878___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__36879)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36879,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37202] :
( c_24__type__37201___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37202)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__37202,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_37547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__37548] :
( c_24__type__37547___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__37548)
<=> ! [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__37548,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_37893',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37894] :
( c_24__type__37893___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__37894)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37894,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_38',axiom,
! [Vvar__39] :
( c_24__type__38___24t(Vvar__39)
<=> ! [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__39,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38240] :
( c_24__type__38239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38240)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__38240,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_38585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__38586] :
( c_24__type__38585___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__38586)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__38586,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_38931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38932] :
( c_24__type__38931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__38932)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__38932,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_39254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__39255] :
( c_24__type__39254___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__39255)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__39255,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_39600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39601] :
( c_24__type__39600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__39601)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__39601,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_39946',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__39947] :
( c_24__type__39946___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__39947)
<=> ! [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__39947,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_40269',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40270] :
( c_24__type__40269___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40270)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__40270,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_403',axiom,
! [Vvar__404] :
( c_24__type__403___24t(Vvar__404)
<=> ! [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__404,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_40592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40593] :
( c_24__type__40592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40593)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__40593,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_408',axiom,
! [Vv__CANONICAL__0,Vvar__409] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vvar__409)
<=> ! [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__409,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_40938',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40939] :
( c_24__type__40938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__40939)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__40939,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_41202',axiom,
! [Vvar__41203] :
( c_24__type__41202___24t(Vvar__41203)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__41203,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('$_type_41286',axiom,
! [Vvar__41287] :
( c_24__type__41286___24t(Vvar__41287)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__41287,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_41412',axiom,
! [Vvar__41413] :
( c_24__type__41412___24t(Vvar__41413)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(Vv__CANONICAL__7,Vv__CANONICAL__10)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__41413,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_41432',axiom,
! [Vvar__41433] :
( c_24__type__41432___24t(Vvar__41433)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__41433,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41435',axiom,
! [Vvar__41436] :
( c_24__type__41435___24t(Vvar__41436)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__41436,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41440',axiom,
! [Vvar__41441] :
( c_24__type__41440___24t(Vvar__41441)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__41441,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41445',axiom,
! [Vvar__41446] :
( c_24__type__41445___24t(Vvar__41446)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__41446,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_41451',axiom,
! [Vvar__41452] :
( c_24__type__41451___24t(Vvar__41452)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__41452,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41453',axiom,
! [Vvar__41454] :
( c_24__type__41453___24t(Vvar__41454)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__41454,Vv__CANONICAL__0)) ) ) ).
fof('$_type_41484',axiom,
! [Vvar__41485] :
( c_24__type__41484___24t(Vvar__41485)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__41488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__41485,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_41488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__41489] :
( c_24__type__41488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__41489)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__41489,Vv__CANONICAL__2)) ) ) ).
fof('$_type_41522',axiom,
! [Vvar__41523] :
( c_24__type__41522___24t(Vvar__41523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__41531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__41523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_41531',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__41532] :
( c_24__type__41531___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__41532)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__41532,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_42245',axiom,
! [Vvar__42246] :
( c_24__type__42245___24t(Vvar__42246)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__42246,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4241',axiom,
! [Vvar__4242] :
( c_24__type__4241___24t(Vvar__4242)
<=> ! [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__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__408___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__1075___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__1080___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__1089___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__4242,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_42841',axiom,
! [Vvar__42842] :
( c_24__type__42841___24t(Vvar__42842)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__42842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42876',axiom,
! [Vvar__42877] :
( c_24__type__42876___24t(Vvar__42877)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__42877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_42899',axiom,
! [Vvar__42900] :
( c_24__type__42899___24t(Vvar__42900)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__42900,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_43162',axiom,
! [Vvar__43163] :
( c_24__type__43162___24t(Vvar__43163)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(Vvar__43163,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43170',axiom,
! [Vvar__43171] :
( c_24__type__43170___24t(Vvar__43171)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__43171,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_43201',axiom,
! [Vvar__43202] :
( c_24__type__43201___24t(Vvar__43202)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__43202,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_43319',axiom,
! [Vvar__43320] :
( c_24__type__43319___24t(Vvar__43320)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__43321___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43320,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43461',axiom,
! [Vvar__43462] :
( c_24__type__43461___24t(Vvar__43462)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__43481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2elist__utils_2eelemsR___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(happ(Vvar__43462,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_43481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43482] :
( c_24__type__43481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43482)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),happ(Vvar__43482,Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_436',axiom,
! [Vvar__437] :
( c_24__type__436___24t(Vvar__437)
<=> ! [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__437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_43726',axiom,
! [Vvar__43727] :
( c_24__type__43726___24t(Vvar__43727)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__43728___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43729___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43727,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43746',axiom,
! [Vvar__43747] :
( c_24__type__43746___24t(Vvar__43747)
<=> ! [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__43747,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43748',axiom,
! [Vvar__43749] :
( c_24__type__43748___24t(Vvar__43749)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__43749,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43766',axiom,
! [Vvar__43767] :
( c_24__type__43766___24t(Vvar__43767)
<=> ! [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_2eZ___24t(happ(happ(Vvar__43767,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43856',axiom,
! [Vvar__43857] :
( c_24__type__43856___24t(Vvar__43857)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__43857,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43861',axiom,
! [Vvar__43862] :
( c_24__type__43861___24t(Vvar__43862)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__43862,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43864',axiom,
! [Vvar__43865] :
( c_24__type__43864___24t(Vvar__43865)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__43865,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43867',axiom,
! [Vvar__43868] :
( c_24__type__43867___24t(Vvar__43868)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43869___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43868,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43874',axiom,
! [Vvar__43875] :
( c_24__type__43874___24t(Vvar__43875)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__43875,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43876',axiom,
! [Vvar__43877] :
( c_24__type__43876___24t(Vvar__43877)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__43877,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43883',axiom,
! [Vvar__43884] :
( c_24__type__43883___24t(Vvar__43884)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__43884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_44012',axiom,
! [Vvar__44013] :
( c_24__type__44012___24t(Vvar__44013)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1062___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__44013,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_44242',axiom,
! [Vvar__44243] :
( c_24__type__44242___24t(Vvar__44243)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__44243,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44247',axiom,
! [Vv__CANONICAL__0,Vvar__44248] :
( c_24__type__44247___24t(Vv__CANONICAL__0,Vvar__44248)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__44248,Vv__CANONICAL__1)) ) ) ).
fof('$_type_4464',axiom,
! [Vvar__4465] :
( c_24__type__4464___24t(Vvar__4465)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__1071___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__1315___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__4465,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_45360',axiom,
! [Vvar__45361] :
( c_24__type__45360___24t(Vvar__45361)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__45361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46391',axiom,
! [Vvar__46392] :
( c_24__type__46391___24t(Vvar__46392)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__46392,Vv__CANONICAL__0)) ) ) ).
fof('$_type_47301',axiom,
! [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__47302] :
( c_24__type__47301___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__47302)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__47302,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_47364',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__47365] :
( c_24__type__47364___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__47365)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__47365,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_47427',axiom,
! [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__47428] :
( c_24__type__47427___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__47428)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__47428,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_47481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__47482] :
( c_24__type__47481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__47482)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__47482,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_47544',axiom,
! [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__47545] :
( c_24__type__47544___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__47545)
<=> ! [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__47545,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_47983',axiom,
! [Vvar__47984] :
( c_24__type__47983___24t(Vvar__47984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__47984,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_47988',axiom,
! [Vvar__47989] :
( c_24__type__47988___24t(Vvar__47989)
<=> ! [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__47989,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_48192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48193] :
( c_24__type__48192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48193)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__48193,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48285',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__48286] :
( c_24__type__48285___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__48286)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__48286,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48378',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48379] :
( c_24__type__48378___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48379)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__48379,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__48461] :
( c_24__type__48460___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__48461)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__48461,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_48553',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48554] :
( c_24__type__48553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48554)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__48554,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48635',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__48636] :
( c_24__type__48635___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__48636)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__48636,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_48728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48729] :
( c_24__type__48728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__48729)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__48729,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_48905',axiom,
! [Vvar__48906] :
( c_24__type__48905___24t(Vvar__48906)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eReals_2eRdefinitions_2eR,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(cCoq_2eQArith_2eQArith__base_2eQ,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__48906,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49743',axiom,
! [Vvar__49744] :
( c_24__type__49743___24t(Vvar__49744)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__49744,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4999',axiom,
! [Vvar__5000] :
( c_24__type__4999___24t(Vvar__5000)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1062___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__5000,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_50',axiom,
! [Vvar__51] :
( c_24__type__50___24t(Vvar__51)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__51,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50058',axiom,
! [Vvar__50059] :
( c_24__type__50058___24t(Vvar__50059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2enonnegreal___24t(happ(Vvar__50059,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_50061',axiom,
! [Vvar__50062] :
( c_24__type__50061___24t(Vvar__50062)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRIneq_2enonposreal___24t(happ(Vvar__50062,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_50063',axiom,
! [Vvar__50064] :
( c_24__type__50063___24t(Vvar__50064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eVarMap_2et___24t(Vv__CANONICAL__0,happ(Vvar__50064,Vv__CANONICAL__0)) ) ) ).
fof('$_type_50081',axiom,
! [Vvar__50082] :
( c_24__type__50081___24t(Vvar__50082)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__50082,Vv__CANONICAL__0)) ) ) ).
fof('$_type_50086',axiom,
! [Vvar__50087] :
( c_24__type__50086___24t(Vvar__50087)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__50087,Vv__CANONICAL__0)) ) ) ).
fof('$_type_50572',axiom,
! [Vvar__50573] :
( c_24__type__50572___24t(Vvar__50573)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__20754___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__50573,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5249',axiom,
! [Vvar__5250] :
( c_24__type__5249___24t(Vvar__5250)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__5250,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5368',axiom,
! [Vvar__5369] :
( c_24__type__5368___24t(Vvar__5369)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__5377___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(Vvar__5369,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5373',axiom,
! [Vv__CANONICAL__0,Vvar__5374] :
( c_24__type__5373___24t(Vv__CANONICAL__0,Vvar__5374)
<=> ! [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__5375___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__5376___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__5374,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_5398',axiom,
! [Vvar__5399] :
( c_24__type__5398___24t(Vvar__5399)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__5399,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5437',axiom,
! [Vvar__5438] :
( c_24__type__5437___24t(Vvar__5438)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__5438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_5572',axiom,
! [Vvar__5573] :
( c_24__type__5572___24t(Vvar__5573)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__5573,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_59196',axiom,
! [Vvar__59197] :
( c_24__type__59196___24t(Vvar__59197)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__59197,Vv__CANONICAL__0)) ) ) ).
fof('$_type_59201',axiom,
! [Vvar__59202] :
( c_24__type__59201___24t(Vvar__59202)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__59202,Vv__CANONICAL__0)) ) ) ).
fof('$_type_59204',axiom,
! [Vvar__59205] :
( c_24__type__59204___24t(Vvar__59205)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__59205,Vv__CANONICAL__0)) ) ) ).
fof('$_type_607',axiom,
! [Vv__CANONICAL__0,Vvar__608] :
( c_24__type__607___24t(Vv__CANONICAL__0,Vvar__608)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__608,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_61407',axiom,
! [Vvar__61408] :
( c_24__type__61407___24t(Vvar__61408)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vv__CANONICAL__0))
=> cCoq_2eReals_2eRIneq_2eposreal___24t(happ(Vvar__61408,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_61410',axiom,
! [Vvar__61411] :
( c_24__type__61410___24t(Vvar__61411)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vv__CANONICAL__0,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRIneq_2enegreal___24t(happ(Vvar__61411,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_618',axiom,
! [Vvar__619] :
( c_24__type__618___24t(Vvar__619)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__607___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__619,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6408',axiom,
! [Vvar__6409] :
( c_24__type__6408___24t(Vvar__6409)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__6409,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6413] :
( c_24__type__6412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6413)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__6413,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6420] :
( c_24__type__6419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6420)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__6420,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_64199',axiom,
! [Vvar__64200] :
( c_24__type__64199___24t(Vvar__64200)
<=> ! [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] :
( c_24__type__44247___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(happ(Vvar__64200,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6478',axiom,
! [Vv__CANONICAL__0,Vvar__6479] :
( c_24__type__6478___24t(Vv__CANONICAL__0,Vvar__6479)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__6479,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6484',axiom,
! [Vvar__6485] :
( c_24__type__6484___24t(Vvar__6485)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6478___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__6485,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6592',axiom,
! [Vvar__6593] :
( c_24__type__6592___24t(Vvar__6593)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__6593,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6644',axiom,
! [Vv__CANONICAL__0,Vvar__6645] :
( c_24__type__6644___24t(Vv__CANONICAL__0,Vvar__6645)
<=> ! [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)
=> cProp___24t(happ(happ(Vvar__6645,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_66702',axiom,
! [Vvar__66703] :
( c_24__type__66702___24t(Vvar__66703)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eZ0,happ(Vvar__66703,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_67',axiom,
! [Vvar__68] :
( c_24__type__67___24t(Vvar__68)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__71___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__68,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6725',axiom,
! [Vvar__6726] :
( c_24__type__6725___24t(Vvar__6726)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__6726,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6755] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6755)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6755,Vv__CANONICAL__3)) ) ) ).
fof('$_type_6910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6911] :
( c_24__type__6910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6911)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6911,Vv__CANONICAL__3)) ) ) ).
fof('$_type_7',axiom,
! [Vvar__8] :
( c_24__type__7___24t(Vvar__8)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__8,Vv__CANONICAL__0)) ) ) ).
fof('$_type_71',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__72] :
( c_24__type__71___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__72)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__72,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_7271',axiom,
! [Vv__CANONICAL__0,Vvar__7272] :
( c_24__type__7271___24t(Vv__CANONICAL__0,Vvar__7272)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__7272,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_7421',axiom,
! [Vvar__7422] :
( c_24__type__7421___24t(Vvar__7422)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7422,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78',axiom,
! [Vvar__79] :
( c_24__type__78___24t(Vvar__79)
<=> ! [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_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__79,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8085',axiom,
! [Vvar__8086] :
( c_24__type__8085___24t(Vvar__8086)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8086,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8088',axiom,
! [Vvar__8089] :
( c_24__type__8088___24t(Vvar__8089)
<=> ! [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__8089,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8093',axiom,
! [Vvar__8094] :
( c_24__type__8093___24t(Vvar__8094)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__8094,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_83',axiom,
! [Vvar__84] :
( c_24__type__83___24t(Vvar__84)
<=> ! [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__84,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8457] :
( c_24__type__8456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8457)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8457,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8519',axiom,
! [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__8520] :
( c_24__type__8519___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__8520)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8520,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8582',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8583] :
( c_24__type__8582___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8583)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8583,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8636',axiom,
! [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__8637] :
( c_24__type__8636___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__8637)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__8637,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_8699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8700] :
( c_24__type__8699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8700)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8700,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_8854',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8855] :
( c_24__type__8854___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8855)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8855,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8885] :
( c_24__type__8884___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8885)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8885,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8908',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8909] :
( c_24__type__8908___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8909)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__8909,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_8938',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8939] :
( c_24__type__8938___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8939)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8939,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_8968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8969] :
( c_24__type__8968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8969)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8969,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8992',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8993] :
( c_24__type__8992___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8993)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__8993,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9',axiom,
! [Vvar__10] :
( c_24__type__9___24t(Vvar__10)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9025',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9026] :
( c_24__type__9025___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9026)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9026,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9049',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9050] :
( c_24__type__9049___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9050)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9050,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9077] :
( c_24__type__9076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9077)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9077,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9149] :
( c_24__type__9148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9149)
<=> ! [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__9149,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_9341',axiom,
! [Vv__CANONICAL__0,Vvar__9342] :
( c_24__type__9341___24t(Vv__CANONICAL__0,Vvar__9342)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__9342,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__7___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
c_24__type__43748___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__19854___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
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('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__3503___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__7___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__2330___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__3482___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__50___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__38___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__3559___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__3536___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__3541___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__1971___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__19___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__3608___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__3608___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__20124___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__3486___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__33___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__19___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__3482___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__353___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__337___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__3571___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__337___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__3482___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__7___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__2062___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__2062___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__2062___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__2738___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__10845___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__10850___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__2718___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__10819___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__2346___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumbool_rec',axiom,
c_24__type__10876___24t(cCoq_2eInit_2eSpecif_2esumbool__rec) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__10906___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__12270___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__1983___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__6592___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__5572___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__21146___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__6484___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.find',axiom,
c_24__type__34102___24t(cCoq_2eLists_2eList_2efind) ).
fof('$_typeof_Coq.Lists.List.flat_map',axiom,
c_24__type__6408___24t(cCoq_2eLists_2eList_2eflat__map) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__2038___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__2659___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__67___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nodup',axiom,
c_24__type__6725___24t(cCoq_2eLists_2eList_2enodup) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__436___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__5398___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_in_or_default',axiom,
c_24__type__34026___24t(cCoq_2eLists_2eList_2enth__in__or__default) ).
