TPTP Problem File: SEV609+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV609+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Cube.prism2
% 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 : Cube.prism2_p [Kal26]
% Status : Theorem
% Rating : 0.74 v9.3.0
% Syntax : Number of formulae : 2901 (1208 unt; 0 def)
% Number of atoms : 10111 (2711 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7297 ( 87 ~; 777 |;1929 &)
% (1075 <=>;3429 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 587 ( 586 usr; 0 prp; 1-23 aty)
% Number of functors : 1677 (1677 usr;1106 con; 0-22 aty)
% Number of variables : 9675 (8859 !; 816 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$119',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24119___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_24119___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$25282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2425282___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__25286] :
( t(Vvar__1___24Anonymous__25286,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__25287] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__25287)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25286,Vvar__2___24Anonymous__25287)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2425282___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25286,c_24__fix__25414__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__25287,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$25369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__25373] :
( t(Vvar__1___24Anonymous__25373,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__25374] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__25374)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25373,Vvar__2___24Anonymous__25374)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25373,c_24__fix__25414__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__25374,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$19960',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419960___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19961] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19961)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19961)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419960___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__19961)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$19982',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19983] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19983)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19983)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__19983)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$16346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__16359___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__16351] :
( t(Vvar__2___24Anonymous__16351,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__16352] :
( t(Vvar__3___24Anonymous__16352,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__16351,Vvar__3___24Anonymous__16352)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416346___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__16351)),Vvar__3___24Anonymous__16352)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$19977',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__19978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19978)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19978)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19978) )
| ? [Vvar__0___24Anonymous__19979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19979)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__19979)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__19979) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$22905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__22906] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22906)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22906)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__22921__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__22906)) )
| ? [Vvar__0___24Anonymous__22913] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22913)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22913)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22913) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_case_Lambda.Redexes.redexes$766',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__3)
=> ( ? [Vvar__0___24Anonymous__767] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__767)
& Vv__CANONICAL__3 = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__767)
& c_24__case__Lambda_2eRedexes_2eredexes_24766___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cLambda_2eSubstitution_2einsert__Var___24a3(Vv__CANONICAL__4,Vvar__0___24Anonymous__767,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__768] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__768)
& Vv__CANONICAL__3 = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__768)
& c_24__case__Lambda_2eRedexes_2eredexes_24766___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cLambda_2eRedexes_2eFun___24a1(c_24__fix__902__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__768,Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__782] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__782)
& ? [Vvar__1___24Anonymous__783] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__783)
& ? [Vvar__2___24Anonymous__784] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__784)
& Vv__CANONICAL__3 = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__782,Vvar__1___24Anonymous__783,Vvar__2___24Anonymous__784)
& c_24__case__Lambda_2eRedexes_2eredexes_24766___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__782,c_24__fix__902__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__783,Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eO),c_24__fix__902__v__CANONICAL__0___24a3(Vvar__2___24Anonymous__784,Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eO)) ) ) ) ) ) ).
fof('$_case_Lambda.Terms.lambda$9752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__2)
=> ( ? [Vvar__0___24Anonymous__9753] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9753)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__9753)
& c_24__case__Lambda_2eTerms_2elambda_249752___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2einsert__Ref___24a3(Vv__CANONICAL__3,Vvar__0___24Anonymous__9753,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__9754] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__9754)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__9754)
& c_24__case__Lambda_2eTerms_2elambda_249752___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eAbs___24a1(c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__9754,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__9767] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__9767)
& ? [Vvar__1___24Anonymous__9768] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__9768)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__9767,Vvar__1___24Anonymous__9768)
& c_24__case__Lambda_2eTerms_2elambda_249752___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eApp___24a2(c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__9767,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eO),c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__9768,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eO)) ) ) ) ) ).
fof('$_def_$_let_var_6_p_20171_20174',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20170] : c_24__let__var__6__p__20171__20174___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20170) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20170) ).
fof('$_def_$_let_var_6_p_20173_20175',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20172] : c_24__let__var__6__p__20173__20175___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20172) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20172) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r))
& p(cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q)) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23224] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23224)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23224)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23225] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23225)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23225)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23228] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23228)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23228)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__23225,Vvar__0___24Anonymous__23228) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.le',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).
fof('$_def_Coq.Arith.PeanoNat.Nat.lt',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__31845___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__24153] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24153)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24153)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__24153,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b))) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.ifb',axiom,
! [V0__b1,V1__b2,V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).
fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31768)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31768)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__3881] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__3881)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3881) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__3902] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__3902)
& ? [Vvar__1___24Anonymous__3903] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__3903)
& ? [Vvar__2___24Anonymous__3904] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__3904)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__3902,Vvar__1___24Anonymous__3903,Vvar__2___24Anonymous__3904)
& ( ? [Vvar__0___24Anonymous__3917] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3917)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3917)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__3917,Vvar__2___24Anonymous__3904) )
| ? [Vvar__0___24Anonymous__3918] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3918)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3918)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__3918,Vvar__0___24Anonymous__3902) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__3903 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__3900] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__3900)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__3900) ) ).
fof('$_def_Coq.Init.Byte.byte_of_byte',axiom,
! [V0__b] : cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V0__b) = V0__b ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__23184] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__23184)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__23184,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__4874] :
( t(Vvar__1___24Anonymous__4874,V0__A)
& ? [Vvar__2___24Anonymous__4875] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4875)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4874,Vvar__2___24Anonymous__4875)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4874,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__4875,V3__m)) ) ) ) ) ) ).
fof('$_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__4769] :
( t(Vvar__2___24Anonymous__4769,V0__A)
& ? [Vvar__3___24Anonymous__4770] :
( t(Vvar__3___24Anonymous__4770,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__4769,Vvar__3___24Anonymous__4770)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__4769 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.id',axiom,
! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).
fof('$_def_Coq.Init.Datatypes.implb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__4864] :
( t(Vvar__1___24Anonymous__4864,V0__A)
& ? [Vvar__2___24Anonymous__4865] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4865)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4864,Vvar__2___24Anonymous__4865)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__4865)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__23065___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__23063] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23063)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23063)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__23063),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__23063)) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__23103] :
( t(Vvar__2___24Anonymous__23103,V0__A)
& ? [Vvar__3___24Anonymous__23104] :
( t(Vvar__3___24Anonymous__23104,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__23103,Vvar__3___24Anonymous__23104)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__23104 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Decimal.int_of_int',axiom,
! [V0__i] : cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V0__i) = V0__i ).
fof('$_def_Coq.Init.Decimal.nzhead',axiom,
! [V1__d] :
( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
=> ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23188] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23188)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__23188)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__23188) )
| ? [Vvar__0___24Anonymous__23189] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23189)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__23189)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23190] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23190)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__23190)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23191] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23191)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__23191)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23192] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23192)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__23192)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23193] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23193)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__23193)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23194] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23194)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__23194)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23195] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23195)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__23195)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23196] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23196)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__23196)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23197] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23197)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__23197)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).
fof('$_def_Coq.Init.Decimal.uint_of_uint',axiom,
! [V0__i] : cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V0__i) = V0__i ).
fof('$_def_Coq.Init.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__1145] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1145)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1145)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__1145,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__23522] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23522)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23522)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__23523] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23523)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23523)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__23526] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23526)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23526)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__23523,Vvar__0___24Anonymous__23526) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__23563] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23563)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23563)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23563)
& ( ( Vvar__0___24Anonymous__23563 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__23566] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23566)
& Vvar__0___24Anonymous__23563 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23566)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__23566)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.double',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23515] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23515)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23515)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__23516] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23516)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23516)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23519] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23519)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23519)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__23516,Vvar__0___24Anonymous__23519) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23537] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23537)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23537)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23537)
& ( ( Vvar__0___24Anonymous__23537 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23540] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23540)
& Vvar__0___24Anonymous__23537 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23540)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__23540) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__8863] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8863)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8863)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8866] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8866)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8866)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__8863,Vvar__0___24Anonymous__8866) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__23550] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23550)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23550)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__23550,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__23553] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23553)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23553)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__23550,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__23553) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__8871] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8871)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8871)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8874] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8874)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8874)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__8871,Vvar__0___24Anonymous__8874)) ) ) ) ) ) ) ) ).
fof('$_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__23531] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23531)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23531)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__23534] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23534)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23534)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__23531,Vvar__0___24Anonymous__23534)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8860] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8860)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8860)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__8860,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.one',axiom,
cCoq_2eInit_2eNat_2eone = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__23544] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23544)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23544)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__23544)) ) ) ) ).
fof('$_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__1143] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1143)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1143)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__1143 ) ) ) ).
fof('$_def_Coq.Init.Nat.square',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esquare___24a1(V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__19907] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19907)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19907)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__19910] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19910)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19910)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__19907,Vvar__0___24Anonymous__19910) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__19905] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__19905)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__19905) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__23547] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23547)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23547)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__23547,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__23568] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23568)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23568)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__23568) ) ) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__24144] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24144)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24144)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(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.Exc',axiom,
! [V0__A] : cCoq_2eInit_2eSpecif_2eExc___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A) ).
fof('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__31357___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__31351] :
( t(Vvar__2__x__31351,V0__A)
& p(happ(V1__P,Vvar__2__x__31351))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__31351)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__31351 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__31380___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__31374] :
( t(Vvar__2__x__31374,V0__A)
& ? [Vvar__3___24Anonymous__31375] :
( t(Vvar__3___24Anonymous__31375,happ(V1__P,Vvar__2__x__31374))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__31374,Vvar__3___24Anonymous__31375)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__31374 ) ) ) ) ) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__8667] :
( t(Vvar__1___24Anonymous__8667,V0__A)
& ? [Vvar__2___24Anonymous__8668] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8668)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8667,Vvar__2___24Anonymous__8668)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__8667 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__8668) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__8759] :
( t(Vvar__1___24Anonymous__8759,V1__B)
& ? [Vvar__2___24Anonymous__8760] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8760)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8759,Vvar__2___24Anonymous__8760)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__8760,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__8759)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__8790] :
( t(Vvar__1___24Anonymous__8790,V1__B)
& ? [Vvar__2___24Anonymous__8791] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8791)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8790,Vvar__2___24Anonymous__8791)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__8790),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__8791)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__23318] :
( t(Vvar__1___24Anonymous__23318,V0__A)
& ? [Vvar__2___24Anonymous__23319] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23319)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__23318,Vvar__2___24Anonymous__23319)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__23318 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__23337] :
( t(Vvar__1___24Anonymous__23337,V0__A)
& ? [Vvar__2___24Anonymous__23338] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23338)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23338)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__23337,Vvar__2___24Anonymous__23338)
& ( ( Vvar__2___24Anonymous__23338 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__23337 )
| ? [Vvar__1___24Anonymous__23349] :
( t(Vvar__1___24Anonymous__23349,V0__A)
& ? [Vvar__2___24Anonymous__23350] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23350)
& Vvar__2___24Anonymous__23338 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__23349,Vvar__2___24Anonymous__23350)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__23338,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__8679] :
( t(Vvar__1___24Anonymous__8679,V0__A)
& ? [Vvar__2___24Anonymous__8680] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8680)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8679,Vvar__2___24Anonymous__8680)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__8679 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__8682] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8682)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8682)
& ( ( 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__8689] :
( t(Vvar__1___24Anonymous__8689,V0__A)
& ? [Vvar__2___24Anonymous__8690] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8690)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8689,Vvar__2___24Anonymous__8690)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__8682,Vvar__2___24Anonymous__8690,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__23329] :
( t(Vvar__1___24Anonymous__23329,V0__A)
& ? [Vvar__2___24Anonymous__23330] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23330)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__23329,Vvar__2___24Anonymous__23330)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__23330 ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__31823___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__17330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17330)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17330)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__17333] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17333)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17333)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__17330,Vvar__0___24Anonymous__17333)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__17365] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17365)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17365)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17365)
& ( ? [Vvar__0___24Anonymous__17369] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17369)
& Vvar__0___24Anonymous__17365 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17369)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17369) )
| ? [Vvar__0___24Anonymous__17370] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17370)
& Vvar__0___24Anonymous__17365 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17370)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17370) )
| ( Vvar__0___24Anonymous__17365 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__17327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17327)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17327)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17327)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__17371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17371)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17371)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17371)
& ( ? [Vvar__0___24Anonymous__17375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17375)
& Vvar__0___24Anonymous__17371 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17375)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17376] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17376)
& Vvar__0___24Anonymous__17371 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17376)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__17371 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__17422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17422)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17422)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__17425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17425)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17425)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__17422,Vvar__0___24Anonymous__17425) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3858)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3858)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3861] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3861)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3861)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3858,Vvar__0___24Anonymous__3861)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__17329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17329)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17329)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__17329) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__17328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17328)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17328)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__17328)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__31820] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__31820)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__31820) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17429)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17429)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__17429,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__17431] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17431)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17431)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__17431) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.eq',axiom,
cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__31879] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31879)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31879)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__31879 )
| ? [Vvar__0___24Anonymous__31880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31880)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31880)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__31880 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31895] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31895)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31895)
& ( ? [Vvar__0___24Anonymous__31899] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31899)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31899)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31895,Vvar__0___24Anonymous__31899) )
| ? [Vvar__0___24Anonymous__31900] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31900)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31900)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__31901] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31901)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31901)
& ( ? [Vvar__0___24Anonymous__31905] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31905)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31905)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31906] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31906)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31906)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31901,Vvar__0___24Anonymous__31906) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__31907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31907)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31907)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31908] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31908)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31908)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__22855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22855)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22855)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__22855),Vvar__0___24Anonymous__22855)) )
| ? [Vvar__0___24Anonymous__22856] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22856)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22856)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__22856),Vvar__0___24Anonymous__22856) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__31943] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31943)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31943)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__31943,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__31944] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31944)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31944)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__31944,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__17591] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17591)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17591)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17591,V2__y))) )
| ? [Vvar__0___24Anonymous__17592] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17592)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17592)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17592,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__31960] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31960)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31960)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31960)
& ( ( Vvar__0___24Anonymous__31960 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__31963] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31963)
& Vvar__0___24Anonymous__31960 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31963)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__31960)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__31967] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31967)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31967)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__31967)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31887] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31887)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31887)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31887)) )
| ? [Vvar__0___24Anonymous__31888] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31888)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31888)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31888)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31882] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31882)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31882)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__31882)) )
| ? [Vvar__0___24Anonymous__31883] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31883)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31883)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__31883)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__31877] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31877)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__31877)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__31877 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__31875] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31875)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31875)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__31875)) )
| ? [Vvar__0___24Anonymous__31876] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31876)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31876)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31876) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__22853] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__22853)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22853) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31913] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31913)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31913)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__31926___24a1(Vvar__0___24Anonymous__31913) )
| ? [Vvar__0___24Anonymous__31917] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31917)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31917)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__31933___24a1(Vvar__0___24Anonymous__31917) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__31937 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9119] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9119)
& ? [Vvar__1__Qden__9120] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9120)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9119,Vvar__1__Qden__9120)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__9120 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9114] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9114)
& ? [Vvar__1__Qden__9115] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9115)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9114,Vvar__1__Qden__9115)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__9114 ) ) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__9405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9405)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9405)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__9405) )
| ? [Vvar__0___24Anonymous__9406] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9406)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9406)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__9406)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1412___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__1412___24a1(V0__U) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__23242___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__23242___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__22851] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__22851)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__22851) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__22852] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__22852)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__22852) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__17263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17263)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17263)
& ( ? [Vvar__0___24Anonymous__17267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17267)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17267)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__17263,Vvar__0___24Anonymous__17267) ) )
| ? [Vvar__0___24Anonymous__17268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17268)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17268)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17269)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17269)
& ( ? [Vvar__0___24Anonymous__17273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17273)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17273)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__17274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17274)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17274)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__17269,Vvar__0___24Anonymous__17274) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__17275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17275)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17275)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__17276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17276)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17276)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__22803] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__22803)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22803) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__22932] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__22932)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22932) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__17831] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__17831)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__17831) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__22934] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__22934)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__22934) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv = cCoq_2eZArith_2eBinIntDef_2eZ_2equot ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo = cCoq_2eZArith_2eBinIntDef_2eZ_2erem ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__17869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17869)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17869)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17869) )
| ? [Vvar__0___24Anonymous__17870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17870)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17870)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17870) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__17875] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17875)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17875)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17875) )
| ? [Vvar__0___24Anonymous__17876] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17876)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17876)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17876) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__17871] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17871)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17871)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__17871) )
| ? [Vvar__0___24Anonymous__17872] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17872)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17872)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__17872) ) ) ) ).