fof('$_typeof_Coq.Lists.List.remove',axiom,
c_24__type__5437___24t(cCoq_2eLists_2eList_2eremove) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__5249___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.ListDec.In_dec',axiom,
c_24__type__5368___24t(cCoq_2eLists_2eListDec_2eIn__dec) ).
fof('$_typeof_Coq.Lists.ListDec.decidable_eq',axiom,
c_24__type__30979___24t(cCoq_2eLists_2eListDec_2edecidable__eq) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__20159___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Full',axiom,
c_24__type__34009___24t(cCoq_2eLogic_2eFinFun_2eFull) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__2523___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__2544___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__2537___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__2523___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__19679___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__2547___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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__327___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__2552___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__2552___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__3329___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__3329___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__21062___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__19777___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__43746___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__19777___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__19814___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__19777___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__3329___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__3348___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__43861___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qdiv',axiom,
c_24__type__25628___24t(cCoq_2eQArith_2eQArith__base_2eQdiv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__25622___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq_bool',axiom,
c_24__type__25625___24t(cCoq_2eQArith_2eQArith__base_2eQeq__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qinv',axiom,
c_24__type__25631___24t(cCoq_2eQArith_2eQArith__base_2eQinv) ).
fof('$_typeof_Coq.QArith.QArith_base.Qle_bool',axiom,
c_24__type__25625___24t(cCoq_2eQArith_2eQArith__base_2eQle__bool) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__25619___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__25628___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__25628___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__43856___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.QArith.QArith_base.Qopp',axiom,
c_24__type__25631___24t(cCoq_2eQArith_2eQArith__base_2eQopp) ).
fof('$_typeof_Coq.QArith.QArith_base.Qplus',axiom,
c_24__type__25628___24t(cCoq_2eQArith_2eQArith__base_2eQplus) ).
fof('$_typeof_Coq.QArith.QArith_base.Qpower',axiom,
c_24__type__25642___24t(cCoq_2eQArith_2eQArith__base_2eQpower) ).
fof('$_typeof_Coq.QArith.QArith_base.Qpower_positive',axiom,
c_24__type__45360___24t(cCoq_2eQArith_2eQArith__base_2eQpower__positive) ).
fof('$_typeof_Coq.QArith.Qreals.Q2R',axiom,
c_24__type__43864___24t(cCoq_2eQArith_2eQreals_2eQ2R) ).
fof('$_typeof_Coq.Reals.RIneq.Req_EM_T',axiom,
c_24__type__43319___24t(cCoq_2eReals_2eRIneq_2eReq__EM__T) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__43867___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_lt_or_eq_dec',axiom,
c_24__type__35325___24t(cCoq_2eReals_2eRIneq_2eRle__lt__or__eq__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rlt_le_dec',axiom,
c_24__type__35320___24t(cCoq_2eReals_2eRIneq_2eRlt__le__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__20760___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.mknegreal',axiom,
c_24__type__61410___24t(cCoq_2eReals_2eRIneq_2emknegreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonnegreal',axiom,
c_24__type__50058___24t(cCoq_2eReals_2eRIneq_2emknonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonposreal',axiom,
c_24__type__50061___24t(cCoq_2eReals_2eRIneq_2emknonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.mknonzeroreal',axiom,
c_24__type__35339___24t(cCoq_2eReals_2eRIneq_2emknonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.mkposreal',axiom,
c_24__type__61407___24t(cCoq_2eReals_2eRIneq_2emkposreal) ).
fof('$_typeof_Coq.Reals.RIneq.neg',axiom,
c_24__type__59201___24t(cCoq_2eReals_2eRIneq_2eneg) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonneg',axiom,
c_24__type__50081___24t(cCoq_2eReals_2eRIneq_2enonneg) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonpos',axiom,
c_24__type__50086___24t(cCoq_2eReals_2eRIneq_2enonpos) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzero',axiom,
c_24__type__43874___24t(cCoq_2eReals_2eRIneq_2enonzero) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.pos',axiom,
c_24__type__59196___24t(cCoq_2eReals_2eRIneq_2epos) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.R_Ifp.Int_part',axiom,
c_24__type__32529___24t(cCoq_2eReals_2eR__Ifp_2eInt__part) ).
fof('$_typeof_Coq.Reals.R_Ifp.frac_part',axiom,
c_24__type__20760___24t(cCoq_2eReals_2eR__Ifp_2efrac__part) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__20754___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Raxioms.total_order_T',axiom,
c_24__type__35519___24t(cCoq_2eReals_2eRaxioms_2etotal__order__T) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rabs',axiom,
c_24__type__20760___24t(cCoq_2eReals_2eRbasic__fun_2eRabs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rcase_abs',axiom,
c_24__type__35522___24t(cCoq_2eReals_2eRbasic__fun_2eRcase__abs) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmax',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRbasic__fun_2eRmax) ).
fof('$_typeof_Coq.Reals.Rbasic_fun.Rmin',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRbasic__fun_2eRmin) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IPR',axiom,
c_24__type__32507___24t(cCoq_2eReals_2eRdefinitions_2eIPR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__20765___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__31016___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__31016___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__20760___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__31016___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__31016___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__20760___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__32529___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.R_dist',axiom,
c_24__type__20757___24t(cCoq_2eReals_2eRfunctions_2eR__dist) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__35617___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.ZintNull',axiom,
c_24__type__66702___24t(cCoq_2eReals_2eRfunctions_2eZintNull) ).
fof('$_typeof_Coq.Reals.Rfunctions.infinite_sum',axiom,
c_24__type__50572___24t(cCoq_2eReals_2eRfunctions_2einfinite__sum) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__35651___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rfunctions.powerRZ',axiom,
c_24__type__32537___24t(cCoq_2eReals_2eRfunctions_2epowerRZ) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_f_R0',axiom,
c_24__type__20786___24t(cCoq_2eReals_2eRfunctions_2esum__f__R0) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__20819___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__19___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__43726___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__2796___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__12191___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__2773___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__46391___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__20061___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__3398___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__20055___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__20055___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__21065___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__3401___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pos_sub',axiom,
c_24__type__43766___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow_pos',axiom,
c_24__type__49743___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__21132___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__3363___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__3367___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__20055___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__13040___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__2550___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Zpower.Zpower_nat',axiom,
c_24__type__20874___24t(cCoq_2eZArith_2eZpower_2eZpower__nat) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__32865___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__47988___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__47983___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__403___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.Pphi',axiom,
c_24__type__33007___24t(cCoq_2emicromega_2eEnvRing_2ePphi) ).
fof('$_typeof_Coq.micromega.QMicromega.QWitness',axiom,
cType___24t(cCoq_2emicromega_2eQMicromega_2eQWitness) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__43876___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.INZ',axiom,
c_24__type__59204___24t(cCoq_2emicromega_2eRMicromega_2eINZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Qeval_nformula',axiom,
c_24__type__48905___24t(cCoq_2emicromega_2eRMicromega_2eQeval__nformula) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RMicromega.Reval_op2',axiom,
c_24__type__43883___24t(cCoq_2emicromega_2eRMicromega_2eReval__op2) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__7421___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__35554___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Build_Formula',axiom,
c_24__type__42245___24t(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__41445___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__41451___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__41432___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__41440___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__41445___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzSquare',axiom,
c_24__type__41435___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__41453___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_nformula',axiom,
c_24__type__41412___24t(cCoq_2emicromega_2eRingMicromega_2eeval__nformula) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__41286___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
c_24__type__41202___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__41484___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
c_24__type__41522___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__42876___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.BFormula',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eTauto_2eBFormula) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__11014___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__42899___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.VarMap.Branch',axiom,
c_24__type__43170___24t(cCoq_2emicromega_2eVarMap_2eBranch) ).
fof('$_typeof_Coq.micromega.VarMap.Elt',axiom,
c_24__type__43162___24t(cCoq_2emicromega_2eVarMap_2eElt) ).
fof('$_typeof_Coq.micromega.VarMap.Empty',axiom,
c_24__type__50063___24t(cCoq_2emicromega_2eVarMap_2eEmpty) ).
fof('$_typeof_Coq.micromega.VarMap.find',axiom,
c_24__type__43201___24t(cCoq_2emicromega_2eVarMap_2efind) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__19___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__33058___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__33063___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__33055___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__33063___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__24386___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__33066___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__33063___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__33066___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__33063___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__33863___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__4464___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fnorm',axiom,
c_24__type__24824___24t(cCoq_2esetoid__ring_2eField__theory_2eFnorm) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__4241___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__20704___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__20684___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.display_pow_linear',axiom,
c_24__type__33748___24t(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__24420___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__20684___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__24456___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__24456___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__24513___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__4999___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__25449___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.get_signZ',axiom,
c_24__type__25460___24t(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__25501___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__8088___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__8093___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__8085___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__1057___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__8093___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__42841___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__8093___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__618___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__19___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__26164___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__1553___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__1738___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__1297___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__1856___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__2330___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__1841___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__1836___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__44012___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_QuicksortComplexity.arith_lems.Req_ne_dec',axiom,
c_24__type__43319___24t(cQuicksortComplexity_2earith__lems_2eReq__ne__dec) ).
fof('$_typeof_QuicksortComplexity.list_utils.add',axiom,
c_24__type__1926___24t(cQuicksortComplexity_2elist__utils_2eadd) ).
fof('$_typeof_QuicksortComplexity.list_utils.concat',axiom,
c_24__type__313___24t(cQuicksortComplexity_2elist__utils_2econcat) ).
fof('$_typeof_QuicksortComplexity.list_utils.count',axiom,
c_24__type__13056___24t(cQuicksortComplexity_2elist__utils_2ecount) ).
fof('$_typeof_QuicksortComplexity.list_utils.elemsRimpl',axiom,
c_24__type__43461___24t(cQuicksortComplexity_2elist__utils_2eelemsRimpl) ).
fof('$_typeof_QuicksortComplexity.list_utils.repeat',axiom,
c_24__type__13392___24t(cQuicksortComplexity_2elist__utils_2erepeat) ).
fof('$_typeof_QuicksortComplexity.nat_below.mkNatBelow',axiom,
c_24__type__2876___24t(cQuicksortComplexity_2enat__below_2emkNatBelow) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow',axiom,
c_24__type__2565___24t(cQuicksortComplexity_2enat__below_2enatBelow) ).
fof('$_typeof_QuicksortComplexity.nat_below.nb_val',axiom,
c_24__type__2885___24t(cQuicksortComplexity_2enat__below_2enb__val) ).
fof('$_typeof_QuicksortComplexity.nat_seqs.nats',axiom,
c_24__type__78___24t(cQuicksortComplexity_2enat__seqs_2enats) ).
fof('$_typeof_QuicksortComplexity.util.ext_eq',axiom,
c_24__type__20895___24t(cQuicksortComplexity_2eutil_2eext__eq) ).
fof('$_typeof_QuicksortComplexity.vec.from_list',axiom,
c_24__type__30853___24t(cQuicksortComplexity_2evec_2efrom__list) ).
fof('$_typeof_QuicksortComplexity.vec.head',axiom,
c_24__type__19289___24t(cQuicksortComplexity_2evec_2ehead) ).
fof('$_typeof_QuicksortComplexity.vec.tail',axiom,
c_24__type__2909___24t(cQuicksortComplexity_2evec_2etail) ).
fof('$_typeof_QuicksortComplexity.vec.to_list',axiom,
c_24__type__12264___24t(cQuicksortComplexity_2evec_2eto__list) ).
fof('$_typeof_l',axiom,
cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,cl) ).
fof('$_typeof_sums_and_averages.Ravg',axiom,
c_24__type__44242___24t(csums__and__averages_2eRavg) ).
fof('$_typeof_sums_and_averages.Rsum',axiom,
c_24__type__44242___24t(csums__and__averages_2eRsum) ).
fof('$_typeof_sums_and_averages.RsumOver',axiom,
c_24__type__64199___24t(csums__and__averages_2eRsumOver) ).
fof('$_typeof_sums_and_averages.sum',axiom,
c_24__type__1926___24t(csums__and__averages_2esum) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Factorial.fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2eFactorial_2efact___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.Gt.gt_Sn_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n) ) ).
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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Minus.le_plus_minus_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n)) = V1__m ) ) ) ).
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_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.le_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
<=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Bool.Bool.orb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
| V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
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.Init.Datatypes.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1958___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__9___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Datatypes.prod_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__3545___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
=> ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
=> p(happ(V2__P,V4__p)) ) ) ) ) ) ).
fof('Coq.Init.Peano.O_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.f_equal2_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__2052___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__7271___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_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__9___24t(V1__P)
=> ( p(happ(V1__P,V0__n))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V3__m))
=> ( p(happ(V1__P,V3__m))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V4__n))
=> p(happ(V1__P,V4__n)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.n_Sn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.plus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__2368___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l_27))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__6644___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2721___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& p(happ(V1__P,V3__x)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_Add',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l_27)
<=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))
<=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l))
& cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1958___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Lists.List.NoDup_nodup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__5373___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__l)) ) ) ) ).
fof('Coq.Lists.List.count_occ_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__5373___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
<=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V3__x),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ) ) ).
fof('Coq.Lists.List.count_occ_not_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__5373___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
<=> cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V2__l,V3__x) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ) ).
fof('Coq.Lists.List.existsb_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__6478___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2etrue
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& happ(V1__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('Coq.Lists.List.filter_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__6478___24t(V0__A,V1__f)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l))
& happ(V1__f,V2__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.find_some',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__6478___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2efind___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
& happ(V1__f,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m)))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l))) ) ) ) ).
fof('Coq.Lists.List.in_flat_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__6412___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l))
& p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,happ(V2__f,V5__x))) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)))
=> ( V1__a = V2__b
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V4__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& happ(V2__f,V5__x) = V4__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ).
fof('Coq.Lists.List.in_or_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m)) )
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))) ) ) ) ) ) ).
fof('Coq.Lists.List.in_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l))) ) ) ) ) ).
fof('Coq.Lists.List.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V3__l,V4__l_27)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__71___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.Lists.List.map_ext_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__71___24t(V0__A,V1__B,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__a,V4__l))
=> happ(V2__f,V5__a) = happ(V3__g,V5__a) ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V4__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__71___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__6419___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__B,V2__C,V4__g,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l)) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V2__C,c_24__lam__6433___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nodup_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__5373___24t(V0__A,V1__decA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__l)))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.nodup_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__decA] :
( c_24__type__5373___24t(V0__A,V1__decA)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__k)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( cCoq_2eLists_2eList_2enodup___24a3(V0__A,V1__decA,V2__k) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__a,V3__l)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__a,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.not_in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)))
<=> ( V1__x != V2__a
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__x)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.remove_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eq__dec] :
( c_24__type__5373___24t(V0__A,V1__eq__dec)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,cCoq_2eLists_2eList_2eremove___24a4(V0__A,V1__eq__dec,V3__x,V2__l))) ) ) ) ) ).
fof('Coq.Lists.ListDec.In_decidable',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__408___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
<=> ? [V4__y] :
( t(V4__y,V0__A)
& p(happ(happ(V1__eqA,V2__x),V4__y))
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.In_InfA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__ltA] :
( c_24__type__408___24t(V0__A,V1__ltA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__y,V2__l))
=> p(happ(happ(V1__ltA,V3__x),V4__y)) ) )
=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V0__A,V1__ltA,V3__x,V2__l) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__20161___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__49745___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__19816___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.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__32477___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x),cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj_add',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(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p),cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj_lt',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p),cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q))) ) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj_mul',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(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V0__p,V1__q)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p),cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj_sub',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p))
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__p,V1__q)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p),cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)) ) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.is_pos',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p))) ) ).
fof('Coq.PArith.Pnat.SuccNat2Pos.id_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
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.QArith.QArith_base.Qeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.Qfield.Qpower_theory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eQArith_2eQArith__base_2eQmult,cCoq_2eQArith_2eQArith__base_2eQeq,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,cCoq_2eQArith_2eQArith__base_2eQpower) ).
fof('Coq.QArith.Qreals.IZR_nz',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.QArith.Qreals.Q2R_inv',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ( ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH))
=> cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x)) ) ) ).
fof('Coq.QArith.Qreals.Q2R_mult',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x),cCoq_2eQArith_2eQreals_2eQ2R___24a1(V1__y)) ) ) ).
fof('Coq.QArith.Qreals.eqR_Qeq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eQArith_2eQreals_2eQ2R___24a1(V1__y)
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Reals.ArithProp.euclidian_division',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( V1__y != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
& ? [V4__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V4__r)
& V0__x = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V3__k),V1__y),V4__r)
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V4__r))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V4__r,cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y))) ) ) ) ) ) ).
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.DiscrR.Rlt_R0_R2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.Reals.RIneq.INR_IPR',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p)) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V0__p) ) ).
fof('Coq.Reals.RIneq.INR_IZR_INZ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.INR_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.INR_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.INR_not_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__n != cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Reals.RIneq.IZN',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ? [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
& V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V2__m) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_le',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_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m))) ) ) ) ).
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.RField_field_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__fe1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__fe1)
=> ! [V4__fe2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__fe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ! [V6__lmp] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V6__lmp)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V2__lpe) = V6__lmp
=> ! [V8__nfe1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,V3__fe1) = V8__nfe1
=> ! [V10__nfe2] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,V4__fe2) = V10__nfe2
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,V6__lmp,cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2))),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,V6__lmp,cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2enum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2),cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1)))) = cCoq_2eInit_2eDatatypes_2etrue
=> ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V8__nfe1),cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V10__nfe2)))
=> cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eReals_2eRdefinitions_2eRdiv,cCoq_2eReals_2eRdefinitions_2eRinv,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__fe1) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eReals_2eRdefinitions_2eRdiv,cCoq_2eReals_2eRdefinitions_2eRinv,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__fe2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.RField_lemma5',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),V1__l1)
=> ( ! [V2__lock] :
( c_24__type__35533___24t(V2__lock)
=> ( V2__lock = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l)
=> p(happ(V2__lock,cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem),V1__l1,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ))))) ) )
=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l,V1__l1) ) ) ) ).
fof('Coq.Reals.RIneq.RField_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32527___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32527___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eReals_2eRdefinitions_2eIZR,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.R_rm',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eReals_2eRdefinitions_2eIZR) ).
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
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rdiv_lt_0_compat',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__a,V1__b))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Req_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> p(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
=> p(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
=> p(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
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_ge_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
& p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) )
<=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rge_gt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
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
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V3__r4))
=> ( V3__r4 = V2__r3
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_0_lt_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Rinv_1',axiom,
cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.RIneq.Rinv_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rinv_l_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),V0__r) ) ) ).
fof('Coq.Reals.RIneq.Rinv_le_contravar',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_lt_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.RIneq.Rinv_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_mult_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_mult_simpl',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)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r3,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1))) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r3,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_simpl_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1)) = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_simpl_m',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1)) = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_simpl_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r1)),V1__r2) = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rinv_r_sym',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) ) ) ).
fof('Coq.Reals.RIneq.Rle_0_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.Reals.RIneq.Rle_0_sqr',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r))) ) ).
fof('Coq.Reals.RIneq.Rle_Rinv',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_le_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) )
<=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_0_plus_1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ) ).
fof('Coq.Reals.RIneq.Rle_lt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_or_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_0_1',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.Reals.RIneq.Rlt_0_sqr',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Rlt_Rminus',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__b,V0__a))) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) )
=> V0__r1 != V1__r2 ) ) ) ).
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
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V3__r4))
=> ( V3__r4 = V2__r3
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ p(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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_le_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) ) ).
fof('Coq.Reals.RIneq.Rminus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rminus_diag_eq',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_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_diag_uniq_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_eq_contra',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_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_gt_0_lt',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__b,V0__a)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq_right',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rmult_1_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r ) ).
fof('Coq.Reals.RIneq.Rmult_eq_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_0_compat_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_0_compat_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
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.Rmult_eq_reg_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)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_reg_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)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r1 = V2__r2 ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ge_0_gt_0_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V2__r3,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ge_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V3__r4,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ge_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ge_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_0_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V2__r3,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_gt_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral',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_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_integral_contrapositive_currified',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_0_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r3))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_compat_neg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_ge_compat_neg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_pos',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_le_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_gt_compat_neg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_lt_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_minus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_ne',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = V0__r
& cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rmult_neq_0_reg',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_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_opp_opp',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) ) ) ).
fof('Coq.Reals.RIneq.Rmult_plus_distr_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0',axiom,
cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Ropp_0_ge_le_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_gt_lt_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_le_ge_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_0_lt_gt_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_Ropp_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
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_ge_le_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_gt_lt_0_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_gt_lt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_inv_permute',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) ) ) ).
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.Ropp_le_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_le_ge_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_lt_gt_0_contravar',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.RIneq.Ropp_lt_gt_contravar',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_minus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_l_reverse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),V1__r2) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_mult_distr_r_reverse',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,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Ropp_neq_0_compat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Ropp_plus_distr',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1),cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ) ) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_0_r_uniq',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = V0__r
=> V1__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_0_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_R0',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ) ).
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.Rplus_eq_reg_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)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)
=> V1__r1 = V2__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_reg_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)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r)
=> V1__r1 = V2__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_ge_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_ge_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_ge_reg_neg_r',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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_gt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_gt_reg_neg_r',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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_pos_r',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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_le_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r)))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_0_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r1))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2))) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_le_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__r3,V3__r4))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V2__r3),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V3__r4))) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2)) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_lt_reg_pos_r',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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1)) = V1__r2 ) ) ).
fof('Coq.Reals.RIneq.Rplus_ne',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r
& cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = V0__r ) ) ).
fof('Coq.Reals.RIneq.Rplus_opp_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.Rplus_opp_r_uniq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V1__r2 = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_sqr_eq_0',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r1),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& V1__r2 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_sqr_eq_0_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r1),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__r2)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rsqr_0',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.RIneq.Rsqr_0_uniq',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.Rtotal_order',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
| V0__r1 = V1__r2
| p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.S_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.RIneq.Z_R_minus',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Reals.RIneq.Zeq_bool_IZR',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__y)
=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Reals.RIneq.cond_neg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eneg___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.Reals.RIneq.cond_nonneg',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2enonneg___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.cond_nonpos',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2enonpos___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.Reals.RIneq.cond_nonzero',axiom,
! [V0__n] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V0__n)
=> cCoq_2eReals_2eRIneq_2enonzero___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.cond_pos',axiom,
! [V0__p] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__p)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2epos___24a1(V0__p))) ) ).
fof('Coq.Reals.RIneq.double',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))),V0__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V0__r1) ) ).
fof('Coq.Reals.RIneq.double_var',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> V0__r1 = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ).
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.eq_IZR_R0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.Reals.RIneq.f_equal_R',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__35329___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.RIneq.le_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.Reals.RIneq.le_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.le_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.le_epsilon',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ! [V2__eps] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__eps)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__eps))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__eps))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.lt_0_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ) ).
fof('Coq.Reals.RIneq.lt_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ).
fof('Coq.Reals.RIneq.lt_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m))) ) ) ) ).
fof('Coq.Reals.RIneq.lt_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.minus_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.minus_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(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.mult_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.mult_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(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.not_0_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.not_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.not_1_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.RIneq.not_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m) ) ) ) ).
fof('Coq.Reals.RIneq.one_IZR_lt1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) )
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.Reals.RIneq.opp_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n)) ) ).
fof('Coq.Reals.RIneq.plus_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.plus_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(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)) ) ) ).
fof('Coq.Reals.RIneq.plus_IZR_NEG_POS',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V1__q))) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V1__q))) ) ) ).
fof('Coq.Reals.RIneq.pos_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n))) ) ).
fof('Coq.Reals.RIneq.pos_INR_nat_of_P',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p)))) ) ).
fof('Coq.Reals.RIneq.pow_IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z),V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__z,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__n))) ) ) ).
fof('Coq.Reals.RIneq.succ_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ).
fof('Coq.Reals.RIneq.tech_Rgt_minus',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2))) ) ) ) ).
fof('Coq.Reals.RIneq.tech_Rplus',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__s] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__s)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__s))
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__s) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('Coq.Reals.R_Ifp.R0_fp_O',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) != cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) != V0__r ) ) ).
fof('Coq.Reals.R_Ifp.base_fp',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.R_Ifp.for_base_fp',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.R_Ifp.fp_R0',axiom,
cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.R_Ifp.fp_nat',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ? [V2__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
& V0__r = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V2__c) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_1',axiom,
cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.R_sqr.Rsqr_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x)) ) ).
fof('Coq.Reals.R_sqr.Rsqr_div',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( V1__y != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)
=> ( V0__x = V1__y
| V0__x = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_eq_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_eq_abs_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_eq_asb_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_gt_0_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)))
=> V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_0_var',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incr_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y)) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_incrst_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_inj',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> ( cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)
=> V0__x = V1__y ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_inv',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x)) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg_pos_le_0',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y),V0__x)) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_neg_pos_le_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__y),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y))) ) ) ) ) ) ).
fof('Coq.Reals.R_sqr.Rsqr_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x))) ) ) ).
fof('Coq.Reals.R_sqr.triangle_rectangle',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__z))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__x),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V1__y)),cCoq_2eReals_2eRIneq_2eRsqr___24a1(V2__z)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V2__z),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V2__z),V1__y))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V2__z)) ) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.R1_neq_R0',axiom,
cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Raxioms.Rinv_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r),V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_asym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3)) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_1_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__r) = V0__r ) ).
fof('Coq.Reals.Raxioms.Rmult_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2))) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_plus_distr_l',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_0_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__r) = V0__r ) ).
fof('Coq.Reals.Raxioms.Rplus_assoc',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2),V2__r3) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V2__r3)) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_lt_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)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r1,V2__r2))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2))) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_opp_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Raxioms.archimed',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRminus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eReals_2eRdefinitions_2eup___24a1(V0__r)),V0__r),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_R0',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Rbasic_fun.Rabs_R1',axiom,
cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rabsolu',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Rinv',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__r)) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Ropp',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__x)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_Zabs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z)) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_left',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_left1',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__a) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__a) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_mult',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V1__y)) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_no_R0',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( V0__r != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x) = V0__x ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_pos_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rabs_right',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = V0__r ) ) ).
fof('Coq.Reals.Rbasic_fun.RmaxRmult',axiom,
! [V0__p] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__r))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,V0__p),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,V1__q)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r,cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__p,V1__q)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_comm',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V1__y,V0__x) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_left',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__y,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_right',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V0__x,V1__y) = V1__y ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmax_stable_in_negreal',axiom,
! [V0__x] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(cCoq_2eReals_2eRIneq_2eneg___24a1(V0__x),cCoq_2eReals_2eRIneq_2eneg___24a1(V1__y)),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_Rgt_r',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r))
& p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V2__r)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__r1,V1__r2),V2__r)) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_comm',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V1__y,V0__x) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_left',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_right',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V0__x))
=> cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V0__x,V1__y) = V1__y ) ) ) ).
fof('Coq.Reals.Rbasic_fun.Rmin_stable_in_posreal',axiom,
! [V0__x] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(cCoq_2eReals_2eRIneq_2epos___24a1(V0__x),cCoq_2eReals_2eRIneq_2epos___24a1(V1__y)))) ) ) ).
fof('Coq.Reals.Rbasic_fun.abs_IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z)) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z)) ) ).
fof('Coq.Reals.Rfunctions.INR_fact_neq_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eArith_2eFactorial_2efact___24a1(V0__n)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.RPow_abs',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),V1__n) = cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)) ) ) ).
fof('Coq.Reals.Rfunctions.R_dist_eq',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V0__x) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.Rfunctions.R_dist_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> p(cCoq_2eReals_2eRdefinitions_2eRge___24a2(cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.Reals.Rfunctions.R_dist_refl',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
<=> V0__x = V1__y ) ) ) ).
fof('Coq.Reals.Rfunctions.R_dist_sym',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V0__x,V1__y) = cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V1__y,V0__x) ) ) ).
fof('Coq.Reals.Rfunctions.Rinv_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n)) = cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x),V1__n) ) ) ) ).
fof('Coq.Reals.Rfunctions.Rlt_pow',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,V2__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m))) ) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.Rpow_mult_distr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,V1__y),V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n)) ) ) ) ).
fof('Coq.Reals.Rfunctions.Zpower_nat_powerRZ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),V1__m)) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.Reals.Rfunctions.Zpower_nat_powerRZ_absolu',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,V1__m))
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V1__m))) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Reals.Rfunctions.Zpower_pos_powerRZ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__m)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__n,V1__m)) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V1__m)) ) ) ).
fof('Coq.Reals.Rfunctions.poly',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),V1__x)),cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V1__x),V0__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = V0__x ) ).
fof('Coq.Reals.Rfunctions.pow_1_abs',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_1_even',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_1_odd',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V0__n))) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_O',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.pow_R1',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eReals_2eRpow__def_2epow___24a2(V0__r,V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
=> ( cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))
| V1__n = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_RN_plus',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m)),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_add',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m)) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_incr',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
& p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V1__y,V2__n))) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_le',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__a,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n))) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_lt_1_zero',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V2__y))
=> ? [V4__N] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__N)
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V5__n,V4__N)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRbasic__fun_2eRabs___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V5__n)),V2__y)) ) ) ) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_ne_zero',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eReals_2eRpow__def_2epow___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.Rfunctions.pow_nonzero',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.Rfunctions.pow_powerRZ',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__r,V1__n) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__r,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__n)) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__x ) ).
fof('Coq.Reals.Rfunctions.powerRZ_NOR',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__z) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_O',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_R1',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_add',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__n),cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V2__m)) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_inv',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__alpha] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__alpha)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x),V1__alpha) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__alpha)) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_le',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__z))) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,V1__z))) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_mult_distr',axiom,
! [V0__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__m)
=> ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__y)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__m))
| cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__x,V2__y) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__x,V2__y),V0__m) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V1__x,V0__m),cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V2__y,V0__m)) ) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_neg',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__alpha] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__alpha)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eR0
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__alpha)) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V0__x),V1__alpha) ) ) ) ).
fof('Coq.Reals.Rfunctions.powerRZ_pos_sub',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__m)
=> ( V0__x != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__n)),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V2__m)))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_in\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9341___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__1958___24a1(V0__A),c_3d___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eLists_2eList_2eIn___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__6644___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l)))) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l)
=> p(happ(happ(V1__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V3__l,V4__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ) ).
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.Sorting.Permutation.Permutation_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V1__l) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__20840___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V3__h] :
( t(V3__h,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> ( p(happ(happ(V1__P,V4__n),V5__t))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> p(happ(happ(V1__P,V4__n),V5__t)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Pos2Z.opp_pos',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V0__p) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(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)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_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_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_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
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__43771___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_mul_0',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
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
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_mul_0_r',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
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.le_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))
<=> p(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__2550,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__2047,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_0_sub',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V1__m,V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_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_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_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_0_l',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.mod_same',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V0__a) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.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.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_nonneg_nonpos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.pos_sub_spec',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V0__p,V1__q) = c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770___24a2(V0__p,V1__q) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_neg_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_2elt___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZ0))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.rem_same',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V0__a) = 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_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.Zmult_integral_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_is_eq_bool',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.ZArith.Zbool.Zle_bool_imp_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.Nat2Z.is_nonneg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n))) ) ).
fof('Coq.ZArith.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_minus2',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_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.nat_N_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) ) ).
fof('Coq.ZArith.Zorder.Znot_ge_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__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.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.dec_Zge',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_2ege___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.Zpower.Zpower_pos_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__z,V1__p) = cCoq_2eZArith_2eZpower_2eZpower__nat___24a2(V0__z,cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__p)) ) ) ).