fof('$_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__17832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17832)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17832)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__17836] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17836)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17836)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__17832,Vvar__0___24Anonymous__17836)) )
| ? [Vvar__0___24Anonymous__17837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17837)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17837)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__17832,Vvar__0___24Anonymous__17837) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17838)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17838)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__17842] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17842)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17842)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__17842,Vvar__0___24Anonymous__17838) )
| ? [Vvar__0___24Anonymous__17843] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17843)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17843)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__17838,Vvar__0___24Anonymous__17843)) ) ) ) ) ) ) ) ).
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__3981] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3981)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3981)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3982] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3982)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3982)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__3983] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3983)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3983)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__3987] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3987)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3987)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__3983,Vvar__0___24Anonymous__3987) )
| ? [Vvar__0___24Anonymous__3988] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3988)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3988)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__3989] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3989)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3989)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3993)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3993)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__3994] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3994)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3994)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__3989,Vvar__0___24Anonymous__3994)) ) ) ) ) ) ) ) ).
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__17975] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__17975)
& ? [Vvar__3___24Anonymous__17976] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__17976)
& 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__17975,Vvar__3___24Anonymous__17976)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__17975 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__18053] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18053)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18053)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18053)
& ( ? [Vvar__0___24Anonymous__18057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18057)
& Vvar__0___24Anonymous__18053 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18057)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18058)
& Vvar__0___24Anonymous__18053 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18058)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__18053 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__18059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18059)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18059)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18059)
& ( ? [Vvar__0___24Anonymous__18063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18063)
& Vvar__0___24Anonymous__18059 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18063)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18064)
& Vvar__0___24Anonymous__18059 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18064)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__18059 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__17983] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__17983)
& ? [Vvar__3___24Anonymous__17984] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__17984)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__17983,Vvar__3___24Anonymous__17984)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__17984 ) ) ) ) ).
fof('$_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__17848] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17848)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17848)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__17852] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17852)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17852)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17848,Vvar__0___24Anonymous__17852)) )
| ? [Vvar__0___24Anonymous__17853] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17853)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17853)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17848,Vvar__0___24Anonymous__17853)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17854] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17854)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17854)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__17858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17858)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17858)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17854,Vvar__0___24Anonymous__17858)) )
| ? [Vvar__0___24Anonymous__17859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17859)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17859)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__17854,Vvar__0___24Anonymous__17859)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__18067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18067)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18067)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18067)
& ( ? [Vvar__0___24Anonymous__18071] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18071)
& Vvar__0___24Anonymous__18067 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18071)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__18072] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18072)
& Vvar__0___24Anonymous__18067 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18072)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__18067 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__18073] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18073)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18073)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18073)
& ( ? [Vvar__0___24Anonymous__18077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18077)
& Vvar__0___24Anonymous__18073 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__18077)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__18078] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18078)
& Vvar__0___24Anonymous__18073 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__18078)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__18073 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__17882] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17882)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__17882)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17882) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3979)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3979)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3979) )
| ? [Vvar__0___24Anonymous__3980] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3980)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3980)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3980) ) ) ) ).
fof('$_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__17861] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17861)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17861)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__17861) )
| ? [Vvar__0___24Anonymous__17862] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17862)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17862)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__22933] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__22933)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__22933) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__32021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32021)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32021)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__32021) )
| ? [Vvar__0___24Anonymous__32022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32022)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32022)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__32019] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32019)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32019)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__32019) )
| ? [Vvar__0___24Anonymous__32020] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32020)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32020)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__17885] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17885)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17885)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__17885 )
| ? [Vvar__0___24Anonymous__17886] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17886)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17886)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__17219] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17219)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17219)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17219)
& ( ? [Vvar__0___24Anonymous__17223] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17223)
& Vvar__0___24Anonymous__17219 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17223)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__17224] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17224)
& Vvar__0___24Anonymous__17219 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17224)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__17219 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17225)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17225)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17225)
& ( ? [Vvar__0___24Anonymous__17229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17229)
& Vvar__0___24Anonymous__17225 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17229)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__17230] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17230)
& Vvar__0___24Anonymous__17225 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17230)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__17225 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__17231] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17231)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17231)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__17231)
& ( ? [Vvar__0___24Anonymous__17235] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17235)
& Vvar__0___24Anonymous__17231 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17235)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__17236] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17236)
& Vvar__0___24Anonymous__17231 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17236)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__17231 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17237] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17237)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17237)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17237)
& ( ? [Vvar__0___24Anonymous__17241] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17241)
& Vvar__0___24Anonymous__17237 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__17241)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__17242] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17242)
& Vvar__0___24Anonymous__17237 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__17242)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__17237 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31773] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31773)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31773)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__31774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31774)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31774)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__31774) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31770)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31770)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__31770)) )
| ? [Vvar__0___24Anonymous__31771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31771)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31771)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__31771)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__18656___24a1(V0__D) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__9941] :
( t(Vvar__1___24Anonymous__9941,V1__A)
& ? [Vvar__2___24Anonymous__9942] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__9942)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__9942)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__9941,Vvar__2___24Anonymous__9942)
& ( ( Vvar__2___24Anonymous__9942 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__9941)) ) )
| ? [Vvar__1___24Anonymous__9953] :
( t(Vvar__1___24Anonymous__9953,V1__A)
& ? [Vvar__2___24Anonymous__9954] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__9954)
& Vvar__2___24Anonymous__9942 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__9953,Vvar__2___24Anonymous__9954)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__9941))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__9942) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__9918] :
( t(Vvar__1___24Anonymous__9918,V1__A)
& ? [Vvar__2___24Anonymous__9919] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__9919)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__9918,Vvar__2___24Anonymous__9919)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__9918))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__9919,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).
fof('$_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__10218___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__10226___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__10234___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__10242___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30815] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30815)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30815)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__30816] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30816)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30816)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30819] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30819)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30819)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__30816,Vvar__0___24Anonymous__30819) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__31711] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__31711)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__31711) ) ).
fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
! [Vvar__31767] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__31767)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__31767) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_N\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__N_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.omega.PreOmega.Zneg\'',axiom,
cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).
fof('$_def_Coq.omega.PreOmega.Zpos\'',axiom,
cCoq_2eomega_2ePreOmega_2eZpos_27 = cCoq_2eNumbers_2eBinNums_2eZpos ).
fof('$_def_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNotConstant = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__8550] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__8550)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__8550) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__23271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23271)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23271)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23271)
& ( ? [Vvar__0___24Anonymous__23275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23275)
& Vvar__0___24Anonymous__23271 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23275)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__23271))) )
| ? [Vvar__0___24Anonymous__23276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23276)
& Vvar__0___24Anonymous__23271 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23276)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__23271))) )
| ( Vvar__0___24Anonymous__23271 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23277)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23277)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23277)
& ( ? [Vvar__0___24Anonymous__23281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23281)
& Vvar__0___24Anonymous__23277 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23281)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__23277)) )
| ? [Vvar__0___24Anonymous__23282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23282)
& Vvar__0___24Anonymous__23277 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23282)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__23277)) )
| ( Vvar__0___24Anonymous__23277 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__19873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19873)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__19873)
& 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__19873))) )
| ? [Vvar__0___24Anonymous__19874] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__19874)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__19874)
& 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__19874)) )
| ( 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.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__10405] :
( t(Vvar__1___24Anonymous__10405,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__10405)
& ( ? [Vvar__1___24Anonymous__10415] :
( t(Vvar__1___24Anonymous__10415,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__10415)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__10405),Vvar__1___24Anonymous__10415) )
| ? [Vvar__1___24Anonymous__10417] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10417)
& ? [Vvar__2___24Anonymous__10418] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__10418)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__10417,Vvar__2___24Anonymous__10418)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__10421] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10421)
& ? [Vvar__2___24Anonymous__10422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10422)
& ? [Vvar__3___24Anonymous__10423] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__10423)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__10421,Vvar__2___24Anonymous__10422,Vvar__3___24Anonymous__10423)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__10428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10428)
& ? [Vvar__2___24Anonymous__10429] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__10429)
& ( 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__10428,Vvar__2___24Anonymous__10429)
& ( ? [Vvar__1___24Anonymous__10449] :
( t(Vvar__1___24Anonymous__10449,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__10449)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__10451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10451)
& ? [Vvar__2___24Anonymous__10452] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__10452)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10428)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10451)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__10451,Vvar__2___24Anonymous__10452)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__10428,Vvar__1___24Anonymous__10451) = 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__10429,Vvar__2___24Anonymous__10452) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__10428,Vvar__1___24Anonymous__10451) = 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__10428,Vvar__1___24Anonymous__10451) = 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__10457] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10457)
& ? [Vvar__2___24Anonymous__10458] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10458)
& ? [Vvar__3___24Anonymous__10459] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__10459)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__10457,Vvar__2___24Anonymous__10458,Vvar__3___24Anonymous__10459)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__10464] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10464)
& ? [Vvar__2___24Anonymous__10465] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10465)
& ? [Vvar__3___24Anonymous__10466] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__10466)
& ( 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__10464,Vvar__2___24Anonymous__10465,Vvar__3___24Anonymous__10466)
& ( ? [Vvar__1___24Anonymous__10499] :
( t(Vvar__1___24Anonymous__10499,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__10499)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__10501] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10501)
& ? [Vvar__2___24Anonymous__10502] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__10502)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__10501,Vvar__2___24Anonymous__10502)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__10505] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10505)
& ? [Vvar__2___24Anonymous__10506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10506)
& ? [Vvar__3___24Anonymous__10507] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__10507)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10465)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10506)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__10505,Vvar__2___24Anonymous__10506,Vvar__3___24Anonymous__10507)
& ( ( cType___24t(V0__C)
=> ( c_24__type__6146___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10464)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__10505)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__10465,Vvar__2___24Anonymous__10506) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__10464,Vvar__1___24Anonymous__10505) = 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__10466,Vvar__3___24Anonymous__10507) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__10464,Vvar__1___24Anonymous__10505) = 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__10465,Vvar__2___24Anonymous__10506) = 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__10465,Vvar__2___24Anonymous__10506) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__30847] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30847)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30847)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__30847),V4__x,Vvar__0___24Anonymous__30847) )
| ? [Vvar__0___24Anonymous__30848] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30848)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30848)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__30848),V4__x,Vvar__0___24Anonymous__30848) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__2826] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2826)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2826)
& 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__2826) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__20170] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20170)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20170)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__20171__20174___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20170)),c_24__let__var__6__p__20171__20174___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20170))) )
| ? [Vvar__0___24Anonymous__20172] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20172)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20172)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__20173__20175___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20172)),c_24__let__var__6__p__20173__20175___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20172)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Lambda.Redexes.bool_max',axiom,
! [V0__b,V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cLambda_2eRedexes_2ebool__max___24a2(V0__b,V1__b_27) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cLambda_2eRedexes_2ebool__max___24a2(V0__b,V1__b_27) = V1__b_27 ) ) ) ).