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.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.Fourier_util.Rle_mult_inv_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y)))) ) ) ) ) ).
fof('Coq.micromega.Fourier_util.Rle_zero_pos_plus1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))) ) ) ).
fof('Coq.micromega.Fourier_util.Rlt_mult_inv_pos',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__y)))) ) ) ) ) ).
fof('Coq.micromega.Fourier_util.Rlt_zero_pos_plus1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__x))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),V0__x))) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__408___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORrt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__408___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORsetoid',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__408___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RMicromega.Q2R_0',axiom,
cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.micromega.RMicromega.Q2R_1',axiom,
cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.micromega.RMicromega.Q2R_inv_ext',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> cCoq_2eQArith_2eQreals_2eQ2R___24a1(cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V0__x)) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2448852___24a1(V0__x) ) ).
fof('Coq.micromega.RMicromega.Qeq_true',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2eQArith_2eQreals_2eQ2R___24a1(V0__x) = cCoq_2eQArith_2eQreals_2eQ2R___24a1(V1__y) ) ) ) ).
fof('Coq.micromega.RMicromega.Qpower0',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( V0__z != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(cCoq_2eQArith_2eQArith__base_2eQpower___24a2(cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH),V0__z),cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2exH)) ) ) ).
fof('Coq.micromega.RMicromega.RTautoChecker_sound',axiom,
! [V0__f] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),V0__f)
=> ! [V1__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eRMicromega_2eRWitness,V1__w)
=> ( cCoq_2emicromega_2eRMicromega_2eRTautoChecker___24a2(V0__f,V1__w) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V3__env] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eReals_2eRdefinitions_2eR,V3__env)
=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(cCoq_2emicromega_2eRMicromega_2eRcst),cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V3__env),V0__f) ) ) ) ) ).
fof('Coq.micromega.RMicromega.Rinv_1',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) = V0__x ) ).
fof('Coq.micromega.Refl.make_conj_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__2721___24t(V0__A,V1__eval)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V2__l)
=> ! [V4__p] :
( t(V4__p,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__p,V2__l))
=> p(happ(V1__eval,V4__p)) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORrm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__1774___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__1774___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__1774___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__1788___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__1795___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__1795___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__1075___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__1080___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__1089___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__408___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Symmetric',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__1062___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1062___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1062___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__408___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__408___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
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.OMEGA17',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_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(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.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.OMEGA7',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)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( 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(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
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.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__2047___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__2047___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__2047___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__2047___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__2047___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__2047___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__2047___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__2047___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_mult_distr_r',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__2047___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__2047___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_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)
=> ! [V3__P] :
( c_24__type__2047___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',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__P] :
( c_24__type__2047___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__2047___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',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__P] :
( c_24__type__2047___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__2047___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__2047___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__2047___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__2047___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),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.setoid_ring.Field_theory.F2AF',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1062___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1071___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__408___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1062___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1071___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__408___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiZ_complete',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1062___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1071___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__408___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V13__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V13__p)),V1__rO)) )
=> ! [V14__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V14__x)
=> ! [V15__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V15__y)
=> ( p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp,V14__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp,V15__y)))
=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V14__x,V15__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_field',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__1062___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__1071___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__408___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req)
=> ( ~ p(happ(happ(V9__req,V2__rI),V1__rO))
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__p),V13__q)),happ(happ(V4__rmul,V12__p),happ(V8__rinv,V13__q)))) ) )
=> ( ! [V13__p] :
( t(V13__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V13__p)),V13__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.Ztriv_div_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__408___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> ! [V3__zphi] :
( c_24__type__25547___24t(V0__R,V3__zphi)
=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V1__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V3__zphi,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.gen_phiZ_morph',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___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_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.get_signZ_th',axiom,
cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eInitialRing_2eget__signZ) ).
fof('Coq.setoid_ring.RealField.RField_lemma5',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),V1__l1)
=> ( ! [V2__lock] :
( c_24__type__35533___24t(V2__lock)
=> ( V2__lock = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l)
=> p(happ(V2__lock,cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem),V1__l1,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ))))) ) )
=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V0__l,V1__l1) ) ) ) ).
fof('Coq.setoid_ring.RealField.RField_ring_lemma1',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ! [V2__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),V2__lpe)
=> ! [V3__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V3__pe1)
=> ! [V4__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(cCoq_2eNumbers_2eBinNums_2eZ,V4__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V2__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32509___24a1(V2__lpe),V3__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,cCoq_2eZArith_2eZbool_2eZeq__bool,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V0__n,c_24__let__6__lmp__32509___24a1(V2__lpe),V4__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V3__pe1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow,V1__l,V4__pe2) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.RealField.RTheory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR)) ).
fof('Coq.setoid_ring.RealField.R_power_theory',axiom,
cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRmult,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,cCoq_2eReals_2eRpow__def_2epow) ).
fof('Coq.setoid_ring.RealField.Rdef_pow_add',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V1__n),cCoq_2eReals_2eRpow__def_2epow___24a2(V0__x,V2__m)) ) ) ) ).
fof('Coq.setoid_ring.RealField.Rfield',axiom,
cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRminus,cCoq_2eReals_2eRdefinitions_2eRopp,cCoq_2eReals_2eRdefinitions_2eRdiv,cCoq_2eReals_2eRdefinitions_2eRinv,c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR)) ).
fof('Coq.setoid_ring.RealField.Rgen_phiPOS',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRgt___24a2(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,V0__x),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))) ) ).
fof('Coq.setoid_ring.RealField.Rgen_phiPOS_not_0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,V0__x) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.setoid_ring.RealField.Rlt_0_2',axiom,
p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ).
fof('Coq.setoid_ring.RealField.Rlt_n_Sn',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__x,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) ) ).
fof('Coq.setoid_ring.RealField.Zeq_bool_complete',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp,V0__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRplus,cCoq_2eReals_2eRdefinitions_2eRmult,cCoq_2eReals_2eRdefinitions_2eRopp,V1__y)
=> cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ring_correct',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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)
=> ! [V11__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__1774___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__1774___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__1774___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__1788___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__1795___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1075___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__Cpow] :
( cType___24t(V21__Cpow)
=> ! [V22__Cp__phi] :
( c_24__type__1080___24t(V0__R,V11__C,V21__Cpow,V22__Cp__phi)
=> ! [V23__rpow] :
( c_24__type__1089___24t(V0__R,V11__C,V21__Cpow,V23__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rmul,V7__req,V21__Cpow,V22__Cp__phi,V23__rpow)
=> ! [V25__cdiv] :
( c_24__type__1816___24t(V0__R,V11__C,V21__Cpow,V25__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V7__req,V11__C,V14__cadd,V15__cmul,V19__phi,V25__cdiv)
=> ! [V27__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V27__n)
=> ! [V28__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V28__l)
=> ! [V29__lpe] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V11__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V11__C)),V29__lpe)
=> ! [V30__pe1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V11__C,V30__pe1)
=> ! [V31__pe2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V11__C,V31__pe2)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V11__C,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V28__l,V29__lpe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V11__C,V18__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V25__cdiv,V27__n,c_24__let__33__lmp__1818___24a12(V0__R,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V21__Cpow,V25__cdiv,V29__lpe),V30__pe1),cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V25__cdiv,V27__n,c_24__let__33__lmp__1818___24a12(V0__R,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V21__Cpow,V25__cdiv,V29__lpe),V31__pe2)) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V11__C,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V28__l,V30__pe1)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V11__C,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V28__l,V31__pe2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_polynom.ring_rw_pow_correct',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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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)
=> ! [V11__C] :
( cType___24t(V11__C)
=> ! [V12__cO] :
( t(V12__cO,V11__C)
=> ! [V13__cI] :
( t(V13__cI,V11__C)
=> ! [V14__cadd] :
( c_24__type__1774___24t(V0__R,V11__C,V14__cadd)
=> ! [V15__cmul] :
( c_24__type__1774___24t(V0__R,V11__C,V15__cmul)
=> ! [V16__csub] :
( c_24__type__1774___24t(V0__R,V11__C,V16__csub)
=> ! [V17__copp] :
( c_24__type__1788___24t(V0__R,V11__C,V17__copp)
=> ! [V18__ceqb] :
( c_24__type__1795___24t(V0__R,V11__C,V18__ceqb)
=> ! [V19__phi] :
( c_24__type__1075___24t(V0__R,V11__C,V19__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,V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V19__phi)
=> ! [V21__Cpow] :
( cType___24t(V21__Cpow)
=> ! [V22__Cp__phi] :
( c_24__type__1080___24t(V0__R,V11__C,V21__Cpow,V22__Cp__phi)
=> ! [V23__rpow] :
( c_24__type__1089___24t(V0__R,V11__C,V21__Cpow,V23__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rmul,V7__req,V21__Cpow,V22__Cp__phi,V23__rpow)
=> ! [V25__cdiv] :
( c_24__type__1816___24t(V0__R,V11__C,V21__Cpow,V25__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V0__R,V7__req,V11__C,V14__cadd,V15__cmul,V19__phi,V25__cdiv)
=> ! [V27__get__sign] :
( c_24__type__2327___24t(V0__R,V11__C,V21__Cpow,V27__get__sign)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V11__C,V17__copp,V18__ceqb,V27__get__sign)
=> ! [V29__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V29__n)
=> ! [V30__lH] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V11__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V11__C)),V30__lH)
=> ! [V31__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V31__l)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V11__C,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V31__l,V30__lH)
=> ! [V33__lmp] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V11__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V11__C)),V33__lmp)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V25__cdiv,V30__lH) = V33__lmp
=> ! [V35__pe] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V11__C,V35__pe)
=> ! [V36__npe] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V11__C,V36__npe)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V11__C,V12__cO,V13__cI,V14__cadd,V15__cmul,V16__csub,V17__copp,V18__ceqb,V25__cdiv,V29__n,V33__lmp,V35__pe) = V36__npe
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V11__C,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V31__l,V35__pe)),cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V11__C,V12__cO,V13__cI,V18__ceqb,V19__phi,V21__Cpow,V22__Cp__phi,V23__rpow,V27__get__sign,V31__l,V36__npe))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1062___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1062___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1071___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Rmul_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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V11__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1062___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1062___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__1071___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__408___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1062___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1071___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1062___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__1071___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1071___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_rt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> ! [V13__y] :
( t(V13__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ! [V15__z] :
( t(V15__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mkmorph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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__1774___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__1774___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__1774___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__1788___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__1795___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1075___24t(V0__R,V8__C,V16__phi)
=> ( p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO))
=> ( p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI))
=> ( ! [V19__x] :
( t(V19__x,V8__C)
=> ! [V20__y] :
( t(V20__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V19__x),V20__y))),happ(happ(V3__radd,happ(V16__phi,V19__x)),happ(V16__phi,V20__y)))) ) )
=> ( ! [V20__x] :
( t(V20__x,V8__C)
=> ! [V21__y] :
( t(V21__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V20__x),V21__y))),happ(happ(V5__rsub,happ(V16__phi,V20__x)),happ(V16__phi,V21__y)))) ) )
=> ( ! [V21__x] :
( t(V21__x,V8__C)
=> ! [V22__y] :
( t(V22__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V21__x),V22__y))),happ(happ(V4__rmul,happ(V16__phi,V21__x)),happ(V16__phi,V22__y)))) ) )
=> ( ! [V22__x] :
( t(V22__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V22__x))),happ(V6__ropp,happ(V16__phi,V22__x)))) )
=> ( ! [V23__x] :
( t(V23__x,V8__C)
=> ! [V24__y] :
( t(V24__y,V8__C)
=> ( happ(happ(V15__ceqb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V23__x)),happ(V16__phi,V24__y))) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mkpow_th',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__1062___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__408___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__29758___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__2014___24t(V0__R,V4__Cpow,V6__rpow)
=> ( ! [V7__r] :
( t(V7__r,V0__R)
=> ! [V8__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V8__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V7__r),happ(V5__Cp__phi,V8__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V7__r,V8__n))) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow) ) ) ) ) ) ) ) ) ).
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__1062___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1062___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1062___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1071___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__408___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__1774___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__1774___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__1774___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__1788___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__1795___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__1075___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('QuicksortComplexity.arith_lems.INR_0_inv',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('QuicksortComplexity.arith_lems.INR_S_ne_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('QuicksortComplexity.arith_lems.O_le_inv_INR_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRdefinitions_2eRinv___24a1(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))))) ) ).
fof('QuicksortComplexity.arith_lems.O_lt_INR_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))) ) ).
fof('QuicksortComplexity.arith_lems.Rdiv_le_1',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__a))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__a,V1__b))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V1__b,V0__a))) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Rdiv_lt_1',axiom,
! [V0__n] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__m)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V0__n))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__n,V1__m))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__n,V1__m),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Req_le_trans',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( V0__x = V1__y
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V2__z))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Rle_eq_trans',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Rmult_0_inv',axiom,
! [V0__a] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__b)
=> ( cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__a,V1__b) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V0__a = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
| V1__b = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.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('QuicksortComplexity.arith_lems.Rne_nlt_lt',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ( V0__x != V1__y
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__x,V1__y))
=> p(cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__y,V0__x)) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.le_exists_plus',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ? [V3__d] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__d)
& V1__y = cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V3__d) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.InP_In',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V1__l)
=> ! [V2__ll] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V2__ll)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V1__l,V2__ll))
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V4__x,V1__l))
=> cQuicksortComplexity_2elist__utils_2eInP___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),cCoq_2eLists_2eList_2eIn___24a2(V0__X,V4__x),V2__ll) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.InP_In_inv',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__ll] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V2__ll)
=> ( cQuicksortComplexity_2elist__utils_2eInP___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),cCoq_2eLists_2eList_2eIn___24a2(V0__X,V1__x),V2__ll)
=> ? [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V4__l))
& p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V4__l,V2__ll)) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1958___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cProp,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3c_3d_3e),cCoq_2eLists_2eList_2eIn___24a2(V0__A,V1__x)) ) ) ).
fof('QuicksortComplexity.list_utils.In_concat',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V1__l)
=> ! [V2__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__s)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__s))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V2__s,V1__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,cQuicksortComplexity_2elist__utils_2econcat___24a2(V0__X,V1__l))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_concat_inv',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,cQuicksortComplexity_2elist__utils_2econcat___24a2(V0__X,V2__l)))
=> ? [V4__s] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__s)
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V4__s))
& p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V4__s,V2__l)) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_filter',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__6478___24t(V0__T,V1__p)
=> ! [V2__t] :
( t(V2__t,V0__T)
=> ( happ(V1__p,V2__t) = cCoq_2eInit_2eDatatypes_2etrue
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V2__t,V4__l))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V2__t,cCoq_2eLists_2eList_2efilter___24a3(V0__T,V1__p,V4__l))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_filter_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__6478___24t(V0__A,V1__f)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l)))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l))
& happ(V1__f,V2__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_map_inv',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__71___24t(V0__T,V1__U,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__U)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__U,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V2__f,V3__l)))
=> ? [V6__x] :
( t(V6__x,V0__T)
& happ(V2__f,V6__x) = V4__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V6__x,V3__l)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.NoDup_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V3__l))
=> ( happ(V2__f,V4__x) = happ(V2__f,V5__y)
=> V4__x = V5__y ) ) ) ) )
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.NoDup_map\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V3__l))
=> ( V4__x != V5__y
=> happ(V2__f,V4__x) != happ(V2__f,V5__y) ) ) ) ) )
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Permutation_concatMap',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__6412___24t(V0__T,V1__U,V2__f)
=> ! [V3__g] :
( c_24__type__6412___24t(V0__T,V1__U,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__l)
=> ( ! [V5__x] :
( t(V5__x,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V5__x,V4__l))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__U,happ(V2__f,V5__x),happ(V3__g,V5__x)) ) )
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__U,cQuicksortComplexity_2elist__utils_2econcat___24a2(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),V2__f,V4__l)),cQuicksortComplexity_2elist__utils_2econcat___24a2(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),V3__g,V4__l))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.add_same',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__c)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V1__l)
=> ( ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__x,V1__l))
=> V2__x = V0__c ) )
=> cQuicksortComplexity_2elist__utils_2eadd___24a1(V1__l) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,V1__l),V0__c) ) ) ) ).
fof('QuicksortComplexity.list_utils.concat_nil',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V1__l)
=> ( ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),V2__x,V1__l))
=> V2__x = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) )
=> cQuicksortComplexity_2elist__utils_2econcat___24a2(V0__X,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) ) ) ).
fof('QuicksortComplexity.list_utils.count_0',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__6478___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V2__l) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('QuicksortComplexity.list_utils.eR_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2490___24t(V0__A,V1__B,V2__R)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> ( p(happ(happ(V2__R,V3__a),V4__b))
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l_27)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V6__l,V7__l_27)
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V6__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V4__b,V7__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.eR_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2490___24t(V0__A,V1__B,V2__R)
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__f] :
( c_24__type__1071___24t(V0__A,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> p(happ(happ(V1__R,happ(V2__f,V4__x)),V4__x)) ) )
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V0__A,V1__R,cCoq_2eLists_2eList_2emap___24a4(V0__A,V0__A,V2__f,V3__l),V3__l) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_map_map',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__1075___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__1075___24t(V0__X,V1__Y,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__Y,V4__l)
=> ! [V5__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V5__R)
=> ( ! [V6__x] :
( t(V6__x,V1__Y)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__Y,V6__x,V4__l))
=> p(happ(happ(V5__R,happ(V2__f,V6__x)),happ(V3__g,V6__x))) ) )
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__X,V0__X,V5__R,cCoq_2eLists_2eList_2emap___24a4(V1__Y,V0__X,V2__f,V4__l),cCoq_2eLists_2eList_2emap___24a4(V1__Y,V0__X,V3__g,V4__l)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsRuniq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__2490___24t(V0__A,V1__B,V2__R)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l))
=> ! [V6__y] :
( t(V6__y,V1__B)
=> ( p(happ(happ(V2__R,V4__x),V6__y))
=> ! [V8__y_27] :
( t(V8__y_27,V1__B)
=> ( p(happ(happ(V2__R,V4__x),V8__y_27))
=> V6__y = V8__y_27 ) ) ) ) ) )
=> ! [V5__r] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__r)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V3__l,V5__r)
=> ! [V7__r_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__r_27)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V3__l,V7__r_27)
=> V5__r = V7__r_27 ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.filter_all',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__6478___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2etrue ) )
=> cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l) = V2__l ) ) ) ) ).
fof('QuicksortComplexity.list_utils.filter_merges',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__6478___24t(V0__T,V1__p)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__y)
=> ( ! [V4__z] :
( t(V4__z,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__z,V2__x))
=> happ(V1__p,V4__z) = cCoq_2eInit_2eDatatypes_2etrue ) )
=> ( ! [V5__z] :
( t(V5__z,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V5__z,V3__y))
=> happ(V1__p,V5__z) = cCoq_2eInit_2eDatatypes_2efalse ) )
=> ! [V6__r] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V6__r)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V6__r,cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eLists_2eList_2efilter___24a2(V0__T,V1__p),cQuicksortComplexity_2elist__utils_2emerges___24a3(V0__T,V2__x,V3__y))))
=> V6__r = V2__x ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.filter_none',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__6478___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l))
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
<=> cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.incl_In',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V2__l))
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l_27)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__X,V2__l,V4__l_27)
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V4__l_27)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.incl_in',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__b)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__T,V1__a,V2__b)
=> ! [V4__x] :
( t(V4__x,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__x,V1__a))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__x,V2__b)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.map_repeat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__71___24t(V0__A,V1__B,V2__f)
=> ! [V3__c] :
( t(V3__c,V1__B)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V4__l))
=> happ(V2__f,V5__x) = V3__c ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__B,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V4__l),V3__c) ) ) ) ) ) ) ).
fof('QuicksortComplexity.nat_seqs.In_nats',axiom,
! [V0__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__w)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__b)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__b,V1__x))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__x,cCoq_2eInit_2eNat_2eadd___24a2(V2__b,V0__w)))
=> p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__x,cQuicksortComplexity_2enat__seqs_2enats___24a2(V2__b,V0__w))) ) ) ) ) ) ).
fof('QuicksortComplexity.nat_seqs.In_nats_inv',axiom,
! [V0__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__w)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__b)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__x,cQuicksortComplexity_2enat__seqs_2enats___24a2(V2__b,V0__w)))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__b,V1__x))
& p(cCoq_2eInit_2ePeano_2elt___24a2(V1__x,cCoq_2eInit_2eNat_2eadd___24a2(V2__b,V0__w))) ) ) ) ) ) ).
fof('sums_and_averages.Ravg_0_le',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ( ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V1__x,V0__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),csums__and__averages_2eRavg___24a1(V0__l))) ) ) ).
fof('sums_and_averages.Ravg_Permutation',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44242,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(cCoq_2eReals_2eRdefinitions_2eR),c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR)),csums__and__averages_2eRavg) ).
fof('sums_and_averages.Ravg_cons',axiom,
! [V0__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__h)
=> ! [V1__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__t)
=> csums__and__averages_2eRavg___24a1(cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eReals_2eRdefinitions_2eR,V0__h,V1__t)) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__h,cCoq_2eReals_2eRdefinitions_2eRmult___24a2(csums__and__averages_2eRavg___24a1(V1__t),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V1__t)))),cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V1__t)))) ) ) ).
fof('sums_and_averages.Ravg_nil',axiom,
csums__and__averages_2eRavg___24a1(cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eReals_2eRdefinitions_2eR)) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('sums_and_averages.Ravg_one',axiom,
! [V0__h] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__h)
=> csums__and__averages_2eRavg___24a1(cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eReals_2eRdefinitions_2eR,V0__h,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eReals_2eRdefinitions_2eR))) = V0__h ) ).
fof('sums_and_averages.RsumOver_constant_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V1__l)
=> ! [V2__f] :
( c_24__type__44247___24t(V0__X,V2__f)
=> ! [V3__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__c)
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V4__x,V1__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V2__f,V4__x),V3__c)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(csums__and__averages_2eRsumOver___24a3(V0__X,V1__l,V2__f),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V1__l)),V3__c))) ) ) ) ) ) ).
fof('sums_and_averages.RsumOver_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( c_24__type__44247___24t(V0__X,V1__f)
=> ! [V2__g] :
( c_24__type__44247___24t(V0__X,V2__g)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V4__x,V3__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__f,V4__x),happ(V2__g,V4__x))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(csums__and__averages_2eRsumOver___24a3(V0__X,V3__l,V1__f),csums__and__averages_2eRsumOver___24a3(V0__X,V3__l,V2__g))) ) ) ) ) ) ).
fof('sums_and_averages.RsumOver_nats_le',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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V2__z))
=> ! [V4__f] :
( c_24__type__20754___24t(V4__f)
=> ( ! [V5__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__q)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V5__q))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),happ(V4__f,V5__q))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(csums__and__averages_2eRsumOver___24a3(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__seqs_2enats___24a2(V0__x,V1__y),V4__f),csums__and__averages_2eRsumOver___24a3(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__seqs_2enats___24a2(V0__x,V2__z),V4__f))) ) ) ) ) ) ) ).
fof('sums_and_averages.Rsum_Permutation',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44242,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(cCoq_2eReals_2eRdefinitions_2eR),c_3d___24a1(cCoq_2eReals_2eRdefinitions_2eR)),csums__and__averages_2eRsum) ).
fof('sums_and_averages.Rsum_app',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__y)
=> csums__and__averages_2eRsum___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eReals_2eRdefinitions_2eR,V0__x,V1__y)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(csums__and__averages_2eRsum___24a1(V0__x),csums__and__averages_2eRsum___24a1(V1__y)) ) ) ).
fof('sums_and_averages.Rsum_concat',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eReals_2eRdefinitions_2eR),V0__l)
=> csums__and__averages_2eRsum___24a1(cQuicksortComplexity_2elist__utils_2econcat___24a2(cCoq_2eReals_2eRdefinitions_2eR,V0__l)) = csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eReals_2eRdefinitions_2eR,csums__and__averages_2eRsum,V0__l)) ) ).
fof('sums_and_averages.Rsum_constant',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> ( ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V2__x,V1__l))
=> V2__x = V0__r ) )
=> csums__and__averages_2eRsum___24a1(V1__l) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V1__l)),V0__r) ) ) ) ).
fof('sums_and_averages.Rsum_le',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ! [V1__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r)
=> ( ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V2__x,V0__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V2__x,V1__r)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(csums__and__averages_2eRsum___24a1(V0__l),cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V0__l)),V1__r))) ) ) ) ).
fof('sums_and_averages.Rsum_map_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( c_24__type__44247___24t(V0__X,V1__f)
=> ! [V2__g] :
( c_24__type__44247___24t(V0__X,V2__g)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V4__x,V3__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(happ(V1__f,V4__x),happ(V2__g,V4__x))) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V1__f,V3__l)),csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V2__g,V3__l)))) ) ) ) ) ) ).
fof('sums_and_averages.Rsum_map_mult',axiom,
! [V0__c] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__c)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V1__l)
=> csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRmult___24a1(V0__c),V1__l)) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__c,csums__and__averages_2eRsum___24a1(V1__l)) ) ) ).
fof('sums_and_averages.Rsum_map_plus',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__f] :
( c_24__type__44247___24t(V0__X,V1__f)
=> ! [V2__g] :
( c_24__type__44247___24t(V0__X,V2__g)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,c_24__lam__50211___24a3(V0__X,V1__f,V2__g),V3__l)) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V1__f,V3__l)),csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__X,cCoq_2eReals_2eRdefinitions_2eR,V2__g,V3__l))) ) ) ) ) ).
fof('sums_and_averages.Rsum_nonneg',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ( ! [V1__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V1__x,V0__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),V1__x)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),csums__and__averages_2eRsum___24a1(V0__l))) ) ) ).
fof('sums_and_averages.Rsum_sum_map',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__fi] :
( c_24__type__12427___24t(V0__T,V1__fi)
=> ! [V2__fr] :
( c_24__type__44247___24t(V0__T,V2__fr)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__T)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__T,V4__x,V3__l))
=> happ(V2__fr,V4__x) = cCoq_2eReals_2eRaxioms_2eINR___24a1(happ(V1__fi,V4__x)) ) )
=> csums__and__averages_2eRsum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eReals_2eRdefinitions_2eR,V2__fr,V3__l)) = cCoq_2eReals_2eRaxioms_2eINR___24a1(csums__and__averages_2esum___24a1(cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2enat,V1__fi,V3__l))) ) ) ) ) ) ).
fof('sums_and_averages.elemsR_le_Rsum',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44242,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eReals_2eRdefinitions_2eR),cCoq_2eReals_2eRdefinitions_2eR,cQuicksortComplexity_2elist__utils_2eelemsR___24a3(cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eR,cCoq_2eReals_2eRdefinitions_2eRle),cCoq_2eReals_2eRdefinitions_2eRle),csums__and__averages_2eRsum) ).
fof('sums_and_averages.le_Rsum',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eReals_2eRdefinitions_2eR,V0__l)
=> ! [V1__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r)
=> ( ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V2__x,V0__l))
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r,V2__x)) ) )
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eRmult___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eReals_2eRdefinitions_2eR,V0__l)),V1__r),csums__and__averages_2eRsum___24a1(V0__l))) ) ) ) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$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.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.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.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.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_$_prop_43894_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43894,V_24X1),V_24X2) = c_24__prop__43894___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq__bool,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEmul_$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_2eField__theory_2eNPEmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.RMicromega.INZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eINZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eINZ___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.nat_seqs.nats_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__seqs_2enats,V_24X1),V_24X2) = cQuicksortComplexity_2enat__seqs_2enats___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2eto__list,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.R_dist_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eR__dist,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eR__dist___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_33_lmp_1818_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__33__lmp__1818,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__let__33__lmp__1818___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$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_$_lam_6433_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6433,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6433___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_6_lmp_32527_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__32527,V_24X1) = c_24__let__6__lmp__32527___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.vec.from_list_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2efrom__list,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2efrom__list___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.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_QuicksortComplexity.vec.tail_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2etail,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2etail___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1165_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1165,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__1165___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Logic.FinFun.Full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eFull,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eFull___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_50211_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__50211,V_24X1),V_24X2),V_24X3) = c_24__lam__50211___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rfunctions.powerRZ_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2epowerRZ,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2epowerRZ___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.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_QuicksortComplexity.list_utils.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2econcat,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2econcat___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.count_occ_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecount__occ,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecount__occ___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.remove_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eremove,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eremove___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_prop_5424_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5424,V_24X1),V_24X2),V_24X3) = c_24__prop__5424___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_var_14_s1_24663_24667_24725_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s1__24663__24667__24725,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s1__24663__24667__24725___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Lists.List.nth_error_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enth__error,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enth__error___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$35605_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2435605___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('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43322_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43322,V_24X1),V_24X2) = c_24__prop__43322___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.setoid_ring.Ring_theory.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xelements_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_17_mkopp_pow_25885_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__25885,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__25885___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_let_17_mkopp_pow_25885_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__25885,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__25885___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_$_lam_50211_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__50211,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__50211___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('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
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('$adef_Coq.QArith.Qreals.Q2R_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQreals_2eQ2R,V_24X1) = cCoq_2eQArith_2eQreals_2eQ2R___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('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$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('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.app_$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('$adef_sums_and_averages.sum_$a1',axiom,
! [V_24X1] : happ(csums__and__averages_2esum,V_24X1) = csums__and__averages_2esum___24a1(V_24X1) ).
fof('$adef_$_prop_5562_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5562,V_24X1),V_24X2),V_24X3) = c_24__prop__5562___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qle_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQle__bool,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQle__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43942_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43942,V_24X1),V_24X2) = c_24__prop__43942___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.Rle_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRIneq_2eRle__dec,V_24X1),V_24X2) = cCoq_2eReals_2eRIneq_2eRle__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_QuicksortComplexity.nat_below.nb_val_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__below_2enb__val,V_24X1),V_24X2) = cQuicksortComplexity_2enat__below_2enb__val___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.R_Ifp.frac_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2efrac__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2efrac__part___24a1(V_24X1) ).
fof('$adef_$_lam_41235_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__41235,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__41235___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Lists.List.fold_right_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2efold__right___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_41227_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41227,V_24X1),V_24X2),V_24X3) = c_24__lam__41227___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$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('$adef_Coq.setoid_ring.Field_theory.FEmul_$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('$adef_Coq.Reals.Rbasic_fun.Rcase_abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRcase__abs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRcase__abs___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.nat_below.natBelow_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enatBelow,V_24X1) = cQuicksortComplexity_2enat__below_2enatBelow___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_25884_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__25884,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__25884___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$35610_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2435610___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_$_prop_6718_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__6718,V_24X1),V_24X2),V_24X3) = c_24__prop__6718___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Reals.Rdefinitions.Rmult_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_41227_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__41227,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__41227___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_let_18_mkmult_pow_25886_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__25886,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__25886___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_5561_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5561,V_24X1),V_24X2),V_24X3) = c_24__prop__5561___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQminus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_$_prop_20161_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__20161,V_24X1),V_24X2) = c_24__prop__20161___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43729_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43729,V_24X1),V_24X2) = c_24__prop__43729___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('$adef_QuicksortComplexity.vec.sorted_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2evec_2esorted,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2evec_2esorted___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.RIneq.nonneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonneg,V_24X1) = cCoq_2eReals_2eRIneq_2enonneg___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2edouble,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.RTautoChecker_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eRTautoChecker,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eRTautoChecker___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('$adef_Coq.Lists.List.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eexistsb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Env.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_var_15_s2_24688_24692_24738_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__15__s2__24688__24692__24738,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__15__s2__24688__24692__24738___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_let_var_var_13_y_24662_24666_24724_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__24662__24666__24724,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__24662__24666__24724___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
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('$adef_Coq.Init.Nat.max_$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('$adef_Coq.ZArith.Zpower.Zpower_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2eZpower__nat,V_24X1) = cCoq_2eZArith_2eZpower_2eZpower__nat___24a1(V_24X1) ).
fof('$adef_$_prop_43728_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43728,V_24X1),V_24X2) = c_24__prop__43728___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.eval_nformula_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11))
<=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEopp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEopp,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eNPEopp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.nat$2850_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_242850,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_242850___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_43771_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43771,V_24X1),V_24X2) = c_24__prop__43771___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.in_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2ein__dec,V_24X1),V_24X2) = cCoq_2eLists_2eList_2ein__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.up_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eup,V_24X1) = cCoq_2eReals_2eRdefinitions_2eup___24a1(V_24X1) ).
fof('$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.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$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.Reals.Rfunctions.sum_f_R0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__f__R0,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__f__R0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_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.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.setoid_ring.Field_theory.NPEsub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_prop_5375_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5375,V_24X1),V_24X2),V_24X3) = c_24__prop__5375___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.list_utils.InP_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eInP,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2elist__utils_2eInP___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('$adef_Coq.micromega.EnvRing.PEopp_$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('$adef_Coq.Init.Datatypes.CompareSpec_$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('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Lists.List.In_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2eIn,V_24X1) = cCoq_2eLists_2eList_2eIn___24a1(V_24X1) ).
fof('$adef_Coq.Lists.ListDec.In_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eListDec_2eIn__dec,V_24X1),V_24X2) = cCoq_2eLists_2eListDec_2eIn__dec___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('$adef_$_prop_5559_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5559,V_24X1),V_24X2),V_24X3) = c_24__prop__5559___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.RIneq.neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eneg,V_24X1) = cCoq_2eReals_2eRIneq_2eneg___24a1(V_24X1) ).
fof('$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.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.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.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.R_Ifp.Int_part_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eR__Ifp_2eInt__part,V_24X1) = cCoq_2eReals_2eR__Ifp_2eInt__part___24a1(V_24X1) ).
fof('$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_$_let_20_lnum_33085_$a18',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__20__lnum__33085,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_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) = c_24__let__20__lnum__33085___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_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) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.BFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eTauto_2eBFormula,V_24X1) = cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.in_dec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ein__dec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ein__dec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$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_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEadd_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eField__theory_2eNPEadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_$_lam_1165_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1165,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__1165___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_$_prop_5376_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5376,V_24X1),V_24X2),V_24X3) = c_24__prop__5376___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.list_utils.NoDupL_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cQuicksortComplexity_2elist__utils_2eNoDupL,V_24X1),V_24X2))
<=> cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',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] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc__double___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2epos,V_24X1) = cCoq_2eReals_2eRIneq_2epos___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.nonzero_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonzero,V_24X1) = cCoq_2eReals_2eRIneq_2enonzero___24a1(V_24X1) ).
fof('$adef_$_prop_43869_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43869,V_24X1),V_24X2) = c_24__prop__43869___24a2(V_24X1,V_24X2) ).
fof('$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.FSets.FSetPositive.PositiveSet.elements_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.list_utils.elemsR_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2eelemsR___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_49745_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49745,V_24X1),V_24X2) = c_24__prop__49745___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.display_pow_linear_$a20',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_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) = cCoq_2esetoid__ring_2eField__theory_2edisplay__pow__linear___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_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) ).
fof('$adef_$_prop_5426_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5426,V_24X1),V_24X2),V_24X3) = c_24__prop__5426___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_43998_44001_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__43998__44001,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__43998__44001___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.list_utils.concat_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2econcat,V_24X1) = cQuicksortComplexity_2elist__utils_2econcat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.Reval_formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__formula,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__formula___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.get_signZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2eget__signZ,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2eget__signZ___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_fix_19747_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__19747__1__add__carry,V_24X1),V_24X2) = c_24__fix__19747__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$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.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_5427_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5427,V_24X1),V_24X2),V_24X3) = c_24__prop__5427___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_20872_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__20872,V_24X1),V_24X2) = c_24__lam__20872___24a2(V_24X1,V_24X2) ).
fof('$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.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_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.setoid_ring.Field_theory.NPEpow_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEpow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_let_var_var_13_y_24649_24652_24715_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__24649__24652__24715,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__24649__24652__24715___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_Coq.micromega.Tauto.X_$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('$adef_$_lam_41219_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41219,V_24X1),V_24X2),V_24X3) = c_24__lam__41219___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_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.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_var_var_14_s_24650_24653_24716_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s__24650__24653__24716,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s__24650__24653__24716___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_let_var_11_x_24677_24727_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__24677__24727,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__24677__24727___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$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.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.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$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.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.setoid_ring.Field_theory.PEsimp_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$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.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.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_20870_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20870,V_24X1) = c_24__lam__20870___24a1(V_24X1) ).