fof('$_def_Lambda.Redexes.redexes_rec',axiom,
! [V0__P] : cLambda_2eRedexes_2eredexes__rec___24a1(V0__P) = cLambda_2eRedexes_2eredexes__rect___24a1(V0__P) ).
fof('$_def_Lambda.Redexes.redexes_rect',axiom,
! [V0__P,V1__f,V2__f,V3__f,V5__r] :
( c_24__type__1166___24t(V0__P,V0__P)
=> ( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ( ? [Vvar__0___24Anonymous__1157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1157)
& V5__r = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__1157)
& cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__r) = happ(V1__f,Vvar__0___24Anonymous__1157) )
| ? [Vvar__0___24Anonymous__1158] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__1158)
& V5__r = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__1158)
& cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__r) = happ(happ(V2__f,Vvar__0___24Anonymous__1158),cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__0___24Anonymous__1158)) )
| ? [Vvar__0___24Anonymous__1159] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__1159)
& ? [Vvar__1___24Anonymous__1160] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__1160)
& ? [Vvar__2___24Anonymous__1161] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__1161)
& V5__r = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__1159,Vvar__1___24Anonymous__1160,Vvar__2___24Anonymous__1161)
& cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__r) = happ(happ(happ(happ(happ(V3__f,Vvar__0___24Anonymous__1159),Vvar__1___24Anonymous__1160),cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__1160)),Vvar__2___24Anonymous__1161),cLambda_2eRedexes_2eredexes__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__2___24Anonymous__1161)) ) ) ) ) ) ) ).
fof('$_def_Lambda.Redexes.regular',axiom,
! [V1__U] :
( cLambda_2eRedexes_2eredexes___24t(V1__U)
=> ( ? [Vvar__0___24Anonymous__269] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__269)
& V1__U = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__269)
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__270] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__270)
& V1__U = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__270)
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> cLambda_2eRedexes_2eregular___24a1(Vvar__0___24Anonymous__270) ) )
| ? [Vvar__0___24Anonymous__271] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__271)
& ? [Vvar__1___24Anonymous__272] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__272)
& ? [Vvar__2___24Anonymous__273] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__273)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__271)
=> ( V1__U = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__271,Vvar__1___24Anonymous__272,Vvar__2___24Anonymous__273)
& ( ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__272)
=> ( Vvar__0___24Anonymous__271 = cCoq_2eInit_2eDatatypes_2etrue
& ( ? [Vvar__0___24Anonymous__298] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__298)
& Vvar__1___24Anonymous__272 = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__298)
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__299] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__299)
& Vvar__1___24Anonymous__272 = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__299)
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> ( cLambda_2eRedexes_2eregular___24a1(Vvar__1___24Anonymous__272)
& cLambda_2eRedexes_2eregular___24a1(Vvar__2___24Anonymous__273) ) ) )
| ? [Vvar__0___24Anonymous__300] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__300)
& ? [Vvar__1___24Anonymous__301] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__301)
& ? [Vvar__2___24Anonymous__302] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__302)
& Vvar__1___24Anonymous__272 = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__300,Vvar__1___24Anonymous__301,Vvar__2___24Anonymous__302)
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> p(c_24False) ) ) ) ) ) ) )
| ( Vvar__0___24Anonymous__271 = cCoq_2eInit_2eDatatypes_2efalse
& ( cLambda_2eRedexes_2eregular___24a1(V1__U)
<=> ( cLambda_2eRedexes_2eregular___24a1(Vvar__1___24Anonymous__272)
& cLambda_2eRedexes_2eregular___24a1(Vvar__2___24Anonymous__273) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Lambda.Substitution.insert_Var',axiom,
! [V0__N,V1__i,V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( ? [Vvar__2___24Anonymous__1076] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1091___24a2(V1__i,V2__k),Vvar__2___24Anonymous__1076)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1092___24a2(V1__i,V2__k),Vvar__2___24Anonymous__1076)
=> ( cLambda_2eTest_2ecompare___24a2(V2__k,V1__i) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1093___24a2(V1__i,V2__k)),cCoq_2eInit_2ePeano_2egt___24a2(V2__k,V1__i),Vvar__2___24Anonymous__1076)
& ( ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i))
& Vvar__2___24Anonymous__1076 = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1094___24a2(V1__i,V2__k))
& cLambda_2eSubstitution_2einsert__Var___24a3(V0__N,V1__i,V2__k) = cLambda_2eRedexes_2eVar___24a1(cCoq_2eInit_2eNat_2epred___24a1(V1__i)) )
| ( V2__k = V1__i
& Vvar__2___24Anonymous__1076 = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1095___24a2(V1__i,V2__k))
& cLambda_2eSubstitution_2einsert__Var___24a3(V0__N,V1__i,V2__k) = cLambda_2eSubstitution_2elift__r___24a2(V2__k,V0__N) ) ) ) ) ) ) )
| ( p(cCoq_2eInit_2ePeano_2egt___24a2(V2__k,V1__i))
& cLambda_2eTest_2ecompare___24a2(V2__k,V1__i) = cCoq_2eInit_2eSpecif_2einright___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(V2__k,V1__i),c_24__prop__1096___24a2(V1__i,V2__k)),cCoq_2eInit_2ePeano_2egt___24a2(V2__k,V1__i))
& cLambda_2eSubstitution_2einsert__Var___24a3(V0__N,V1__i,V2__k) = cLambda_2eRedexes_2eVar___24a1(V1__i) ) ) ) ) ).
fof('$_def_Lambda.Substitution.lift_r',axiom,
! [V0__n,V1__N] : cLambda_2eSubstitution_2elift__r___24a2(V0__n,V1__N) = cLambda_2eSubstitution_2elift__rec__r___24a3(V1__N,cCoq_2eInit_2eDatatypes_2eO,V0__n) ).
fof('$_def_Lambda.Substitution.lift_rec_r',axiom,
! [V1__L,V2__k,V3__n] :
( cLambda_2eRedexes_2eredexes___24t(V1__L)
=> ( ? [Vvar__0___24Anonymous__1056] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1056)
& V1__L = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__1056)
& cLambda_2eSubstitution_2elift__rec__r___24a3(V1__L,V2__k,V3__n) = cLambda_2eRedexes_2eVar___24a1(cLambda_2eTerms_2erelocate___24a3(Vvar__0___24Anonymous__1056,V2__k,V3__n)) )
| ? [Vvar__0___24Anonymous__1057] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__1057)
& V1__L = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__1057)
& cLambda_2eSubstitution_2elift__rec__r___24a3(V1__L,V2__k,V3__n) = cLambda_2eRedexes_2eFun___24a1(cLambda_2eSubstitution_2elift__rec__r___24a3(Vvar__0___24Anonymous__1057,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__k),V3__n)) )
| ? [Vvar__0___24Anonymous__1058] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__1058)
& ? [Vvar__1___24Anonymous__1059] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__1059)
& ? [Vvar__2___24Anonymous__1060] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__1060)
& V1__L = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__1058,Vvar__1___24Anonymous__1059,Vvar__2___24Anonymous__1060)
& cLambda_2eSubstitution_2elift__rec__r___24a3(V1__L,V2__k,V3__n) = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__1058,cLambda_2eSubstitution_2elift__rec__r___24a3(Vvar__1___24Anonymous__1059,V2__k,V3__n),cLambda_2eSubstitution_2elift__rec__r___24a3(Vvar__2___24Anonymous__1060,V2__k,V3__n)) ) ) ) ) ) ).
fof('$_def_Lambda.Substitution.subst_r',axiom,
! [V0__N,V1__M] : cLambda_2eSubstitution_2esubst__r___24a2(V0__N,V1__M) = cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__M,V0__N,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Lambda.Substitution.subst_rec_r',axiom,
! [V1__L,V2__N,V3__k] :
( cLambda_2eRedexes_2eredexes___24t(V1__L)
=> ( ? [Vvar__0___24Anonymous__1101] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1101)
& V1__L = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__1101)
& cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__L,V2__N,V3__k) = cLambda_2eSubstitution_2einsert__Var___24a3(V2__N,Vvar__0___24Anonymous__1101,V3__k) )
| ? [Vvar__0___24Anonymous__1102] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__1102)
& V1__L = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__1102)
& cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__L,V2__N,V3__k) = cLambda_2eRedexes_2eFun___24a1(cLambda_2eSubstitution_2esubst__rec__r___24a3(Vvar__0___24Anonymous__1102,V2__N,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k))) )
| ? [Vvar__0___24Anonymous__1103] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__1103)
& ? [Vvar__1___24Anonymous__1104] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__1104)
& ? [Vvar__2___24Anonymous__1105] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__1105)
& V1__L = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__1103,Vvar__1___24Anonymous__1104,Vvar__2___24Anonymous__1105)
& cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__L,V2__N,V3__k) = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__1103,cLambda_2eSubstitution_2esubst__rec__r___24a3(Vvar__1___24Anonymous__1104,V2__N,V3__k),cLambda_2eSubstitution_2esubst__rec__r___24a3(Vvar__2___24Anonymous__1105,V2__N,V3__k)) ) ) ) ) ) ).
fof('$_def_Lambda.Terms.relocate',axiom,
! [V0__i,V1__k,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__i)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i))
& cLambda_2eTest_2etest___24a2(V1__k,V0__i) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i),cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTerms_2erelocate___24a3(V0__i,V1__k,V2__n) = cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__i) )
| ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTest_2etest___24a2(V1__k,V0__i) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i),cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTerms_2erelocate___24a3(V0__i,V1__k,V2__n) = V0__i ) ) ) ) ).
fof('$_def_Lambda.Test.compare',axiom,
! [V0__n,V1__m] : cLambda_2eTest_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m),cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m),c_24__lam__1129___24a2(V0__n,V1__m),c_24__lam__1133___24a2(V0__n,V1__m),c_24__lam__1137___24a2(V0__n,V1__m),cLambda_2eTest_2etest___24a2(V0__n,V1__m)) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__18591,Vvar__1___24Anonymous__18592,Vvar__0__P__18593,Vvar__1___24Anonymous__18594] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__18591) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__18593) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__3886,Vvar__1___24Anonymous__3887,Vvar__2___24Anonymous__3888] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__3886,Vvar__1___24Anonymous__3887,Vvar__2___24Anonymous__3888) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__23152,Vvar__1__Plt__23153,Vvar__2__Pgt__23154,Vvar__3___24Anonymous__23155,Vvar__0__Peq__23156,Vvar__1__Plt__23157,Vvar__2__Pgt__23158,Vvar__3___24Anonymous__23159] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23152,Vvar__1__Plt__23153,Vvar__2__Pgt__23154) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23156,Vvar__1__Plt__23157,Vvar__2__Pgt__23158) ).