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('$adef_Coq.Reals.Rdefinitions.IPR_2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR__2,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR__2___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$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('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43893_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43893,V_24X1),V_24X2) = c_24__prop__43893___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.Reval_op2_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eReval__op2,V_24X1) = cCoq_2emicromega_2eRMicromega_2eReval__op2___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.list_utils.elemsR_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2elist__utils_2eelemsR___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fnorm_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFnorm,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2eFnorm___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred__double___24a1(V_24X1) ).
fof('$adef_$_prop_43321_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43321,V_24X1),V_24X2) = c_24__prop__43321___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_$_prop_5560_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5560,V_24X1),V_24X2),V_24X3) = c_24__prop__5560___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_20872_$a1',axiom,
! [V_24X1] : happ(c_24__lam__20872,V_24X1) = c_24__lam__20872___24a1(V_24X1) ).
fof('$adef_$_prop_6706_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__6706,V_24X1),V_24X2),V_24X3) = c_24__prop__6706___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_case_Coq.Init.Datatypes.nat$35588_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2435588,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2435588___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.combine_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecombine,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecombine___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.ZArith.BinIntDef.Z.mul_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a1(V_24X1) ).
fof('$adef_$_lam_41243_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__41243,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__41243___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.find_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efind,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efind___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.nonpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2enonpos,V_24X1) = cCoq_2eReals_2eRIneq_2enonpos___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.nat_below.mkNatBelow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__below_2emkNatBelow,V_24X1),V_24X2) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.find_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2efind,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2efind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_let_var_var_7_n_5516_5520_5529_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__5516__5520__5529,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__5516__5520__5529___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rfunctions.infinite_sum_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRfunctions_2einfinite__sum,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRfunctions_2einfinite__sum___24a2(V_24X1,V_24X2) ) ).
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('$adef_$_let_var_var_15_s2_24664_24668_24726_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__15__s2__24664__24668__24726,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__15__s2__24664__24668__24726___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_41243_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41243,V_24X1),V_24X2),V_24X3) = c_24__lam__41243___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_let_var_var_12_x_24661_24665_24723_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__24661__24665__24723,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__24661__24665__24723___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.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.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.QArith.QArith_base.Qinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQinv,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQinv___24a1(V_24X1) ).
fof('$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.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.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.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$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.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_$_let_var_var_12_x_24702_24704_24739_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__24702__24704__24739,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__24702__24704__24739___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_prop_32477_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__32477,V_24X1),V_24X2) = c_24__prop__32477___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nodup_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enodup,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enodup___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a18',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a18(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18) ).
fof('$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_$_let_var_var_12_x_24685_24689_24735_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__24685__24689__24735,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__24685__24689__24735___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_Coq.micromega.Env.hd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2ehd,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2ehd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQplus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.setoid_ring.Ring_polynom.Pol$33389_$a20',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_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) = c_24__case__Coq_2esetoid__ring_2eRing__polynom_2ePol_2433389___24a20(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_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) ).
fof('$adef_$_let_16_mkpow_25884_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__25884,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__25884___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.rev_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_prop_30978_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30978,V_24X1),V_24X2),V_24X3) = c_24__prop__30978___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.ListDec.decidable_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLists_2eListDec_2edecidable__eq,V_24X1))
<=> cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V_24X1) ) ).
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('$adef_sums_and_averages.Rsum_$a1',axiom,
! [V_24X1] : happ(csums__and__averages_2eRsum,V_24X1) = csums__and__averages_2eRsum___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rabs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRbasic__fun_2eRabs,V_24X1) = cCoq_2eReals_2eRbasic__fun_2eRabs___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('$adef_$_prop_43941_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43941,V_24X1),V_24X2) = c_24__prop__43941___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.filter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2) = cCoq_2eLists_2eList_2efilter___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_34028_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34028,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34028___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.list_utils.add_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2eadd,V_24X1) = cQuicksortComplexity_2elist__utils_2eadd___24a1(V_24X1) ).
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('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_var_var_13_y_24686_24690_24736_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__24686__24690__24736,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__24686__24690__24736___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_let_var_var_12_x_24635_24638_24708_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__24635__24638__24708,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__24635__24638__24708___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_11_x_24680_24728_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__11__x__24680__24728,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__11__x__24680__24728___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$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.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eField__theory_2ePCond___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.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.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ).
fof('$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.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.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.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_$_let_var_var_14_s1_24687_24691_24737_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s1__24687__24691__24737,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s1__24687__24691__24737___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_QuicksortComplexity.list_utils.merges_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2emerges___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Zpower.Zpower_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZpower__nat,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZpower__nat___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('$adef_Coq.micromega.Tauto.eval_bf_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__bf,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eTauto_2eeval__bf___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_35327_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35327,V_24X1),V_24X2) = c_24__prop__35327___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_let_11_subst_l_1093_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__1093,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__1093___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_$_let_var_var_14_s_24637_24640_24710_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__14__s__24637__24640__24710,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__var__var__14__s__24637__24640__24710___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.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.micromega.Env.tail_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2etail,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2etail___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_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_$_case_Coq.Init.Specif.sumbool$5547_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_245547,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_245547___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_case_Coq.Init.Datatypes.comparison$43770_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_2443770___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('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.flat_map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eflat__map,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eflat__map___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_5377_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5377,V_24X1),V_24X2),V_24X3) = c_24__prop__5377___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_sums_and_averages.RsumOver_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(csums__and__averages_2eRsumOver,V_24X1),V_24X2),V_24X3) = csums__and__averages_2eRsumOver___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_35521_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35521,V_24X1),V_24X2) = c_24__prop__35521___24a2(V_24X1,V_24X2) ).
fof('$adef_sums_and_averages.Ravg_$a1',axiom,
! [V_24X1] : happ(csums__and__averages_2eRavg,V_24X1) = csums__and__averages_2eRavg___24a1(V_24X1) ).
fof('$adef_$_let_18_mkmult_pow_25886_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__25886,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__25886___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.micromega.RingMicromega.eval_op1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_6433_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6433,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6433___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.QArith.QArith_base.Qdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQdiv,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_5425_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__5425,V_24X1),V_24X2),V_24X3) = c_24__prop__5425___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$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.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.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.head_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2ehead,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2ehead___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rbasic_fun.Rmin_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmin,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_43879_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__43879,V_24X1),V_24X2))
<=> c_24__lam__43879___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$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('$adef_Coq.Init.Specif.sumbool_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esumbool__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$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('$adef_Coq.micromega.OrderedRing.SOR_$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('$adef_Coq.micromega.EnvRing.PX_$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('$adef_Coq.Init.Datatypes.sum_$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('$adef_Coq.micromega.EnvRing.PEadd_$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('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_var_var_13_y_24636_24639_24709_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__13__y__24636__24639__24709,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__13__y__24636__24639__24709___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$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.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_$_case_Coq.Init.Datatypes.bool$48852_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2448852,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2448852___24a1(V_24X1) ).
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('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_$_fix_2869_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__2869__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__2869__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.QArith.QArith_base.Qpower_positive_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQpower__positive,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQpower__positive___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41219_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__41219,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__41219___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_var_var_12_x_24648_24651_24714_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__var__var__12__x__24648__24651__24714,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__var__var__12__x__24648__24651__24714___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_let_var_6_p_44000_44002_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__44000__44002,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__44000__44002___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : 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('$adef_$_lam_41235_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__41235,V_24X1),V_24X2),V_24X3) = c_24__lam__41235___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.eval_pol_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_let_6_lmp_32509_$a1',axiom,
! [V_24X1] : happ(c_24__let__6__lmp__32509,V_24X1) = c_24__let__6__lmp__32509___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('$adef_Coq.micromega.RingMicromega.eval_nformula_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
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('$adef_Coq.Reals.Rbasic_fun.Rmax_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRbasic__fun_2eRmax,V_24X1),V_24X2) = cCoq_2eReals_2eRbasic__fun_2eRmax___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.QArith.QArith_base.Qopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQopp,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_34687',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__34687___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__34687___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_46391',axiom,
! [V_24Y] :
( c_24__type__46391___24t(V_24Y)
<=> t(V_24Y,c_24__type__46391) ) ).
fof('$tdef_$_type_24420',axiom,
! [V_24Y] :
( c_24__type__24420___24t(V_24Y)
<=> t(V_24Y,c_24__type__24420) ) ).
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.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19814',axiom,
! [V_24Y] :
( c_24__type__19814___24t(V_24Y)
<=> t(V_24Y,c_24__type__19814) ) ).
fof('$tdef_$_type_44012',axiom,
! [V_24Y] :
( c_24__type__44012___24t(V_24Y)
<=> t(V_24Y,c_24__type__44012) ) ).
fof('$tdef_$_type_24513',axiom,
! [V_24Y] :
( c_24__type__24513___24t(V_24Y)
<=> t(V_24Y,c_24__type__24513) ) ).
fof('$tdef_$_type_42899',axiom,
! [V_24Y] :
( c_24__type__42899___24t(V_24Y)
<=> t(V_24Y,c_24__type__42899) ) ).
fof('$tdef_$_type_4241',axiom,
! [V_24Y] :
( c_24__type__4241___24t(V_24Y)
<=> t(V_24Y,c_24__type__4241) ) ).
fof('$tdef_$_type_20760',axiom,
! [V_24Y] :
( c_24__type__20760___24t(V_24Y)
<=> t(V_24Y,c_24__type__20760) ) ).
fof('$tdef_$_type_47544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__47544___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__47544___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_3559',axiom,
! [V_24Y] :
( c_24__type__3559___24t(V_24Y)
<=> t(V_24Y,c_24__type__3559) ) ).
fof('$tdef_$_type_2490',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2490___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2490___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20819',axiom,
! [V_24Y] :
( c_24__type__20819___24t(V_24Y)
<=> t(V_24Y,c_24__type__20819) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_13056',axiom,
! [V_24Y] :
( c_24__type__13056___24t(V_24Y)
<=> t(V_24Y,c_24__type__13056) ) ).
fof('$tdef_$_type_42245',axiom,
! [V_24Y] :
( c_24__type__42245___24t(V_24Y)
<=> t(V_24Y,c_24__type__42245) ) ).
fof('$tdef_$_type_20684',axiom,
! [V_24Y] :
( c_24__type__20684___24t(V_24Y)
<=> t(V_24Y,c_24__type__20684) ) ).
fof('$tdef_$_type_5437',axiom,
! [V_24Y] :
( c_24__type__5437___24t(V_24Y)
<=> t(V_24Y,c_24__type__5437) ) ).
fof('$tdef_$_type_11014',axiom,
! [V_24Y] :
( c_24__type__11014___24t(V_24Y)
<=> t(V_24Y,c_24__type__11014) ) ).
fof('$tdef_$_type_353',axiom,
! [V_24Y] :
( c_24__type__353___24t(V_24Y)
<=> t(V_24Y,c_24__type__353) ) ).
fof('$tdef_$_type_327',axiom,
! [V_24Y] :
( c_24__type__327___24t(V_24Y)
<=> t(V_24Y,c_24__type__327) ) ).
fof('$tdef_$_type_19',axiom,
! [V_24Y] :
( c_24__type__19___24t(V_24Y)
<=> t(V_24Y,c_24__type__19) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_43864',axiom,
! [V_24Y] :
( c_24__type__43864___24t(V_24Y)
<=> t(V_24Y,c_24__type__43864) ) ).
fof('$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_38931',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__38931___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__38931___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('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33412',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33412___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33412___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_41432',axiom,
! [V_24Y] :
( c_24__type__41432___24t(V_24Y)
<=> t(V_24Y,c_24__type__41432) ) ).
fof('$tdef_$_type_35339',axiom,
! [V_24Y] :
( c_24__type__35339___24t(V_24Y)
<=> t(V_24Y,c_24__type__35339) ) ).
fof('$tdef_$_type_21146',axiom,
! [V_24Y] :
( c_24__type__21146___24t(V_24Y)
<=> t(V_24Y,c_24__type__21146) ) ).
fof('$tdef_Coq.micromega.QMicromega.QWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eQMicromega_2eQWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eQMicromega_2eQWitness) ) ).
fof('$tdef_$_type_26164',axiom,
! [V_24Y] :
( c_24__type__26164___24t(V_24Y)
<=> t(V_24Y,c_24__type__26164) ) ).
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_9076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9076___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35519',axiom,
! [V_24Y] :
( c_24__type__35519___24t(V_24Y)
<=> t(V_24Y,c_24__type__35519) ) ).
fof('$tdef_$_type_3545',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3545___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3545___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29758',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29758___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29758___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28089',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__28089___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__28089___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_33058',axiom,
! [V_24Y] :
( c_24__type__33058___24t(V_24Y)
<=> t(V_24Y,c_24__type__33058) ) ).
fof('$tdef_$_type_1795',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1795___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1795___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34026',axiom,
! [V_24Y] :
( c_24__type__34026___24t(V_24Y)
<=> t(V_24Y,c_24__type__34026) ) ).
fof('$tdef_$_type_43861',axiom,
! [V_24Y] :
( c_24__type__43861___24t(V_24Y)
<=> t(V_24Y,c_24__type__43861) ) ).
fof('$tdef_$_type_40269',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__40269___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__40269___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_4999',axiom,
! [V_24Y] :
( c_24__type__4999___24t(V_24Y)
<=> t(V_24Y,c_24__type__4999) ) ).
fof('$tdef_$_type_2796',axiom,
! [V_24Y] :
( c_24__type__2796___24t(V_24Y)
<=> t(V_24Y,c_24__type__2796) ) ).
fof('$tdef_$_type_13040',axiom,
! [V_24Y] :
( c_24__type__13040___24t(V_24Y)
<=> t(V_24Y,c_24__type__13040) ) ).
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_$_type_6725',axiom,
! [V_24Y] :
( c_24__type__6725___24t(V_24Y)
<=> t(V_24Y,c_24__type__6725) ) ).
fof('$tdef_$_type_5398',axiom,
! [V_24Y] :
( c_24__type__5398___24t(V_24Y)
<=> t(V_24Y,c_24__type__5398) ) ).
fof('$tdef_$_type_20061',axiom,
! [V_24Y] :
( c_24__type__20061___24t(V_24Y)
<=> t(V_24Y,c_24__type__20061) ) ).
fof('$tdef_$_type_28497',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__28497___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__28497___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_7421',axiom,
! [V_24Y] :
( c_24__type__7421___24t(V_24Y)
<=> t(V_24Y,c_24__type__7421) ) ).
fof('$tdef_$_type_50063',axiom,
! [V_24Y] :
( c_24__type__50063___24t(V_24Y)
<=> t(V_24Y,c_24__type__50063) ) ).
fof('$tdef_$_type_35329',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35329___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35329___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25449',axiom,
! [V_24Y] :
( c_24__type__25449___24t(V_24Y)
<=> t(V_24Y,c_24__type__25449) ) ).
fof('$tdef_$_type_47983',axiom,
! [V_24Y] :
( c_24__type__47983___24t(V_24Y)
<=> t(V_24Y,c_24__type__47983) ) ).
fof('$tdef_$_type_9',axiom,
! [V_24Y] :
( c_24__type__9___24t(V_24Y)
<=> t(V_24Y,c_24__type__9) ) ).
fof('$tdef_$_type_28302',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__28302___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__28302___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_8085',axiom,
! [V_24Y] :
( c_24__type__8085___24t(V_24Y)
<=> t(V_24Y,c_24__type__8085) ) ).
fof('$tdef_$_type_27450',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__27450___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__27450___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1983',axiom,
! [V_24Y] :
( c_24__type__1983___24t(V_24Y)
<=> t(V_24Y,c_24__type__1983) ) ).
fof('$tdef_$_type_5368',axiom,
! [V_24Y] :
( c_24__type__5368___24t(V_24Y)
<=> t(V_24Y,c_24__type__5368) ) ).
fof('$tdef_$_type_33863',axiom,
! [V_24Y] :
( c_24__type__33863___24t(V_24Y)
<=> t(V_24Y,c_24__type__33863) ) ).
fof('$tdef_$_type_10894',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10894___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10894___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_$_type_41445',axiom,
! [V_24Y] :
( c_24__type__41445___24t(V_24Y)
<=> t(V_24Y,c_24__type__41445) ) ).
fof('$tdef_$_type_42841',axiom,
! [V_24Y] :
( c_24__type__42841___24t(V_24Y)
<=> t(V_24Y,c_24__type__42841) ) ).