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__6] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__4691,Vvar__1___24Anonymous__4692,Vvar__0__A__4693] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4691,Vvar__1___24Anonymous__4692) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4693) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4717,Vvar__1__B__4718,Vvar__2___24Anonymous__4719,Vvar__0__A__4720,Vvar__1__B__4721,Vvar__2___24Anonymous__4722] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4717,Vvar__1__B__4718,Vvar__2___24Anonymous__4719) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4720,Vvar__1__B__4721,Vvar__2___24Anonymous__4722) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4783,Vvar__0__A__4784,Vvar__1___24Anonymous__4785,Vvar__2___24Anonymous__4786] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4783) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4784,Vvar__1___24Anonymous__4785,Vvar__2___24Anonymous__4786) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__18635,Vvar__1__f__18636,Vvar__0__i__18637,Vvar__1__f__18638,Vvar__2__e__18639] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18635,Vvar__1__f__18636) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18637,Vvar__1__f__18638,Vvar__2__e__18639) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__5014] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5014) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__18623,Vvar__0__d__18624] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18623) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18624) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__1031,Vvar__1__B__1032,Vvar__2___24Anonymous__1033,Vvar__0__A__1034,Vvar__1__B__1035,Vvar__2___24Anonymous__1036] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1031,Vvar__1__B__1032,Vvar__2___24Anonymous__1033) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1034,Vvar__1__B__1035) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__995,Vvar__1__B__996,Vvar__2___24Anonymous__997,Vvar__0__A__998,Vvar__1__B__999,Vvar__2___24Anonymous__1000] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__995,Vvar__1__B__996) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__998,Vvar__1__B__999) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1388] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1388) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1397] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1397) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1372,Vvar__0___24Anonymous__1373] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1372) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1373) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__22926,Vvar__1___24Anonymous__22927] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__22926,Vvar__1___24Anonymous__22927) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__17585] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__17585) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__20002,Vvar__1___24Anonymous__20003,Vvar__0__x__20004,Vvar__1__n__20005,Vvar__2___24Anonymous__20006] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__20002) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__20004,Vvar__1__n__20005) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__16844,Vvar__1___24Anonymous__16845] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__16844,Vvar__1___24Anonymous__16845) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9022,Vvar__1__lt__9023,Vvar__2__eq__9024,Vvar__3__x__9025,Vvar__4__y__9026,Vvar__5___24Anonymous__9027,Vvar__0__X__9028,Vvar__1__lt__9029,Vvar__2__eq__9030,Vvar__3__x__9031,Vvar__4__y__9032,Vvar__5___24Anonymous__9033] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9022,Vvar__1__lt__9023,Vvar__2__eq__9024,Vvar__3__x__9025,Vvar__4__y__9026) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9028,Vvar__1__lt__9029,Vvar__2__eq__9030,Vvar__3__x__9031,Vvar__4__y__9032) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__8419,Vvar__0__n__8420,Vvar__1___24Anonymous__8421] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8419) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8420,Vvar__1___24Anonymous__8421) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__3121,Vvar__0__A__3122,Vvar__1__h__3123,Vvar__2__n__3124,Vvar__3___24Anonymous__3125] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3121) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3122,Vvar__1__h__3123,Vvar__2__n__3124,Vvar__3___24Anonymous__3125) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__5166,Vvar__1___24Anonymous__5167,Vvar__0__C__5168,Vvar__1___24Anonymous__5169] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5166,Vvar__1___24Anonymous__5167) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5168,Vvar__1___24Anonymous__5169) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5230,Vvar__1___24Anonymous__5231,Vvar__0__C__5232,Vvar__1___24Anonymous__5233,Vvar__2___24Anonymous__5234] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5230,Vvar__1___24Anonymous__5231) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5232,Vvar__1___24Anonymous__5233,Vvar__2___24Anonymous__5234) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__18669,Vvar__1___24Anonymous__18670] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__18669,Vvar__1___24Anonymous__18670) ).
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__20133,Vvar__1___24Anonymous__20134,Vvar__0__C__20135,Vvar__1___24Anonymous__20136] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20133,Vvar__1___24Anonymous__20134) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20135,Vvar__1___24Anonymous__20136) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22609,Vvar__1__TX__22610,Vvar__2__AA__22611,Vvar__3__AF__22612,Vvar__0__TA__22613,Vvar__1__TX__22614,Vvar__2__AA__22615,Vvar__3__AF__22616] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22609,Vvar__1__TX__22610,Vvar__2__AA__22611,Vvar__3__AF__22612) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22613,Vvar__1__TX__22614,Vvar__2__AA__22615,Vvar__3__AF__22616) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__22723,Vvar__0__A__22724,Vvar__1___24Anonymous__22725] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__22723) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__22724,Vvar__1___24Anonymous__22725) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__3352,Vvar__1___24Anonymous__3353] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__3352,Vvar__1___24Anonymous__3353) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7071,Vvar__0__C__7072] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7071) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7072) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__10735,Vvar__0__C__10736] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10735) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10736) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__10379,Vvar__1___24Anonymous__10380,Vvar__0__C__10381,Vvar__1___24Anonymous__10382,Vvar__2___24Anonymous__10383] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__10379,Vvar__1___24Anonymous__10380) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__10381,Vvar__1___24Anonymous__10382,Vvar__2___24Anonymous__10383) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__10545,Vvar__1___24Anonymous__10546] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10545,Vvar__1___24Anonymous__10546) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__22100,Vvar__1__req__22101,Vvar__2__reqb__22102,Vvar__3___24Anonymous__22103] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22100,Vvar__1__req__22101,Vvar__2__reqb__22102) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_discrim_Lambda.Redexes.Var$Lambda.Redexes.Fun',axiom,
! [Vvar__0___24Anonymous__23,Vvar__0___24Anonymous__24] : cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__23) != cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__24) ).
fof('$_discrim_Lambda.Terms.Ref$Lambda.Terms.Abs',axiom,
! [Vvar__0___24Anonymous__17020,Vvar__0___24Anonymous__17021] : cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__17020) != cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__17021) ).
fof('$_fix_22921_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__22922] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22922)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22922)
& c_24__fix__22921__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__22921__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__22922)) )
| ? [Vvar__0___24Anonymous__22923] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22923)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22923)
& c_24__fix__22921__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22923) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__22921__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_fix_25414_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__25414__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__25418] :
( t(Vvar__1___24Anonymous__25418,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__25419] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__25419)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25418,Vvar__2___24Anonymous__25419)
& c_24__fix__25414__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__25418,c_24__fix__25414__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__25419,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_902_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__903] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__903)
& Vv__CANONICAL__1 = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__903)
& c_24__fix__902__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eSubstitution_2einsert__Var___24a3(Vv__CANONICAL__2,Vvar__0___24Anonymous__903,Vv__CANONICAL__3) )
| ? [Vvar__0___24Anonymous__904] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__904)
& Vv__CANONICAL__1 = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__904)
& c_24__fix__902__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eRedexes_2eFun___24a1(c_24__fix__902__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__904,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3))) )
| ? [Vvar__0___24Anonymous__905] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__905)
& ? [Vvar__1___24Anonymous__906] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__906)
& ? [Vvar__2___24Anonymous__907] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__907)
& Vv__CANONICAL__1 = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__905,Vvar__1___24Anonymous__906,Vvar__2___24Anonymous__907)
& c_24__fix__902__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__905,c_24__fix__902__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__906,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__fix__902__v__CANONICAL__0___24a3(Vvar__2___24Anonymous__907,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_9848_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__9849] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9849)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__9849)
& c_24__fix__9848__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2einsert__Ref___24a3(Vv__CANONICAL__2,Vvar__0___24Anonymous__9849,Vv__CANONICAL__3) )
| ? [Vvar__0___24Anonymous__9850] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__9850)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__9850)
& c_24__fix__9848__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eAbs___24a1(c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__9850,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3))) )
| ? [Vvar__0___24Anonymous__9851] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__9851)
& ? [Vvar__1___24Anonymous__9852] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__9852)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__9851,Vvar__1___24Anonymous__9852)
& c_24__fix__9848__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eApp___24a2(c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__9851,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__fix__9848__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__9852,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__18599,Vvar__0__P__18600,Vvar__1___24Anonymous__18601,Vvar__1___24Anonymous__18602] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__18599) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__18600)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__18599 = Vvar__0__P__18600 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__18595,Vvar__0__P__18596,Vvar__1___24Anonymous__18597,Vvar__1___24Anonymous__18598] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__18595) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__18596)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__18595 = Vvar__0__P__18596 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__3889,Vvar__0___24Anonymous__3890,Vvar__1___24Anonymous__3891,Vvar__1___24Anonymous__3892,Vvar__2___24Anonymous__3893,Vvar__2___24Anonymous__3894] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__3889,Vvar__1___24Anonymous__3891,Vvar__2___24Anonymous__3893) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__3890,Vvar__1___24Anonymous__3892,Vvar__2___24Anonymous__3894)
=> ( Vvar__2___24Anonymous__3893 = Vvar__2___24Anonymous__3894
& Vvar__1___24Anonymous__3891 = Vvar__1___24Anonymous__3892
& Vvar__0___24Anonymous__3889 = Vvar__0___24Anonymous__3890 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__23160,Vvar__0__Peq__23161,Vvar__1__Plt__23162,Vvar__1__Plt__23163,Vvar__2__Pgt__23164,Vvar__2__Pgt__23165,Vvar__3___24Anonymous__23166,Vvar__3___24Anonymous__23167] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23160,Vvar__1__Plt__23162,Vvar__2__Pgt__23164) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23161,Vvar__1__Plt__23163,Vvar__2__Pgt__23165)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23164 = Vvar__2__Pgt__23165
& Vvar__1__Plt__23162 = Vvar__1__Plt__23163
& Vvar__0__Peq__23160 = Vvar__0__Peq__23161 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__23176,Vvar__0__Peq__23177,Vvar__1__Plt__23178,Vvar__1__Plt__23179,Vvar__2__Pgt__23180,Vvar__2__Pgt__23181,Vvar__3___24Anonymous__23182,Vvar__3___24Anonymous__23183] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23176,Vvar__1__Plt__23178,Vvar__2__Pgt__23180) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23177,Vvar__1__Plt__23179,Vvar__2__Pgt__23181)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23180 = Vvar__2__Pgt__23181
& Vvar__1__Plt__23178 = Vvar__1__Plt__23179
& Vvar__0__Peq__23176 = Vvar__0__Peq__23177 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__23168,Vvar__0__Peq__23169,Vvar__1__Plt__23170,Vvar__1__Plt__23171,Vvar__2__Pgt__23172,Vvar__2__Pgt__23173,Vvar__3___24Anonymous__23174,Vvar__3___24Anonymous__23175] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23168,Vvar__1__Plt__23170,Vvar__2__Pgt__23172) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23169,Vvar__1__Plt__23171,Vvar__2__Pgt__23173)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23172 = Vvar__2__Pgt__23173
& Vvar__1__Plt__23170 = Vvar__1__Plt__23171
& Vvar__0__Peq__23168 = Vvar__0__Peq__23169 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__4698,Vvar__0__A__4699] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4698) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4699)
=> Vvar__0__A__4698 = Vvar__0__A__4699 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__7,Vvar__0___24Anonymous__8] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8)
=> Vvar__0___24Anonymous__7 = Vvar__0___24Anonymous__8 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__4694,Vvar__0__A__4695,Vvar__1___24Anonymous__4696,Vvar__1___24Anonymous__4697] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4694,Vvar__1___24Anonymous__4696) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4695,Vvar__1___24Anonymous__4697)
=> ( Vvar__1___24Anonymous__4696 = Vvar__1___24Anonymous__4697
& Vvar__0__A__4694 = Vvar__0__A__4695 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4789,Vvar__0__A__4790,Vvar__1___24Anonymous__4791,Vvar__1___24Anonymous__4792,Vvar__2___24Anonymous__4793,Vvar__2___24Anonymous__4794] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4789,Vvar__1___24Anonymous__4791,Vvar__2___24Anonymous__4793) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4790,Vvar__1___24Anonymous__4792,Vvar__2___24Anonymous__4794)
=> ( Vvar__2___24Anonymous__4793 = Vvar__2___24Anonymous__4794
& Vvar__1___24Anonymous__4791 = Vvar__1___24Anonymous__4792
& Vvar__0__A__4789 = Vvar__0__A__4790 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__4723,Vvar__0__A__4724,Vvar__1__B__4725,Vvar__1__B__4726,Vvar__2___24Anonymous__4727,Vvar__2___24Anonymous__4728] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4723,Vvar__1__B__4725,Vvar__2___24Anonymous__4727) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4724,Vvar__1__B__4726,Vvar__2___24Anonymous__4728)
=> ( Vvar__2___24Anonymous__4727 = Vvar__2___24Anonymous__4728
& Vvar__1__B__4725 = Vvar__1__B__4726
& Vvar__0__A__4723 = Vvar__0__A__4724 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__4729,Vvar__0__A__4730,Vvar__1__B__4731,Vvar__1__B__4732,Vvar__2___24Anonymous__4733,Vvar__2___24Anonymous__4734] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4729,Vvar__1__B__4731,Vvar__2___24Anonymous__4733) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4730,Vvar__1__B__4732,Vvar__2___24Anonymous__4734)
=> ( Vvar__2___24Anonymous__4733 = Vvar__2___24Anonymous__4734
& Vvar__1__B__4731 = Vvar__1__B__4732
& Vvar__0__A__4729 = Vvar__0__A__4730 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__4787,Vvar__0__A__4788] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4787) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4788)
=> Vvar__0__A__4787 = Vvar__0__A__4788 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__4743,Vvar__0__A__4744,Vvar__1__B__4745,Vvar__1__B__4746,Vvar__2___24Anonymous__4747,Vvar__2___24Anonymous__4748,Vvar__3___24Anonymous__4749,Vvar__3___24Anonymous__4750] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4743,Vvar__1__B__4745,Vvar__2___24Anonymous__4747,Vvar__3___24Anonymous__4749) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4744,Vvar__1__B__4746,Vvar__2___24Anonymous__4748,Vvar__3___24Anonymous__4750)
=> ( Vvar__3___24Anonymous__4749 = Vvar__3___24Anonymous__4750
& Vvar__2___24Anonymous__4747 = Vvar__2___24Anonymous__4748
& Vvar__1__B__4745 = Vvar__1__B__4746
& Vvar__0__A__4743 = Vvar__0__A__4744 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__5015,Vvar__0___24Anonymous__5016] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5015) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__5016)
=> Vvar__0___24Anonymous__5015 = Vvar__0___24Anonymous__5016 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__5017,Vvar__0___24Anonymous__5018] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__5017) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__5018)
=> Vvar__0___24Anonymous__5017 = Vvar__0___24Anonymous__5018 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__5019,Vvar__0___24Anonymous__5020] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__5019) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__5020)
=> Vvar__0___24Anonymous__5019 = Vvar__0___24Anonymous__5020 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__5021,Vvar__0___24Anonymous__5022] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__5021) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__5022)
=> Vvar__0___24Anonymous__5021 = Vvar__0___24Anonymous__5022 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__5023,Vvar__0___24Anonymous__5024] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__5023) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__5024)
=> Vvar__0___24Anonymous__5023 = Vvar__0___24Anonymous__5024 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__5025,Vvar__0___24Anonymous__5026] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__5025) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__5026)
=> Vvar__0___24Anonymous__5025 = Vvar__0___24Anonymous__5026 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__5027,Vvar__0___24Anonymous__5028] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__5027) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__5028)
=> Vvar__0___24Anonymous__5027 = Vvar__0___24Anonymous__5028 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__5029,Vvar__0___24Anonymous__5030] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__5029) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__5030)
=> Vvar__0___24Anonymous__5029 = Vvar__0___24Anonymous__5030 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__5031,Vvar__0___24Anonymous__5032] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__5031) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__5032)
=> Vvar__0___24Anonymous__5031 = Vvar__0___24Anonymous__5032 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__5033,Vvar__0___24Anonymous__5034] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__5033) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__5034)
=> Vvar__0___24Anonymous__5033 = Vvar__0___24Anonymous__5034 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__18640,Vvar__0__i__18641,Vvar__1__f__18642,Vvar__1__f__18643] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18640,Vvar__1__f__18642) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18641,Vvar__1__f__18643)
=> ( Vvar__1__f__18642 = Vvar__1__f__18643
& Vvar__0__i__18640 = Vvar__0__i__18641 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__18644,Vvar__0__i__18645,Vvar__1__f__18646,Vvar__1__f__18647,Vvar__2__e__18648,Vvar__2__e__18649] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18644,Vvar__1__f__18646,Vvar__2__e__18648) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18645,Vvar__1__f__18647,Vvar__2__e__18649)
=> ( Vvar__2__e__18648 = Vvar__2__e__18649
& Vvar__1__f__18646 = Vvar__1__f__18647
& Vvar__0__i__18644 = Vvar__0__i__18645 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__18627,Vvar__0__d__18628] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18627) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18628)
=> Vvar__0__d__18627 = Vvar__0__d__18628 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__18625,Vvar__0__d__18626] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18625) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18626)
=> Vvar__0__d__18625 = Vvar__0__d__18626 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__16784,Vvar__0__A__16785,Vvar__1__P__16786,Vvar__1__P__16787,Vvar__2__x__16788,Vvar__2__x__16789,Vvar__3___24Anonymous__16790,Vvar__3___24Anonymous__16791] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__16784,Vvar__1__P__16786,Vvar__2__x__16788) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__16785,Vvar__1__P__16787,Vvar__2__x__16789)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__16788 = Vvar__2__x__16789
& Vvar__1__P__16786 = Vvar__1__P__16787
& Vvar__0__A__16784 = Vvar__0__A__16785 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__22192,Vvar__0__A__22193,Vvar__1__P__22194,Vvar__1__P__22195,Vvar__2__Q__22196,Vvar__2__Q__22197,Vvar__3__x__22198,Vvar__3__x__22199,Vvar__4___24Anonymous__22200,Vvar__4___24Anonymous__22201,Vvar__5___24Anonymous__22202,Vvar__5___24Anonymous__22203] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22192,Vvar__1__P__22194,Vvar__2__Q__22196,Vvar__3__x__22198) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22193,Vvar__1__P__22195,Vvar__2__Q__22197,Vvar__3__x__22199)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__22198 = Vvar__3__x__22199
& Vvar__2__Q__22196 = Vvar__2__Q__22197
& Vvar__1__P__22194 = Vvar__1__P__22195
& Vvar__0__A__22192 = Vvar__0__A__22193 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__16823,Vvar__0__A__16824,Vvar__1__P__16825,Vvar__1__P__16826,Vvar__2__x__16827,Vvar__2__x__16828,Vvar__3___24Anonymous__16829,Vvar__3___24Anonymous__16830] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16823,Vvar__1__P__16825,Vvar__2__x__16827,Vvar__3___24Anonymous__16829) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16824,Vvar__1__P__16826,Vvar__2__x__16828,Vvar__3___24Anonymous__16830)
=> ( Vvar__3___24Anonymous__16829 = Vvar__3___24Anonymous__16830
& Vvar__2__x__16827 = Vvar__2__x__16828
& Vvar__1__P__16825 = Vvar__1__P__16826
& Vvar__0__A__16823 = Vvar__0__A__16824 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__22248,Vvar__0__A__22249,Vvar__1__P__22250,Vvar__1__P__22251,Vvar__2__Q__22252,Vvar__2__Q__22253,Vvar__3__x__22254,Vvar__3__x__22255,Vvar__4___24Anonymous__22256,Vvar__4___24Anonymous__22257,Vvar__5___24Anonymous__22258,Vvar__5___24Anonymous__22259] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22248,Vvar__1__P__22250,Vvar__2__Q__22252,Vvar__3__x__22254,Vvar__4___24Anonymous__22256,Vvar__5___24Anonymous__22258) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22249,Vvar__1__P__22251,Vvar__2__Q__22253,Vvar__3__x__22255,Vvar__4___24Anonymous__22257,Vvar__5___24Anonymous__22259)
=> ( Vvar__5___24Anonymous__22258 = Vvar__5___24Anonymous__22259
& Vvar__4___24Anonymous__22256 = Vvar__4___24Anonymous__22257
& Vvar__3__x__22254 = Vvar__3__x__22255
& Vvar__2__Q__22252 = Vvar__2__Q__22253
& Vvar__1__P__22250 = Vvar__1__P__22251
& Vvar__0__A__22248 = Vvar__0__A__22249 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__1037,Vvar__0__A__1038,Vvar__1__B__1039,Vvar__1__B__1040,Vvar__2___24Anonymous__1041,Vvar__2___24Anonymous__1042] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1037,Vvar__1__B__1039,Vvar__2___24Anonymous__1041) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1038,Vvar__1__B__1040,Vvar__2___24Anonymous__1042)
=> ( Vvar__2___24Anonymous__1041 = Vvar__2___24Anonymous__1042
& Vvar__1__B__1039 = Vvar__1__B__1040
& Vvar__0__A__1037 = Vvar__0__A__1038 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__1043,Vvar__0__A__1044,Vvar__1__B__1045,Vvar__1__B__1046,Vvar__2___24Anonymous__1047,Vvar__2___24Anonymous__1048] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1043,Vvar__1__B__1045) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1044,Vvar__1__B__1046)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__1045 = Vvar__1__B__1046
& Vvar__0__A__1043 = Vvar__0__A__1044 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__1001,Vvar__0__A__1002,Vvar__1__B__1003,Vvar__1__B__1004,Vvar__2___24Anonymous__1005,Vvar__2___24Anonymous__1006] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1001,Vvar__1__B__1003) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1002,Vvar__1__B__1004)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__1003 = Vvar__1__B__1004
& Vvar__0__A__1001 = Vvar__0__A__1002 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__1007,Vvar__0__A__1008,Vvar__1__B__1009,Vvar__1__B__1010,Vvar__2___24Anonymous__1011,Vvar__2___24Anonymous__1012] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1007,Vvar__1__B__1009) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1008,Vvar__1__B__1010)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__1009 = Vvar__1__B__1010
& Vvar__0__A__1007 = Vvar__0__A__1008 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1389,Vvar__0___24Anonymous__1390] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1389) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1390)