fof('$tdef_$_type_41286',axiom,
! [V_24Y] :
( c_24__type__41286___24t(V_24Y)
<=> t(V_24Y,c_24__type__41286) ) ).
fof('$tdef_$_type_7271',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7271___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7271___24a1(V_24X1)) ) ).
fof('$tdef_$_type_50058',axiom,
! [V_24Y] :
( c_24__type__50058___24t(V_24Y)
<=> t(V_24Y,c_24__type__50058) ) ).
fof('$tdef_$_type_43162',axiom,
! [V_24Y] :
( c_24__type__43162___24t(V_24Y)
<=> t(V_24Y,c_24__type__43162) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_21132',axiom,
! [V_24Y] :
( c_24__type__21132___24t(V_24Y)
<=> t(V_24Y,c_24__type__21132) ) ).
fof('$tdef_$_type_20129',axiom,
! [V_24X1,V_24Y] :
( c_24__type__20129___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__20129___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35522',axiom,
! [V_24Y] :
( c_24__type__35522___24t(V_24Y)
<=> t(V_24Y,c_24__type__35522) ) ).
fof('$tdef_$_type_10906',axiom,
! [V_24Y] :
( c_24__type__10906___24t(V_24Y)
<=> t(V_24Y,c_24__type__10906) ) ).
fof('$tdef_$_type_41522',axiom,
! [V_24Y] :
( c_24__type__41522___24t(V_24Y)
<=> t(V_24Y,c_24__type__41522) ) ).
fof('$tdef_$_type_3363',axiom,
! [V_24Y] :
( c_24__type__3363___24t(V_24Y)
<=> t(V_24Y,c_24__type__3363) ) ).
fof('$tdef_$_type_48728',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__48728___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__48728___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_43883',axiom,
! [V_24Y] :
( c_24__type__43883___24t(V_24Y)
<=> t(V_24Y,c_24__type__43883) ) ).
fof('$tdef_$_type_10845',axiom,
! [V_24Y] :
( c_24__type__10845___24t(V_24Y)
<=> t(V_24Y,c_24__type__10845) ) ).
fof('$tdef_$_type_66702',axiom,
! [V_24Y] :
( c_24__type__66702___24t(V_24Y)
<=> t(V_24Y,c_24__type__66702) ) ).
fof('$tdef_$_type_6412',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6412___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6412___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35617',axiom,
! [V_24Y] :
( c_24__type__35617___24t(V_24Y)
<=> t(V_24Y,c_24__type__35617) ) ).
fof('$tdef_$_type_48285',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__48285___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__48285___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.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_42876',axiom,
! [V_24Y] :
( c_24__type__42876___24t(V_24Y)
<=> t(V_24Y,c_24__type__42876) ) ).
fof('$tdef_$_type_8088',axiom,
! [V_24Y] :
( c_24__type__8088___24t(V_24Y)
<=> t(V_24Y,c_24__type__8088) ) ).
fof('$tdef_$_type_3571',axiom,
! [V_24Y] :
( c_24__type__3571___24t(V_24Y)
<=> t(V_24Y,c_24__type__3571) ) ).
fof('$tdef_$_type_36532',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__36532___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__36532___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_10815',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10815___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10815___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_QuicksortComplexity.nat_below.natBelow',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2enat__below_2enatBelow___24a1(V_24X1)) ) ).
fof('$tdef_$_type_436',axiom,
! [V_24Y] :
( c_24__type__436___24t(V_24Y)
<=> t(V_24Y,c_24__type__436) ) ).
fof('$tdef_$_type_1856',axiom,
! [V_24Y] :
( c_24__type__1856___24t(V_24Y)
<=> t(V_24Y,c_24__type__1856) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_Coq.micromega.Tauto.BFormula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eTauto_2eBFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eBFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4464',axiom,
! [V_24Y] :
( c_24__type__4464___24t(V_24Y)
<=> t(V_24Y,c_24__type__4464) ) ).
fof('$tdef_$_type_43746',axiom,
! [V_24Y] :
( c_24__type__43746___24t(V_24Y)
<=> t(V_24Y,c_24__type__43746) ) ).
fof('$tdef_$_type_20757',axiom,
! [V_24Y] :
( c_24__type__20757___24t(V_24Y)
<=> t(V_24Y,c_24__type__20757) ) ).
fof('$tdef_$_type_2885',axiom,
! [V_24Y] :
( c_24__type__2885___24t(V_24Y)
<=> t(V_24Y,c_24__type__2885) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_9341',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9341___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9341___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39946',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__39946___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__39946___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_37547',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__37547___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__37547___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_20111',axiom,
! [V_24X1,V_24Y] :
( c_24__type__20111___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__20111___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9025',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9025___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9025___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2909',axiom,
! [V_24Y] :
( c_24__type__2909___24t(V_24Y)
<=> t(V_24Y,c_24__type__2909) ) ).
fof('$tdef_$_type_9049',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9049___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9049___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2047',axiom,
! [V_24Y] :
( c_24__type__2047___24t(V_24Y)
<=> t(V_24Y,c_24__type__2047) ) ).
fof('$tdef_$_type_1841',axiom,
! [V_24Y] :
( c_24__type__1841___24t(V_24Y)
<=> t(V_24Y,c_24__type__1841) ) ).
fof('$tdef_$_type_5249',axiom,
! [V_24Y] :
( c_24__type__5249___24t(V_24Y)
<=> t(V_24Y,c_24__type__5249) ) ).
fof('$tdef_$_type_43867',axiom,
! [V_24Y] :
( c_24__type__43867___24t(V_24Y)
<=> t(V_24Y,c_24__type__43867) ) ).
fof('$tdef_$_type_34586',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__34586___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__34586___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_59201',axiom,
! [V_24Y] :
( c_24__type__59201___24t(V_24Y)
<=> t(V_24Y,c_24__type__59201) ) ).
fof('$tdef_$_type_1836',axiom,
! [V_24Y] :
( c_24__type__1836___24t(V_24Y)
<=> t(V_24Y,c_24__type__1836) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_618',axiom,
! [V_24Y] :
( c_24__type__618___24t(V_24Y)
<=> t(V_24Y,c_24__type__618) ) ).
fof('$tdef_$_type_3486',axiom,
! [V_24Y] :
( c_24__type__3486___24t(V_24Y)
<=> t(V_24Y,c_24__type__3486) ) ).
fof('$tdef_$_type_33748',axiom,
! [V_24Y] :
( c_24__type__33748___24t(V_24Y)
<=> t(V_24Y,c_24__type__33748) ) ).
fof('$tdef_$_type_2714',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2714___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2714___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_33055',axiom,
! [V_24Y] :
( c_24__type__33055___24t(V_24Y)
<=> t(V_24Y,c_24__type__33055) ) ).
fof('$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_33',axiom,
! [V_24Y] :
( c_24__type__33___24t(V_24Y)
<=> t(V_24Y,c_24__type__33) ) ).
fof('$tdef_$_type_12191',axiom,
! [V_24Y] :
( c_24__type__12191___24t(V_24Y)
<=> t(V_24Y,c_24__type__12191) ) ).
fof('$tdef_$_type_48192',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__48192___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__48192___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_35181',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35181___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35181___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35080',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35080___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35080___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_34102',axiom,
! [V_24Y] :
( c_24__type__34102___24t(V_24Y)
<=> t(V_24Y,c_24__type__34102) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8456',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8456___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8456___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_48905',axiom,
! [V_24Y] :
( c_24__type__48905___24t(V_24Y)
<=> t(V_24Y,c_24__type__48905) ) ).
fof('$tdef_$_type_43319',axiom,
! [V_24Y] :
( c_24__type__43319___24t(V_24Y)
<=> t(V_24Y,c_24__type__43319) ) ).
fof('$tdef_$_type_32865',axiom,
! [V_24Y] :
( c_24__type__32865___24t(V_24Y)
<=> t(V_24Y,c_24__type__32865) ) ).
fof('$tdef_$_type_313',axiom,
! [V_24Y] :
( c_24__type__313___24t(V_24Y)
<=> t(V_24Y,c_24__type__313) ) ).
fof('$tdef_$_type_8519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8519___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8519___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21065',axiom,
! [V_24Y] :
( c_24__type__21065___24t(V_24Y)
<=> t(V_24Y,c_24__type__21065) ) ).
fof('$tdef_$_type_1788',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1788___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1788___24a2(V_24X1,V_24X2)) ) ).
fof('$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_34878',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__34878___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__34878___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25460',axiom,
! [V_24Y] :
( c_24__type__25460___24t(V_24Y)
<=> t(V_24Y,c_24__type__25460) ) ).
fof('$tdef_$_type_32507',axiom,
! [V_24Y] :
( c_24__type__32507___24t(V_24Y)
<=> t(V_24Y,c_24__type__32507) ) ).
fof('$tdef_$_type_25625',axiom,
! [V_24Y] :
( c_24__type__25625___24t(V_24Y)
<=> t(V_24Y,c_24__type__25625) ) ).
fof('$tdef_$_type_2014',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2014___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2014___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20124',axiom,
! [V_24Y] :
( c_24__type__20124___24t(V_24Y)
<=> t(V_24Y,c_24__type__20124) ) ).
fof('$tdef_$_type_50',axiom,
! [V_24Y] :
( c_24__type__50___24t(V_24Y)
<=> t(V_24Y,c_24__type__50) ) ).
fof('$tdef_$_type_20159',axiom,
! [V_24Y] :
( c_24__type__20159___24t(V_24Y)
<=> t(V_24Y,c_24__type__20159) ) ).
fof('$tdef_$_type_6754',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6754___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6754___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25642',axiom,
! [V_24Y] :
( c_24__type__25642___24t(V_24Y)
<=> t(V_24Y,c_24__type__25642) ) ).
fof('$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('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_44247',axiom,
! [V_24X1,V_24Y] :
( c_24__type__44247___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__44247___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20786',axiom,
! [V_24Y] :
( c_24__type__20786___24t(V_24Y)
<=> t(V_24Y,c_24__type__20786) ) ).
fof('$tdef_$_type_12270',axiom,
! [V_24Y] :
( c_24__type__12270___24t(V_24Y)
<=> t(V_24Y,c_24__type__12270) ) ).
fof('$tdef_$_type_9148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__9148___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__9148___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35320',axiom,
! [V_24Y] :
( c_24__type__35320___24t(V_24Y)
<=> t(V_24Y,c_24__type__35320) ) ).
fof('$tdef_$_type_1057',axiom,
! [V_24Y] :
( c_24__type__1057___24t(V_24Y)
<=> t(V_24Y,c_24__type__1057) ) ).
fof('$tdef_$_type_10850',axiom,
! [V_24Y] :
( c_24__type__10850___24t(V_24Y)
<=> t(V_24Y,c_24__type__10850) ) ).
fof('$tdef_$_type_5572',axiom,
! [V_24Y] :
( c_24__type__5572___24t(V_24Y)
<=> t(V_24Y,c_24__type__5572) ) ).
fof('$tdef_$_type_1071',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1071___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1071___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2659',axiom,
! [V_24Y] :
( c_24__type__2659___24t(V_24Y)
<=> t(V_24Y,c_24__type__2659) ) ).
fof('$tdef_$_type_1738',axiom,
! [V_24Y] :
( c_24__type__1738___24t(V_24Y)
<=> t(V_24Y,c_24__type__1738) ) ).
fof('$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_8908',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8908___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8908___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_607',axiom,
! [V_24X1,V_24Y] :
( c_24__type__607___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__607___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6484',axiom,
! [V_24Y] :
( c_24__type__6484___24t(V_24Y)
<=> t(V_24Y,c_24__type__6484) ) ).
fof('$tdef_$_type_41451',axiom,
! [V_24Y] :
( c_24__type__41451___24t(V_24Y)
<=> t(V_24Y,c_24__type__41451) ) ).
fof('$tdef_$_type_41412',axiom,
! [V_24Y] :
( c_24__type__41412___24t(V_24Y)
<=> t(V_24Y,c_24__type__41412) ) ).
fof('$tdef_$_type_2552',axiom,
! [V_24Y] :
( c_24__type__2552___24t(V_24Y)
<=> t(V_24Y,c_24__type__2552) ) ).
fof('$tdef_$_type_2547',axiom,
! [V_24Y] :
( c_24__type__2547___24t(V_24Y)
<=> t(V_24Y,c_24__type__2547) ) ).
fof('$tdef_$_type_6419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6419___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6419___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25619',axiom,
! [V_24Y] :
( c_24__type__25619___24t(V_24Y)
<=> t(V_24Y,c_24__type__25619) ) ).
fof('$tdef_$_type_2718',axiom,
! [V_24Y] :
( c_24__type__2718___24t(V_24Y)
<=> t(V_24Y,c_24__type__2718) ) ).
fof('$tdef_$_type_19679',axiom,
! [V_24Y] :
( c_24__type__19679___24t(V_24Y)
<=> t(V_24Y,c_24__type__19679) ) ).
fof('$tdef_$_type_34009',axiom,
! [V_24Y] :
( c_24__type__34009___24t(V_24Y)
<=> t(V_24Y,c_24__type__34009) ) ).
fof('$tdef_$_type_39600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39600___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_8093',axiom,
! [V_24Y] :
( c_24__type__8093___24t(V_24Y)
<=> t(V_24Y,c_24__type__8093) ) ).
fof('$tdef_$_type_43170',axiom,
! [V_24Y] :
( c_24__type__43170___24t(V_24Y)
<=> t(V_24Y,c_24__type__43170) ) ).
fof('$tdef_$_type_38585',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__38585___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__38585___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_19777',axiom,
! [V_24Y] :
( c_24__type__19777___24t(V_24Y)
<=> t(V_24Y,c_24__type__19777) ) ).
fof('$tdef_$_type_29666',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29666___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29666___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_3541',axiom,
! [V_24Y] :
( c_24__type__3541___24t(V_24Y)
<=> t(V_24Y,c_24__type__3541) ) ).
fof('$tdef_$_type_28710',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__28710___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__28710___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_8884',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8884___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8884___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2876',axiom,
! [V_24Y] :
( c_24__type__2876___24t(V_24Y)
<=> t(V_24Y,c_24__type__2876) ) ).
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_$_type_34979',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__34979___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__34979___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_83',axiom,
! [V_24Y] :
( c_24__type__83___24t(V_24Y)
<=> t(V_24Y,c_24__type__83) ) ).
fof('$tdef_$_type_3503',axiom,
! [V_24Y] :
( c_24__type__3503___24t(V_24Y)
<=> t(V_24Y,c_24__type__3503) ) ).
fof('$tdef_$_type_2038',axiom,
! [V_24Y] :
( c_24__type__2038___24t(V_24Y)
<=> t(V_24Y,c_24__type__2038) ) ).
fof('$tdef_$_type_43726',axiom,
! [V_24Y] :
( c_24__type__43726___24t(V_24Y)
<=> t(V_24Y,c_24__type__43726) ) ).
fof('$tdef_$_type_41440',axiom,
! [V_24Y] :
( c_24__type__41440___24t(V_24Y)
<=> t(V_24Y,c_24__type__41440) ) ).
fof('$tdef_$_type_43876',axiom,
! [V_24Y] :
( c_24__type__43876___24t(V_24Y)
<=> t(V_24Y,c_24__type__43876) ) ).
fof('$tdef_$_type_43481',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__43481___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__43481___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_25631',axiom,
! [V_24Y] :
( c_24__type__25631___24t(V_24Y)
<=> t(V_24Y,c_24__type__25631) ) ).
fof('$tdef_$_type_48460',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__48460___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__48460___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_337',axiom,
! [V_24Y] :
( c_24__type__337___24t(V_24Y)
<=> t(V_24Y,c_24__type__337) ) ).
fof('$tdef_$_type_21062',axiom,
! [V_24Y] :
( c_24__type__21062___24t(V_24Y)
<=> t(V_24Y,c_24__type__21062) ) ).
fof('$tdef_$_type_43874',axiom,
! [V_24Y] :
( c_24__type__43874___24t(V_24Y)
<=> t(V_24Y,c_24__type__43874) ) ).
fof('$tdef_$_type_1958',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1958___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1958___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8938',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8938___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8938___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_49743',axiom,
! [V_24Y] :
( c_24__type__49743___24t(V_24Y)
<=> t(V_24Y,c_24__type__49743) ) ).
fof('$tdef_$_type_2565',axiom,
! [V_24Y] :
( c_24__type__2565___24t(V_24Y)
<=> t(V_24Y,c_24__type__2565) ) ).
fof('$tdef_$_type_2062',axiom,
! [V_24Y] :
( c_24__type__2062___24t(V_24Y)
<=> t(V_24Y,c_24__type__2062) ) ).
fof('$tdef_$_type_43856',axiom,
! [V_24Y] :
( c_24__type__43856___24t(V_24Y)
<=> t(V_24Y,c_24__type__43856) ) ).
fof('$tdef_$_type_47364',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__47364___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__47364___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_8854',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8854___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8854___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_403',axiom,
! [V_24Y] :
( c_24__type__403___24t(V_24Y)
<=> t(V_24Y,c_24__type__403) ) ).
fof('$tdef_$_type_20704',axiom,
! [V_24Y] :
( c_24__type__20704___24t(V_24Y)
<=> t(V_24Y,c_24__type__20704) ) ).