=> Vvar__0___24Anonymous__1389 = Vvar__0___24Anonymous__1390 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1400,Vvar__0___24Anonymous__1401] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1400) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1401)
=> Vvar__0___24Anonymous__1400 = Vvar__0___24Anonymous__1401 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1398,Vvar__0___24Anonymous__1399] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1398) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1399)
=> Vvar__0___24Anonymous__1398 = Vvar__0___24Anonymous__1399 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1374,Vvar__0___24Anonymous__1375] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1374) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1375)
=> Vvar__0___24Anonymous__1374 = Vvar__0___24Anonymous__1375 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1376,Vvar__0___24Anonymous__1377] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1376) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1377)
=> Vvar__0___24Anonymous__1376 = Vvar__0___24Anonymous__1377 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__22928,Vvar__0__p__22929,Vvar__1___24Anonymous__22930,Vvar__1___24Anonymous__22931] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__22928,Vvar__1___24Anonymous__22930) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__22929,Vvar__1___24Anonymous__22931)
=> ( Vvar__1___24Anonymous__22930 = Vvar__1___24Anonymous__22931
& Vvar__0__p__22928 = Vvar__0__p__22929 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__17586,Vvar__0___24Anonymous__17587] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__17586) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__17587)
=> Vvar__0___24Anonymous__17586 = Vvar__0___24Anonymous__17587 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__9107,Vvar__0__Qnum__9108,Vvar__1__Qden__9109,Vvar__1__Qden__9110] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9107,Vvar__1__Qden__9109) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9108,Vvar__1__Qden__9110)
=> ( Vvar__1__Qden__9109 = Vvar__1__Qden__9110
& Vvar__0__Qnum__9107 = Vvar__0__Qnum__9108 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__19922,Vvar__0__neg__19923,Vvar__1__cond__neg__19924,Vvar__1__cond__neg__19925] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__19922) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__19923)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__19922 = Vvar__0__neg__19923 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__24158,Vvar__0__nonneg__24159,Vvar__1__cond__nonneg__24160,Vvar__1__cond__nonneg__24161] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__24158) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__24159)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__24158 = Vvar__0__nonneg__24159 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__9172,Vvar__0__nonpos__9173,Vvar__1__cond__nonpos__9174,Vvar__1__cond__nonpos__9175] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9172) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9173)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__9172 = Vvar__0__nonpos__9173 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__19929,Vvar__0__nonzero__19930,Vvar__1__cond__nonzero__19931,Vvar__1__cond__nonzero__19932] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__19929) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__19930)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__19929 = Vvar__0__nonzero__19930 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__19915,Vvar__0__pos__19916,Vvar__1__cond__pos__19917,Vvar__1__cond__pos__19918] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__19915) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__19916)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__19915 = Vvar__0__pos__19916 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__20017,Vvar__0__x__20018,Vvar__1__n__20019,Vvar__1__n__20020,Vvar__2___24Anonymous__20021,Vvar__2___24Anonymous__20022] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__20017,Vvar__1__n__20019) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__20018,Vvar__1__n__20020)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__20019 = Vvar__1__n__20020
& Vvar__0__x__20017 = Vvar__0__x__20018 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__20007,Vvar__0__x__20008,Vvar__1___24Anonymous__20009,Vvar__1___24Anonymous__20010] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__20007) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__20008)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__20007 = Vvar__0__x__20008 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__20011,Vvar__0__x__20012,Vvar__1__n__20013,Vvar__1__n__20014,Vvar__2___24Anonymous__20015,Vvar__2___24Anonymous__20016] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__20011,Vvar__1__n__20013) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__20012,Vvar__1__n__20014)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__20013 = Vvar__1__n__20014
& Vvar__0__x__20011 = Vvar__0__x__20012 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__4012,Vvar__0___24Anonymous__4013,Vvar__1___24Anonymous__4014,Vvar__1___24Anonymous__4015,Vvar__2___24Anonymous__4016,Vvar__2___24Anonymous__4017,Vvar__3___24Anonymous__4018,Vvar__3___24Anonymous__4019,Vvar__4___24Anonymous__4020,Vvar__4___24Anonymous__4021,Vvar__5___24Anonymous__4022,Vvar__5___24Anonymous__4023,Vvar__6___24Anonymous__4024,Vvar__6___24Anonymous__4025,Vvar__7___24Anonymous__4026,Vvar__7___24Anonymous__4027] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4012,Vvar__1___24Anonymous__4014,Vvar__2___24Anonymous__4016,Vvar__3___24Anonymous__4018,Vvar__4___24Anonymous__4020,Vvar__5___24Anonymous__4022,Vvar__6___24Anonymous__4024,Vvar__7___24Anonymous__4026) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4013,Vvar__1___24Anonymous__4015,Vvar__2___24Anonymous__4017,Vvar__3___24Anonymous__4019,Vvar__4___24Anonymous__4021,Vvar__5___24Anonymous__4023,Vvar__6___24Anonymous__4025,Vvar__7___24Anonymous__4027)
=> ( Vvar__7___24Anonymous__4026 = Vvar__7___24Anonymous__4027
& Vvar__6___24Anonymous__4024 = Vvar__6___24Anonymous__4025
& Vvar__5___24Anonymous__4022 = Vvar__5___24Anonymous__4023
& Vvar__4___24Anonymous__4020 = Vvar__4___24Anonymous__4021
& Vvar__3___24Anonymous__4018 = Vvar__3___24Anonymous__4019
& Vvar__2___24Anonymous__4016 = Vvar__2___24Anonymous__4017
& Vvar__1___24Anonymous__4014 = Vvar__1___24Anonymous__4015
& Vvar__0___24Anonymous__4012 = Vvar__0___24Anonymous__4013 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__16846,Vvar__0___24Anonymous__16847,Vvar__1___24Anonymous__16848,Vvar__1___24Anonymous__16849] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__16846,Vvar__1___24Anonymous__16848) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__16847,Vvar__1___24Anonymous__16849)
=> ( Vvar__1___24Anonymous__16848 = Vvar__1___24Anonymous__16849
& Vvar__0___24Anonymous__16846 = Vvar__0___24Anonymous__16847 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9046,Vvar__0__X__9047,Vvar__1__lt__9048,Vvar__1__lt__9049,Vvar__2__eq__9050,Vvar__2__eq__9051,Vvar__3__x__9052,Vvar__3__x__9053,Vvar__4__y__9054,Vvar__4__y__9055,Vvar__5___24Anonymous__9056,Vvar__5___24Anonymous__9057] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9046,Vvar__1__lt__9048,Vvar__2__eq__9050,Vvar__3__x__9052,Vvar__4__y__9054) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9047,Vvar__1__lt__9049,Vvar__2__eq__9051,Vvar__3__x__9053,Vvar__4__y__9055)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9054 = Vvar__4__y__9055
& Vvar__3__x__9052 = Vvar__3__x__9053
& Vvar__2__eq__9050 = Vvar__2__eq__9051
& Vvar__1__lt__9048 = Vvar__1__lt__9049
& Vvar__0__X__9046 = Vvar__0__X__9047 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__9058,Vvar__0__X__9059,Vvar__1__lt__9060,Vvar__1__lt__9061,Vvar__2__eq__9062,Vvar__2__eq__9063,Vvar__3__x__9064,Vvar__3__x__9065,Vvar__4__y__9066,Vvar__4__y__9067,Vvar__5___24Anonymous__9068,Vvar__5___24Anonymous__9069] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9058,Vvar__1__lt__9060,Vvar__2__eq__9062,Vvar__3__x__9064,Vvar__4__y__9066) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9059,Vvar__1__lt__9061,Vvar__2__eq__9063,Vvar__3__x__9065,Vvar__4__y__9067)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9066 = Vvar__4__y__9067
& Vvar__3__x__9064 = Vvar__3__x__9065
& Vvar__2__eq__9062 = Vvar__2__eq__9063
& Vvar__1__lt__9060 = Vvar__1__lt__9061
& Vvar__0__X__9058 = Vvar__0__X__9059 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__9034,Vvar__0__X__9035,Vvar__1__lt__9036,Vvar__1__lt__9037,Vvar__2__eq__9038,Vvar__2__eq__9039,Vvar__3__x__9040,Vvar__3__x__9041,Vvar__4__y__9042,Vvar__4__y__9043,Vvar__5___24Anonymous__9044,Vvar__5___24Anonymous__9045] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9034,Vvar__1__lt__9036,Vvar__2__eq__9038,Vvar__3__x__9040,Vvar__4__y__9042) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9035,Vvar__1__lt__9037,Vvar__2__eq__9039,Vvar__3__x__9041,Vvar__4__y__9043)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9042 = Vvar__4__y__9043
& Vvar__3__x__9040 = Vvar__3__x__9041
& Vvar__2__eq__9038 = Vvar__2__eq__9039
& Vvar__1__lt__9036 = Vvar__1__lt__9037
& Vvar__0__X__9034 = Vvar__0__X__9035 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__8422,Vvar__0__n__8423] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8422) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8423)
=> Vvar__0__n__8422 = Vvar__0__n__8423 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__8424,Vvar__0__n__8425,Vvar__1___24Anonymous__8426,Vvar__1___24Anonymous__8427] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8424,Vvar__1___24Anonymous__8426) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8425,Vvar__1___24Anonymous__8427)
=> ( Vvar__1___24Anonymous__8426 = Vvar__1___24Anonymous__8427
& Vvar__0__n__8424 = Vvar__0__n__8425 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__3128,Vvar__0__A__3129,Vvar__1__h__3130,Vvar__1__h__3131,Vvar__2__n__3132,Vvar__2__n__3133,Vvar__3___24Anonymous__3134,Vvar__3___24Anonymous__3135] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3128,Vvar__1__h__3130,Vvar__2__n__3132,Vvar__3___24Anonymous__3134) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3129,Vvar__1__h__3131,Vvar__2__n__3133,Vvar__3___24Anonymous__3135)
=> ( Vvar__3___24Anonymous__3134 = Vvar__3___24Anonymous__3135
& Vvar__2__n__3132 = Vvar__2__n__3133
& Vvar__1__h__3130 = Vvar__1__h__3131
& Vvar__0__A__3128 = Vvar__0__A__3129 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__3126,Vvar__0__A__3127] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3126) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3127)
=> Vvar__0__A__3126 = Vvar__0__A__3127 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__22779,Vvar__0__a__22780,Vvar__1__b__22781,Vvar__1__b__22782,Vvar__2__u__22783,Vvar__2__u__22784,Vvar__3__v__22785,Vvar__3__v__22786,Vvar__4__d__22787,Vvar__4__d__22788,Vvar__5___24Anonymous__22789,Vvar__5___24Anonymous__22790,Vvar__6___24Anonymous__22791,Vvar__6___24Anonymous__22792] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__22779,Vvar__1__b__22781,Vvar__2__u__22783,Vvar__3__v__22785,Vvar__4__d__22787) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__22780,Vvar__1__b__22782,Vvar__2__u__22784,Vvar__3__v__22786,Vvar__4__d__22788)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__22787 = Vvar__4__d__22788
& Vvar__3__v__22785 = Vvar__3__v__22786
& Vvar__2__u__22783 = Vvar__2__u__22784
& Vvar__1__b__22781 = Vvar__1__b__22782
& Vvar__0__a__22779 = Vvar__0__a__22780 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__31799,Vvar__0__x__31800,Vvar__1__p__31801,Vvar__1__p__31802,Vvar__2__q__31803,Vvar__2__q__31804,Vvar__3__r__31805,Vvar__3__r__31806,Vvar__4___24Anonymous__31807,Vvar__4___24Anonymous__31808,Vvar__5___24Anonymous__31809,Vvar__5___24Anonymous__31810,Vvar__6___24Anonymous__31811,Vvar__6___24Anonymous__31812] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__31799,Vvar__1__p__31801,Vvar__2__q__31803,Vvar__3__r__31805) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__31800,Vvar__1__p__31802,Vvar__2__q__31804,Vvar__3__r__31806)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__31805 = Vvar__3__r__31806
& Vvar__2__q__31803 = Vvar__2__q__31804
& Vvar__1__p__31801 = Vvar__1__p__31802
& Vvar__0__x__31799 = Vvar__0__x__31800 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__5174,Vvar__0__C__5175,Vvar__1___24Anonymous__5176,Vvar__1___24Anonymous__5177] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5174,Vvar__1___24Anonymous__5176) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5175,Vvar__1___24Anonymous__5177)
=> ( Vvar__1___24Anonymous__5176 = Vvar__1___24Anonymous__5177
& Vvar__0__C__5174 = Vvar__0__C__5175 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__5178,Vvar__0__C__5179,Vvar__1___24Anonymous__5180,Vvar__1___24Anonymous__5181,Vvar__2___24Anonymous__5182,Vvar__2___24Anonymous__5183] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5178,Vvar__1___24Anonymous__5180,Vvar__2___24Anonymous__5182) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5179,Vvar__1___24Anonymous__5181,Vvar__2___24Anonymous__5183)
=> ( Vvar__2___24Anonymous__5182 = Vvar__2___24Anonymous__5183
& Vvar__1___24Anonymous__5180 = Vvar__1___24Anonymous__5181
& Vvar__0__C__5178 = Vvar__0__C__5179 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__5170,Vvar__0__C__5171,Vvar__1___24Anonymous__5172,Vvar__1___24Anonymous__5173] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5170,Vvar__1___24Anonymous__5172) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5171,Vvar__1___24Anonymous__5173)
=> ( Vvar__1___24Anonymous__5172 = Vvar__1___24Anonymous__5173
& Vvar__0__C__5170 = Vvar__0__C__5171 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__5190,Vvar__0__C__5191,Vvar__1___24Anonymous__5192,Vvar__1___24Anonymous__5193,Vvar__2___24Anonymous__5194,Vvar__2___24Anonymous__5195] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5190,Vvar__1___24Anonymous__5192,Vvar__2___24Anonymous__5194) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5191,Vvar__1___24Anonymous__5193,Vvar__2___24Anonymous__5195)
=> ( Vvar__2___24Anonymous__5194 = Vvar__2___24Anonymous__5195
& Vvar__1___24Anonymous__5192 = Vvar__1___24Anonymous__5193
& Vvar__0__C__5190 = Vvar__0__C__5191 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__5196,Vvar__0__C__5197,Vvar__1___24Anonymous__5198,Vvar__1___24Anonymous__5199] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5196,Vvar__1___24Anonymous__5198) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5197,Vvar__1___24Anonymous__5199)
=> ( Vvar__1___24Anonymous__5198 = Vvar__1___24Anonymous__5199
& Vvar__0__C__5196 = Vvar__0__C__5197 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__5200,Vvar__0__C__5201,Vvar__1___24Anonymous__5202,Vvar__1___24Anonymous__5203,Vvar__2___24Anonymous__5204,Vvar__2___24Anonymous__5205] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5200,Vvar__1___24Anonymous__5202,Vvar__2___24Anonymous__5204) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5201,Vvar__1___24Anonymous__5203,Vvar__2___24Anonymous__5205)
=> ( Vvar__2___24Anonymous__5204 = Vvar__2___24Anonymous__5205
& Vvar__1___24Anonymous__5202 = Vvar__1___24Anonymous__5203
& Vvar__0__C__5200 = Vvar__0__C__5201 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__5184,Vvar__0__C__5185,Vvar__1___24Anonymous__5186,Vvar__1___24Anonymous__5187,Vvar__2___24Anonymous__5188,Vvar__2___24Anonymous__5189] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5184,Vvar__1___24Anonymous__5186,Vvar__2___24Anonymous__5188) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5185,Vvar__1___24Anonymous__5187,Vvar__2___24Anonymous__5189)
=> ( Vvar__2___24Anonymous__5188 = Vvar__2___24Anonymous__5189
& Vvar__1___24Anonymous__5186 = Vvar__1___24Anonymous__5187
& Vvar__0__C__5184 = Vvar__0__C__5185 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__5245,Vvar__0__C__5246,Vvar__1___24Anonymous__5247,Vvar__1___24Anonymous__5248,Vvar__2___24Anonymous__5249,Vvar__2___24Anonymous__5250,Vvar__3___24Anonymous__5251,Vvar__3___24Anonymous__5252] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5245,Vvar__1___24Anonymous__5247,Vvar__2___24Anonymous__5249,Vvar__3___24Anonymous__5251) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5246,Vvar__1___24Anonymous__5248,Vvar__2___24Anonymous__5250,Vvar__3___24Anonymous__5252)
=> ( Vvar__3___24Anonymous__5251 = Vvar__3___24Anonymous__5252
& Vvar__2___24Anonymous__5249 = Vvar__2___24Anonymous__5250
& Vvar__1___24Anonymous__5247 = Vvar__1___24Anonymous__5248
& Vvar__0__C__5245 = Vvar__0__C__5246 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__5235,Vvar__0__C__5236,Vvar__1___24Anonymous__5237,Vvar__1___24Anonymous__5238] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5235,Vvar__1___24Anonymous__5237) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5236,Vvar__1___24Anonymous__5238)
=> ( Vvar__1___24Anonymous__5237 = Vvar__1___24Anonymous__5238
& Vvar__0__C__5235 = Vvar__0__C__5236 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__5239,Vvar__0__C__5240,Vvar__1___24Anonymous__5241,Vvar__1___24Anonymous__5242,Vvar__2___24Anonymous__5243,Vvar__2___24Anonymous__5244] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5239,Vvar__1___24Anonymous__5241,Vvar__2___24Anonymous__5243) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5240,Vvar__1___24Anonymous__5242,Vvar__2___24Anonymous__5244)
=> ( Vvar__2___24Anonymous__5243 = Vvar__2___24Anonymous__5244
& Vvar__1___24Anonymous__5241 = Vvar__1___24Anonymous__5242
& Vvar__0__C__5239 = Vvar__0__C__5240 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__18675,Vvar__0___24Anonymous__18676,Vvar__1___24Anonymous__18677,Vvar__1___24Anonymous__18678] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__18675,Vvar__1___24Anonymous__18677) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__18676,Vvar__1___24Anonymous__18678)
=> ( Vvar__1___24Anonymous__18677 = Vvar__1___24Anonymous__18678
& Vvar__0___24Anonymous__18675 = Vvar__0___24Anonymous__18676 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__18671,Vvar__0___24Anonymous__18672,Vvar__1___24Anonymous__18673,Vvar__1___24Anonymous__18674] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__18671,Vvar__1___24Anonymous__18673) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__18672,Vvar__1___24Anonymous__18674)
=> ( Vvar__1___24Anonymous__18673 = Vvar__1___24Anonymous__18674
& Vvar__0___24Anonymous__18671 = Vvar__0___24Anonymous__18672 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__9322,Vvar__0__r__9323] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__9322) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__9323)
=> Vvar__0__r__9322 = Vvar__0__r__9323 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__9310,Vvar__0__r1__9311,Vvar__1__r2__9312,Vvar__1__r2__9313] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__9310,Vvar__1__r2__9312) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__9311,Vvar__1__r2__9313)
=> ( Vvar__1__r2__9312 = Vvar__1__r2__9313
& Vvar__0__r1__9310 = Vvar__0__r1__9311 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__9314,Vvar__0__r1__9315,Vvar__1__r2__9316,Vvar__1__r2__9317] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__9314,Vvar__1__r2__9316) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__9315,Vvar__1__r2__9317)
=> ( Vvar__1__r2__9316 = Vvar__1__r2__9317
& Vvar__0__r1__9314 = Vvar__0__r1__9315 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__9324,Vvar__0__r__9325] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__9324) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__9325)
=> Vvar__0__r__9324 = Vvar__0__r__9325 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__9306,Vvar__0__r1__9307,Vvar__1__r2__9308,Vvar__1__r2__9309] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__9306,Vvar__1__r2__9308) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__9307,Vvar__1__r2__9309)
=> ( Vvar__1__r2__9308 = Vvar__1__r2__9309
& Vvar__0__r1__9306 = Vvar__0__r1__9307 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__9318,Vvar__0__r1__9319,Vvar__1__z__9320,Vvar__1__z__9321] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__9318,Vvar__1__z__9320) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__9319,Vvar__1__z__9321)
=> ( Vvar__1__z__9320 = Vvar__1__z__9321
& Vvar__0__r1__9318 = Vvar__0__r1__9319 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__9302,Vvar__0__r__9303] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__9302) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__9303)
=> Vvar__0__r__9302 = Vvar__0__r__9303 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__9304,Vvar__0__r__9305] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__9304) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__9305)
=> Vvar__0__r__9304 = Vvar__0__r__9305 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__2818,Vvar__0__T__2819,Vvar__1__Flhs__2820,Vvar__1__Flhs__2821,Vvar__2__Fop__2822,Vvar__2__Fop__2823,Vvar__3__Frhs__2824,Vvar__3__Frhs__2825] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2818,Vvar__1__Flhs__2820,Vvar__2__Fop__2822,Vvar__3__Frhs__2824) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2819,Vvar__1__Flhs__2821,Vvar__2__Fop__2823,Vvar__3__Frhs__2825)
=> ( Vvar__3__Frhs__2824 = Vvar__3__Frhs__2825
& Vvar__2__Fop__2822 = Vvar__2__Fop__2823
& Vvar__1__Flhs__2820 = Vvar__1__Flhs__2821
& Vvar__0__T__2818 = Vvar__0__T__2819 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__20157,Vvar__0__C__20158,Vvar__1___24Anonymous__20159,Vvar__1___24Anonymous__20160,Vvar__2___24Anonymous__20161,Vvar__2___24Anonymous__20162] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20157,Vvar__1___24Anonymous__20159,Vvar__2___24Anonymous__20161) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20158,Vvar__1___24Anonymous__20160,Vvar__2___24Anonymous__20162)
=> ( Vvar__2___24Anonymous__20161 = Vvar__2___24Anonymous__20162
& Vvar__1___24Anonymous__20159 = Vvar__1___24Anonymous__20160
& Vvar__0__C__20157 = Vvar__0__C__20158 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__20163,Vvar__0__C__20164,Vvar__1___24Anonymous__20165,Vvar__1___24Anonymous__20166] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20163,Vvar__1___24Anonymous__20165) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20164,Vvar__1___24Anonymous__20166)
=> ( Vvar__1___24Anonymous__20165 = Vvar__1___24Anonymous__20166
& Vvar__0__C__20163 = Vvar__0__C__20164 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__20137,Vvar__0__C__20138,Vvar__1___24Anonymous__20139,Vvar__1___24Anonymous__20140] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20137,Vvar__1___24Anonymous__20139) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20138,Vvar__1___24Anonymous__20140)
=> ( Vvar__1___24Anonymous__20139 = Vvar__1___24Anonymous__20140
& Vvar__0__C__20137 = Vvar__0__C__20138 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__20145,Vvar__0__C__20146,Vvar__1___24Anonymous__20147,Vvar__1___24Anonymous__20148,Vvar__2___24Anonymous__20149,Vvar__2___24Anonymous__20150] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20145,Vvar__1___24Anonymous__20147,Vvar__2___24Anonymous__20149) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20146,Vvar__1___24Anonymous__20148,Vvar__2___24Anonymous__20150)
=> ( Vvar__2___24Anonymous__20149 = Vvar__2___24Anonymous__20150
& Vvar__1___24Anonymous__20147 = Vvar__1___24Anonymous__20148
& Vvar__0__C__20145 = Vvar__0__C__20146 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__20151,Vvar__0__C__20152,Vvar__1___24Anonymous__20153,Vvar__1___24Anonymous__20154,Vvar__2___24Anonymous__20155,Vvar__2___24Anonymous__20156] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20151,Vvar__1___24Anonymous__20153,Vvar__2___24Anonymous__20155) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20152,Vvar__1___24Anonymous__20154,Vvar__2___24Anonymous__20156)
=> ( Vvar__2___24Anonymous__20155 = Vvar__2___24Anonymous__20156
& Vvar__1___24Anonymous__20153 = Vvar__1___24Anonymous__20154
& Vvar__0__C__20151 = Vvar__0__C__20152 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__20141,Vvar__0__C__20142,Vvar__1___24Anonymous__20143,Vvar__1___24Anonymous__20144] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20141,Vvar__1___24Anonymous__20143) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20142,Vvar__1___24Anonymous__20144)
=> ( Vvar__1___24Anonymous__20143 = Vvar__1___24Anonymous__20144
& Vvar__0__C__20141 = Vvar__0__C__20142 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__20167,Vvar__0__C__20168] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20167) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20168)
=> Vvar__0__C__20167 = Vvar__0__C__20168 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__22643,Vvar__0__TA__22644,Vvar__1__TX__22645,Vvar__1__TX__22646,Vvar__2__AA__22647,Vvar__2__AA__22648,Vvar__3__AF__22649,Vvar__3__AF__22650,Vvar__4___24Anonymous__22651,Vvar__4___24Anonymous__22652,Vvar__5___24Anonymous__22653,Vvar__5___24Anonymous__22654] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22643,Vvar__1__TX__22645,Vvar__2__AA__22647,Vvar__3__AF__22649,Vvar__4___24Anonymous__22651,Vvar__5___24Anonymous__22653) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22644,Vvar__1__TX__22646,Vvar__2__AA__22648,Vvar__3__AF__22650,Vvar__4___24Anonymous__22652,Vvar__5___24Anonymous__22654)
=> ( Vvar__5___24Anonymous__22653 = Vvar__5___24Anonymous__22654
& Vvar__4___24Anonymous__22651 = Vvar__4___24Anonymous__22652
& Vvar__3__AF__22649 = Vvar__3__AF__22650
& Vvar__2__AA__22647 = Vvar__2__AA__22648
& Vvar__1__TX__22645 = Vvar__1__TX__22646
& Vvar__0__TA__22643 = Vvar__0__TA__22644 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__22655,Vvar__0__TA__22656,Vvar__1__TX__22657,Vvar__1__TX__22658,Vvar__2__AA__22659,Vvar__2__AA__22660,Vvar__3__AF__22661,Vvar__3__AF__22662,Vvar__4___24Anonymous__22663,Vvar__4___24Anonymous__22664,Vvar__5___24Anonymous__22665,Vvar__5___24Anonymous__22666] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22655,Vvar__1__TX__22657,Vvar__2__AA__22659,Vvar__3__AF__22661,Vvar__4___24Anonymous__22663,Vvar__5___24Anonymous__22665) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22656,Vvar__1__TX__22658,Vvar__2__AA__22660,Vvar__3__AF__22662,Vvar__4___24Anonymous__22664,Vvar__5___24Anonymous__22666)
=> ( Vvar__5___24Anonymous__22665 = Vvar__5___24Anonymous__22666
& Vvar__4___24Anonymous__22663 = Vvar__4___24Anonymous__22664
& Vvar__3__AF__22661 = Vvar__3__AF__22662
& Vvar__2__AA__22659 = Vvar__2__AA__22660
& Vvar__1__TX__22657 = Vvar__1__TX__22658
& Vvar__0__TA__22655 = Vvar__0__TA__22656 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__22667,Vvar__0__TA__22668,Vvar__1__TX__22669,Vvar__1__TX__22670,Vvar__2__AA__22671,Vvar__2__AA__22672,Vvar__3__AF__22673,Vvar__3__AF__22674,Vvar__4___24Anonymous__22675,Vvar__4___24Anonymous__22676,Vvar__5___24Anonymous__22677,Vvar__5___24Anonymous__22678] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22667,Vvar__1__TX__22669,Vvar__2__AA__22671,Vvar__3__AF__22673,Vvar__4___24Anonymous__22675,Vvar__5___24Anonymous__22677) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22668,Vvar__1__TX__22670,Vvar__2__AA__22672,Vvar__3__AF__22674,Vvar__4___24Anonymous__22676,Vvar__5___24Anonymous__22678)
=> ( Vvar__5___24Anonymous__22677 = Vvar__5___24Anonymous__22678