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_$_type_59204',axiom,
! [V_24Y] :
( c_24__type__59204___24t(V_24Y)
<=> t(V_24Y,c_24__type__59204) ) ).
fof('$tdef_$_type_2368',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2368___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2368___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8968',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8968___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8968___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2773',axiom,
! [V_24Y] :
( c_24__type__2773___24t(V_24Y)
<=> t(V_24Y,c_24__type__2773) ) ).
fof('$tdef_$_type_408',axiom,
! [V_24X1,V_24Y] :
( c_24__type__408___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__408___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6478',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6478___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6478___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1062',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1062___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1062___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6592',axiom,
! [V_24Y] :
( c_24__type__6592___24t(V_24Y)
<=> t(V_24Y,c_24__type__6592) ) ).
fof('$tdef_$_type_47481',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__47481___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__47481___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_50061',axiom,
! [V_24Y] :
( c_24__type__50061___24t(V_24Y)
<=> t(V_24Y,c_24__type__50061) ) ).
fof('$tdef_$_type_25501',axiom,
! [V_24Y] :
( c_24__type__25501___24t(V_24Y)
<=> t(V_24Y,c_24__type__25501) ) ).
fof('$tdef_$_type_50081',axiom,
! [V_24Y] :
( c_24__type__50081___24t(V_24Y)
<=> t(V_24Y,c_24__type__50081) ) ).
fof('$tdef_$_type_48635',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__48635___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__48635___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3623',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3623___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3623___24a2(V_24X1,V_24X2)) ) ).
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_$_type_67',axiom,
! [V_24Y] :
( c_24__type__67___24t(V_24Y)
<=> t(V_24Y,c_24__type__67) ) ).
fof('$tdef_$_type_2330',axiom,
! [V_24Y] :
( c_24__type__2330___24t(V_24Y)
<=> t(V_24Y,c_24__type__2330) ) ).
fof('$tdef_$_type_25622',axiom,
! [V_24Y] :
( c_24__type__25622___24t(V_24Y)
<=> t(V_24Y,c_24__type__25622) ) ).
fof('$tdef_$_type_40938',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__40938___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__40938___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_29746',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29746___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29746___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_33007',axiom,
! [V_24Y] :
( c_24__type__33007___24t(V_24Y)
<=> t(V_24Y,c_24__type__33007) ) ).
fof('$tdef_$_type_3367',axiom,
! [V_24Y] :
( c_24__type__3367___24t(V_24Y)
<=> t(V_24Y,c_24__type__3367) ) ).
fof('$tdef_$_type_8992',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8992___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8992___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_50572',axiom,
! [V_24Y] :
( c_24__type__50572___24t(V_24Y)
<=> t(V_24Y,c_24__type__50572) ) ).
fof('$tdef_$_type_59196',axiom,
! [V_24Y] :
( c_24__type__59196___24t(V_24Y)
<=> t(V_24Y,c_24__type__59196) ) ).
fof('$tdef_$_type_41488',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__41488___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__41488___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2537',axiom,
! [V_24Y] :
( c_24__type__2537___24t(V_24Y)
<=> t(V_24Y,c_24__type__2537) ) ).
fof('$tdef_$_type_13087',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13087___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13087___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39254',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__39254___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__39254___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1315',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1315___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1315___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1971',axiom,
! [V_24Y] :
( c_24__type__1971___24t(V_24Y)
<=> t(V_24Y,c_24__type__1971) ) ).
fof('$tdef_$_type_1297',axiom,
! [V_24Y] :
( c_24__type__1297___24t(V_24Y)
<=> t(V_24Y,c_24__type__1297) ) ).
fof('$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_41453',axiom,
! [V_24Y] :
( c_24__type__41453___24t(V_24Y)
<=> t(V_24Y,c_24__type__41453) ) ).
fof('$tdef_$_type_35533',axiom,
! [V_24Y] :
( c_24__type__35533___24t(V_24Y)
<=> t(V_24Y,c_24__type__35533) ) ).
fof('$tdef_$_type_3401',axiom,
! [V_24Y] :
( c_24__type__3401___24t(V_24Y)
<=> t(V_24Y,c_24__type__3401) ) ).
fof('$tdef_$_type_27255',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__27255___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__27255___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_3348',axiom,
! [V_24Y] :
( c_24__type__3348___24t(V_24Y)
<=> t(V_24Y,c_24__type__3348) ) ).
fof('$tdef_$_type_27042',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__27042___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__27042___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_37893',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__37893___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__37893___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_2523',axiom,
! [V_24Y] :
( c_24__type__2523___24t(V_24Y)
<=> t(V_24Y,c_24__type__2523) ) ).
fof('$tdef_$_type_43461',axiom,
! [V_24Y] :
( c_24__type__43461___24t(V_24Y)
<=> t(V_24Y,c_24__type__43461) ) ).
fof('$tdef_$_type_50086',axiom,
! [V_24Y] :
( c_24__type__50086___24t(V_24Y)
<=> t(V_24Y,c_24__type__50086) ) ).
fof('$tdef_$_type_27876',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__27876___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__27876___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_27663',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__27663___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__27663___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_61407',axiom,
! [V_24Y] :
( c_24__type__61407___24t(V_24Y)
<=> t(V_24Y,c_24__type__61407) ) ).
fof('$tdef_$_type_48553',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__48553___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__48553___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33063',axiom,
! [V_24Y] :
( c_24__type__33063___24t(V_24Y)
<=> t(V_24Y,c_24__type__33063) ) ).
fof('$tdef_$_type_10822',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10822___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10822___24a1(V_24X1)) ) ).
fof('$tdef_$_type_36186',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__36186___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__36186___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_41531',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__41531___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__41531___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1926',axiom,
! [V_24Y] :
( c_24__type__1926___24t(V_24Y)
<=> t(V_24Y,c_24__type__1926) ) ).
fof('$tdef_$_type_3398',axiom,
! [V_24Y] :
( c_24__type__3398___24t(V_24Y)
<=> t(V_24Y,c_24__type__3398) ) ).
fof('$tdef_$_type_2327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2327___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2327___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_71',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__71___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__71___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38',axiom,
! [V_24Y] :
( c_24__type__38___24t(V_24Y)
<=> t(V_24Y,c_24__type__38) ) ).
fof('$tdef_$_type_32537',axiom,
! [V_24Y] :
( c_24__type__32537___24t(V_24Y)
<=> t(V_24Y,c_24__type__32537) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_3611',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3611___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3611___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35554',axiom,
! [V_24Y] :
( c_24__type__35554___24t(V_24Y)
<=> t(V_24Y,c_24__type__35554) ) ).
fof('$tdef_$_type_20840',axiom,
! [V_24X1,V_24Y] :
( c_24__type__20840___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__20840___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10880',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10880___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10880___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_41435',axiom,
! [V_24Y] :
( c_24__type__41435___24t(V_24Y)
<=> t(V_24Y,c_24__type__41435) ) ).
fof('$tdef_$_type_5373',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5373___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5373___24a1(V_24X1)) ) ).
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_$_type_2544',axiom,
! [V_24Y] :
( c_24__type__2544___24t(V_24Y)
<=> t(V_24Y,c_24__type__2544) ) ).
fof('$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_25628',axiom,
! [V_24Y] :
( c_24__type__25628___24t(V_24Y)
<=> t(V_24Y,c_24__type__25628) ) ).
fof('$tdef_$_type_29702',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29702___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29702___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_1080',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1080___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1080___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31016',axiom,
! [V_24Y] :
( c_24__type__31016___24t(V_24Y)
<=> t(V_24Y,c_24__type__31016) ) ).
fof('$tdef_$_type_19816',axiom,
! [V_24Y] :
( c_24__type__19816___24t(V_24Y)
<=> t(V_24Y,c_24__type__19816) ) ).
fof('$tdef_$_type_10819',axiom,
! [V_24Y] :
( c_24__type__10819___24t(V_24Y)
<=> t(V_24Y,c_24__type__10819) ) ).
fof('$tdef_$_type_2045',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2045___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2045___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10431',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__10431___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__10431___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_35325',axiom,
! [V_24Y] :
( c_24__type__35325___24t(V_24Y)
<=> t(V_24Y,c_24__type__35325) ) ).
fof('$tdef_$_type_33868',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33868___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33868___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30853',axiom,
! [V_24Y] :
( c_24__type__30853___24t(V_24Y)
<=> t(V_24Y,c_24__type__30853) ) ).
fof('$tdef_$_type_24456',axiom,
! [V_24Y] :
( c_24__type__24456___24t(V_24Y)
<=> t(V_24Y,c_24__type__24456) ) ).
fof('$tdef_$_type_29622',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__29622___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__29622___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_3536',axiom,
! [V_24Y] :
( c_24__type__3536___24t(V_24Y)
<=> t(V_24Y,c_24__type__3536) ) ).
fof('$tdef_$_type_3608',axiom,
! [V_24Y] :
( c_24__type__3608___24t(V_24Y)
<=> t(V_24Y,c_24__type__3608) ) ).
fof('$tdef_$_type_3329',axiom,
! [V_24Y] :
( c_24__type__3329___24t(V_24Y)
<=> t(V_24Y,c_24__type__3329) ) ).
fof('$tdef_$_type_10887',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__10887___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__10887___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6408',axiom,
! [V_24Y] :
( c_24__type__6408___24t(V_24Y)
<=> t(V_24Y,c_24__type__6408) ) ).
fof('$tdef_$_type_47301',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__47301___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__47301___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_3583',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3583___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3583___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20055',axiom,
! [V_24Y] :
( c_24__type__20055___24t(V_24Y)
<=> t(V_24Y,c_24__type__20055) ) ).
fof('$tdef_$_type_1553',axiom,
! [V_24Y] :
( c_24__type__1553___24t(V_24Y)
<=> t(V_24Y,c_24__type__1553) ) ).
fof('$tdef_$_type_2550',axiom,
! [V_24Y] :
( c_24__type__2550___24t(V_24Y)
<=> t(V_24Y,c_24__type__2550) ) ).
fof('$tdef_$_type_1089',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1089___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1089___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1816',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__1816___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__1816___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12427',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12427___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12427___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37201',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__37201___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__37201___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30979',axiom,
! [V_24Y] :
( c_24__type__30979___24t(V_24Y)
<=> t(V_24Y,c_24__type__30979) ) ).
fof('$tdef_$_type_20895',axiom,
! [V_24Y] :
( c_24__type__20895___24t(V_24Y)
<=> t(V_24Y,c_24__type__20895) ) ).
fof('$tdef_$_type_35651',axiom,
! [V_24Y] :
( c_24__type__35651___24t(V_24Y)
<=> t(V_24Y,c_24__type__35651) ) ).
fof('$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_1075',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1075___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1075___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_40592',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__40592___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__40592___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_2483',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__2483___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__2483___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_61410',axiom,
! [V_24Y] :
( c_24__type__61410___24t(V_24Y)
<=> t(V_24Y,c_24__type__61410) ) ).
fof('$tdef_$_type_30900',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30900___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30900___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_41484',axiom,
! [V_24Y] :
( c_24__type__41484___24t(V_24Y)
<=> t(V_24Y,c_24__type__41484) ) ).
fof('$tdef_$_type_45360',axiom,
! [V_24Y] :
( c_24__type__45360___24t(V_24Y)
<=> t(V_24Y,c_24__type__45360) ) ).
fof('$tdef_$_type_43748',axiom,
! [V_24Y] :
( c_24__type__43748___24t(V_24Y)
<=> t(V_24Y,c_24__type__43748) ) ).
fof('$tdef_$_type_20874',axiom,
! [V_24Y] :
( c_24__type__20874___24t(V_24Y)
<=> t(V_24Y,c_24__type__20874) ) ).
fof('$tdef_$_type_48378',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__48378___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__48378___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_2738',axiom,
! [V_24Y] :
( c_24__type__2738___24t(V_24Y)
<=> t(V_24Y,c_24__type__2738) ) ).
fof('$tdef_$_type_7',axiom,
! [V_24Y] :
( c_24__type__7___24t(V_24Y)
<=> t(V_24Y,c_24__type__7) ) ).
fof('$tdef_$_type_2346',axiom,
! [V_24Y] :
( c_24__type__2346___24t(V_24Y)
<=> t(V_24Y,c_24__type__2346) ) ).
fof('$tdef_$_type_36878',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__36878___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__36878___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.NFormula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19289',axiom,
! [V_24Y] :
( c_24__type__19289___24t(V_24Y)
<=> t(V_24Y,c_24__type__19289) ) ).
fof('$tdef_$_type_41202',axiom,
! [V_24Y] :
( c_24__type__41202___24t(V_24Y)
<=> t(V_24Y,c_24__type__41202) ) ).
fof('$tdef_$_type_34788',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__34788___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__34788___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32529',axiom,
! [V_24Y] :
( c_24__type__32529___24t(V_24Y)
<=> t(V_24Y,c_24__type__32529) ) ).
fof('$tdef_$_type_78',axiom,
! [V_24Y] :
( c_24__type__78___24t(V_24Y)
<=> t(V_24Y,c_24__type__78) ) ).
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_$_type_2721',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2721___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2721___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13392',axiom,
! [V_24Y] :
( c_24__type__13392___24t(V_24Y)
<=> t(V_24Y,c_24__type__13392) ) ).
fof('$tdef_$_type_33066',axiom,
! [V_24Y] :
( c_24__type__33066___24t(V_24Y)
<=> t(V_24Y,c_24__type__33066) ) ).
fof('$tdef_$_type_43766',axiom,
! [V_24Y] :
( c_24__type__43766___24t(V_24Y)
<=> t(V_24Y,c_24__type__43766) ) ).
fof('$tdef_$_type_3482',axiom,
! [V_24Y] :
( c_24__type__3482___24t(V_24Y)
<=> t(V_24Y,c_24__type__3482) ) ).
fof('$tdef_$_type_25547',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25547___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25547___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2052',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2052___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2052___24a1(V_24X1)) ) ).
fof('$tdef_$_type_47427',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__47427___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__47427___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_26829',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__26829___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__26829___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_43201',axiom,
! [V_24Y] :
( c_24__type__43201___24t(V_24Y)
<=> t(V_24Y,c_24__type__43201) ) ).
fof('$tdef_$_type_20754',axiom,
! [V_24Y] :
( c_24__type__20754___24t(V_24Y)
<=> t(V_24Y,c_24__type__20754) ) ).
fof('$tdef_$_type_8699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8699___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8699___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38239',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__38239___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__38239___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_20765',axiom,
! [V_24Y] :
( c_24__type__20765___24t(V_24Y)
<=> t(V_24Y,c_24__type__20765) ) ).
fof('$tdef_$_type_24824',axiom,
! [V_24Y] :
( c_24__type__24824___24t(V_24Y)
<=> t(V_24Y,c_24__type__24824) ) ).
fof('$tdef_$_type_28905',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__28905___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__28905___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_64199',axiom,
! [V_24Y] :
( c_24__type__64199___24t(V_24Y)
<=> t(V_24Y,c_24__type__64199) ) ).
fof('$tdef_$_type_1774',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1774___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1774___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8636',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8636___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__8636___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6910___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6910___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_19854',axiom,
! [V_24Y] :
( c_24__type__19854___24t(V_24Y)
<=> t(V_24Y,c_24__type__19854) ) ).
fof('$tdef_$_type_10876',axiom,
! [V_24Y] :
( c_24__type__10876___24t(V_24Y)
<=> t(V_24Y,c_24__type__10876) ) ).
fof('$tdef_$_type_6644',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6644___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6644___24a1(V_24X1)) ) ).
fof('$tdef_$_type_44242',axiom,
! [V_24Y] :
( c_24__type__44242___24t(V_24Y)
<=> t(V_24Y,c_24__type__44242) ) ).
fof('$tdef_$_type_24386',axiom,
! [V_24Y] :
( c_24__type__24386___24t(V_24Y)
<=> t(V_24Y,c_24__type__24386) ) ).
fof('$tdef_$_type_8582',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8582___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__8582___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_12264',axiom,
! [V_24Y] :
( c_24__type__12264___24t(V_24Y)
<=> t(V_24Y,c_24__type__12264) ) ).
fof('$tdef_$_type_47988',axiom,
! [V_24Y] :
( c_24__type__47988___24t(V_24Y)
<=> t(V_24Y,c_24__type__47988) ) ).
fof('_HAMMER_GOAL',conjecture,
( ! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eReals_2eRdefinitions_2eR,V0__x,cl))
=> V0__x = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) )
=> csums__and__averages_2eRavg___24a1(cl) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
%------------------------------------------------------------------------------