& Vvar__4___24Anonymous__22675 = Vvar__4___24Anonymous__22676
& Vvar__3__AF__22673 = Vvar__3__AF__22674
& Vvar__2__AA__22671 = Vvar__2__AA__22672
& Vvar__1__TX__22669 = Vvar__1__TX__22670
& Vvar__0__TA__22667 = Vvar__0__TA__22668 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22625,Vvar__0__TA__22626,Vvar__1__TX__22627,Vvar__1__TX__22628,Vvar__2__AA__22629,Vvar__2__AA__22630,Vvar__3__AF__22631,Vvar__3__AF__22632] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22625,Vvar__1__TX__22627,Vvar__2__AA__22629,Vvar__3__AF__22631) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22626,Vvar__1__TX__22628,Vvar__2__AA__22630,Vvar__3__AF__22632)
=> ( Vvar__3__AF__22631 = Vvar__3__AF__22632
& Vvar__2__AA__22629 = Vvar__2__AA__22630
& Vvar__1__TX__22627 = Vvar__1__TX__22628
& Vvar__0__TA__22625 = Vvar__0__TA__22626 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__22689,Vvar__0__TA__22690,Vvar__1__TX__22691,Vvar__1__TX__22692,Vvar__2__AA__22693,Vvar__2__AA__22694,Vvar__3__AF__22695,Vvar__3__AF__22696,Vvar__4___24Anonymous__22697,Vvar__4___24Anonymous__22698,Vvar__5___24Anonymous__22699,Vvar__5___24Anonymous__22700,Vvar__6___24Anonymous__22701,Vvar__6___24Anonymous__22702] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22689,Vvar__1__TX__22691,Vvar__2__AA__22693,Vvar__3__AF__22695,Vvar__4___24Anonymous__22697,Vvar__5___24Anonymous__22699,Vvar__6___24Anonymous__22701) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22690,Vvar__1__TX__22692,Vvar__2__AA__22694,Vvar__3__AF__22696,Vvar__4___24Anonymous__22698,Vvar__5___24Anonymous__22700,Vvar__6___24Anonymous__22702)
=> ( Vvar__6___24Anonymous__22701 = Vvar__6___24Anonymous__22702
& Vvar__5___24Anonymous__22699 = Vvar__5___24Anonymous__22700
& Vvar__4___24Anonymous__22697 = Vvar__4___24Anonymous__22698
& Vvar__3__AF__22695 = Vvar__3__AF__22696
& Vvar__2__AA__22693 = Vvar__2__AA__22694
& Vvar__1__TX__22691 = Vvar__1__TX__22692
& Vvar__0__TA__22689 = Vvar__0__TA__22690 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__22679,Vvar__0__TA__22680,Vvar__1__TX__22681,Vvar__1__TX__22682,Vvar__2__AA__22683,Vvar__2__AA__22684,Vvar__3__AF__22685,Vvar__3__AF__22686,Vvar__4___24Anonymous__22687,Vvar__4___24Anonymous__22688] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22679,Vvar__1__TX__22681,Vvar__2__AA__22683,Vvar__3__AF__22685,Vvar__4___24Anonymous__22687) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22680,Vvar__1__TX__22682,Vvar__2__AA__22684,Vvar__3__AF__22686,Vvar__4___24Anonymous__22688)
=> ( Vvar__4___24Anonymous__22687 = Vvar__4___24Anonymous__22688
& Vvar__3__AF__22685 = Vvar__3__AF__22686
& Vvar__2__AA__22683 = Vvar__2__AA__22684
& Vvar__1__TX__22681 = Vvar__1__TX__22682
& Vvar__0__TA__22679 = Vvar__0__TA__22680 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__22617,Vvar__0__TA__22618,Vvar__1__TX__22619,Vvar__1__TX__22620,Vvar__2__AA__22621,Vvar__2__AA__22622,Vvar__3__AF__22623,Vvar__3__AF__22624] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22617,Vvar__1__TX__22619,Vvar__2__AA__22621,Vvar__3__AF__22623) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22618,Vvar__1__TX__22620,Vvar__2__AA__22622,Vvar__3__AF__22624)
=> ( Vvar__3__AF__22623 = Vvar__3__AF__22624
& Vvar__2__AA__22621 = Vvar__2__AA__22622
& Vvar__1__TX__22619 = Vvar__1__TX__22620
& Vvar__0__TA__22617 = Vvar__0__TA__22618 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__22633,Vvar__0__TA__22634,Vvar__1__TX__22635,Vvar__1__TX__22636,Vvar__2__AA__22637,Vvar__2__AA__22638,Vvar__3__AF__22639,Vvar__3__AF__22640,Vvar__4___24Anonymous__22641,Vvar__4___24Anonymous__22642] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22633,Vvar__1__TX__22635,Vvar__2__AA__22637,Vvar__3__AF__22639,Vvar__4___24Anonymous__22641) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22634,Vvar__1__TX__22636,Vvar__2__AA__22638,Vvar__3__AF__22640,Vvar__4___24Anonymous__22642)
=> ( Vvar__4___24Anonymous__22641 = Vvar__4___24Anonymous__22642
& Vvar__3__AF__22639 = Vvar__3__AF__22640
& Vvar__2__AA__22637 = Vvar__2__AA__22638
& Vvar__1__TX__22635 = Vvar__1__TX__22636
& Vvar__0__TA__22633 = Vvar__0__TA__22634 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__22732,Vvar__0__A__22733,Vvar__1___24Anonymous__22734,Vvar__1___24Anonymous__22735,Vvar__2___24Anonymous__22736,Vvar__2___24Anonymous__22737,Vvar__3___24Anonymous__22738,Vvar__3___24Anonymous__22739] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__22732,Vvar__1___24Anonymous__22734,Vvar__2___24Anonymous__22736,Vvar__3___24Anonymous__22738) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__22733,Vvar__1___24Anonymous__22735,Vvar__2___24Anonymous__22737,Vvar__3___24Anonymous__22739)
=> ( Vvar__3___24Anonymous__22738 = Vvar__3___24Anonymous__22739
& Vvar__2___24Anonymous__22736 = Vvar__2___24Anonymous__22737
& Vvar__1___24Anonymous__22734 = Vvar__1___24Anonymous__22735
& Vvar__0__A__22732 = Vvar__0__A__22733 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__22728,Vvar__0__A__22729,Vvar__1___24Anonymous__22730,Vvar__1___24Anonymous__22731] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__22728,Vvar__1___24Anonymous__22730) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__22729,Vvar__1___24Anonymous__22731)
=> ( Vvar__1___24Anonymous__22730 = Vvar__1___24Anonymous__22731
& Vvar__0__A__22728 = Vvar__0__A__22729 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__22726,Vvar__0__A__22727] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__22726) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__22727)
=> Vvar__0__A__22726 = Vvar__0__A__22727 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__3358,Vvar__0___24Anonymous__3359,Vvar__1___24Anonymous__3360,Vvar__1___24Anonymous__3361] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__3358,Vvar__1___24Anonymous__3360) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__3359,Vvar__1___24Anonymous__3361)
=> ( Vvar__1___24Anonymous__3360 = Vvar__1___24Anonymous__3361
& Vvar__0___24Anonymous__3358 = Vvar__0___24Anonymous__3359 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__3362,Vvar__0___24Anonymous__3363,Vvar__1___24Anonymous__3364,Vvar__1___24Anonymous__3365,Vvar__2___24Anonymous__3366,Vvar__2___24Anonymous__3367] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__3362,Vvar__1___24Anonymous__3364,Vvar__2___24Anonymous__3366) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__3363,Vvar__1___24Anonymous__3365,Vvar__2___24Anonymous__3367)
=> ( Vvar__2___24Anonymous__3366 = Vvar__2___24Anonymous__3367
& Vvar__1___24Anonymous__3364 = Vvar__1___24Anonymous__3365
& Vvar__0___24Anonymous__3362 = Vvar__0___24Anonymous__3363 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__3354,Vvar__0___24Anonymous__3355,Vvar__1___24Anonymous__3356,Vvar__1___24Anonymous__3357] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__3354,Vvar__1___24Anonymous__3356) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__3355,Vvar__1___24Anonymous__3357)
=> ( Vvar__1___24Anonymous__3356 = Vvar__1___24Anonymous__3357
& Vvar__0___24Anonymous__3354 = Vvar__0___24Anonymous__3355 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7075,Vvar__0__C__7076] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7075) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7076)
=> Vvar__0__C__7075 = Vvar__0__C__7076 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__7073,Vvar__0__C__7074] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7073) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7074)
=> Vvar__0__C__7073 = Vvar__0__C__7074 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__7081,Vvar__0__C__7082,Vvar__1___24Anonymous__7083,Vvar__1___24Anonymous__7084] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7081,Vvar__1___24Anonymous__7083) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7082,Vvar__1___24Anonymous__7084)
=> ( Vvar__1___24Anonymous__7083 = Vvar__1___24Anonymous__7084
& Vvar__0__C__7081 = Vvar__0__C__7082 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__7085,Vvar__0__C__7086,Vvar__1___24Anonymous__7087,Vvar__1___24Anonymous__7088,Vvar__2___24Anonymous__7089,Vvar__2___24Anonymous__7090] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7085,Vvar__1___24Anonymous__7087,Vvar__2___24Anonymous__7089) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7086,Vvar__1___24Anonymous__7088,Vvar__2___24Anonymous__7090)
=> ( Vvar__2___24Anonymous__7089 = Vvar__2___24Anonymous__7090
& Vvar__1___24Anonymous__7087 = Vvar__1___24Anonymous__7088
& Vvar__0__C__7085 = Vvar__0__C__7086 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__7077,Vvar__0__C__7078,Vvar__1___24Anonymous__7079,Vvar__1___24Anonymous__7080] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7077,Vvar__1___24Anonymous__7079) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7078,Vvar__1___24Anonymous__7080)
=> ( Vvar__1___24Anonymous__7079 = Vvar__1___24Anonymous__7080
& Vvar__0__C__7077 = Vvar__0__C__7078 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__7111,Vvar__0__C__7112,Vvar__1___24Anonymous__7113,Vvar__1___24Anonymous__7114,Vvar__2___24Anonymous__7115,Vvar__2___24Anonymous__7116] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7111,Vvar__1___24Anonymous__7113,Vvar__2___24Anonymous__7115) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7112,Vvar__1___24Anonymous__7114,Vvar__2___24Anonymous__7116)
=> ( Vvar__2___24Anonymous__7115 = Vvar__2___24Anonymous__7116
& Vvar__1___24Anonymous__7113 = Vvar__1___24Anonymous__7114
& Vvar__0__C__7111 = Vvar__0__C__7112 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__7107,Vvar__0__C__7108,Vvar__1___24Anonymous__7109,Vvar__1___24Anonymous__7110] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7107,Vvar__1___24Anonymous__7109) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7108,Vvar__1___24Anonymous__7110)
=> ( Vvar__1___24Anonymous__7109 = Vvar__1___24Anonymous__7110
& Vvar__0__C__7107 = Vvar__0__C__7108 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__7097,Vvar__0__C__7098,Vvar__1___24Anonymous__7099,Vvar__1___24Anonymous__7100,Vvar__2___24Anonymous__7101,Vvar__2___24Anonymous__7102] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7097,Vvar__1___24Anonymous__7099,Vvar__2___24Anonymous__7101) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7098,Vvar__1___24Anonymous__7100,Vvar__2___24Anonymous__7102)
=> ( Vvar__2___24Anonymous__7101 = Vvar__2___24Anonymous__7102
& Vvar__1___24Anonymous__7099 = Vvar__1___24Anonymous__7100
& Vvar__0__C__7097 = Vvar__0__C__7098 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__7103,Vvar__0__C__7104,Vvar__1___24Anonymous__7105,Vvar__1___24Anonymous__7106] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7103,Vvar__1___24Anonymous__7105) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7104,Vvar__1___24Anonymous__7106)
=> ( Vvar__1___24Anonymous__7105 = Vvar__1___24Anonymous__7106
& Vvar__0__C__7103 = Vvar__0__C__7104 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__7117,Vvar__0__C__7118,Vvar__1___24Anonymous__7119,Vvar__1___24Anonymous__7120,Vvar__2___24Anonymous__7121,Vvar__2___24Anonymous__7122] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7117,Vvar__1___24Anonymous__7119,Vvar__2___24Anonymous__7121) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7118,Vvar__1___24Anonymous__7120,Vvar__2___24Anonymous__7122)
=> ( Vvar__2___24Anonymous__7121 = Vvar__2___24Anonymous__7122
& Vvar__1___24Anonymous__7119 = Vvar__1___24Anonymous__7120
& Vvar__0__C__7117 = Vvar__0__C__7118 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__7091,Vvar__0__C__7092,Vvar__1___24Anonymous__7093,Vvar__1___24Anonymous__7094,Vvar__2___24Anonymous__7095,Vvar__2___24Anonymous__7096] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7091,Vvar__1___24Anonymous__7093,Vvar__2___24Anonymous__7095) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7092,Vvar__1___24Anonymous__7094,Vvar__2___24Anonymous__7096)
=> ( Vvar__2___24Anonymous__7095 = Vvar__2___24Anonymous__7096
& Vvar__1___24Anonymous__7093 = Vvar__1___24Anonymous__7094
& Vvar__0__C__7091 = Vvar__0__C__7092 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__7428,Vvar__0__C__7429,Vvar__1__num__7430,Vvar__1__num__7431,Vvar__2__denum__7432,Vvar__2__denum__7433,Vvar__3__condition__7434,Vvar__3__condition__7435] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7428,Vvar__1__num__7430,Vvar__2__denum__7432,Vvar__3__condition__7434) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7429,Vvar__1__num__7431,Vvar__2__denum__7433,Vvar__3__condition__7435)
=> ( Vvar__3__condition__7434 = Vvar__3__condition__7435
& Vvar__2__denum__7432 = Vvar__2__denum__7433
& Vvar__1__num__7430 = Vvar__1__num__7431
& Vvar__0__C__7428 = Vvar__0__C__7429 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__7725,Vvar__0__C__7726,Vvar__1__rsplit__left__7727,Vvar__1__rsplit__left__7728,Vvar__2__rsplit__common__7729,Vvar__2__rsplit__common__7730,Vvar__3__rsplit__right__7731,Vvar__3__rsplit__right__7732] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7725,Vvar__1__rsplit__left__7727,Vvar__2__rsplit__common__7729,Vvar__3__rsplit__right__7731) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7726,Vvar__1__rsplit__left__7728,Vvar__2__rsplit__common__7730,Vvar__3__rsplit__right__7732)
=> ( Vvar__3__rsplit__right__7731 = Vvar__3__rsplit__right__7732
& Vvar__2__rsplit__common__7729 = Vvar__2__rsplit__common__7730
& Vvar__1__rsplit__left__7727 = Vvar__1__rsplit__left__7728
& Vvar__0__C__7725 = Vvar__0__C__7726 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__23308,Vvar__0__hypo__type__23309,Vvar__1__hypo__proof__23310,Vvar__1__hypo__proof__23311] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__23308,Vvar__1__hypo__proof__23310) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__23309,Vvar__1__hypo__proof__23311)
=> ( Vvar__1__hypo__proof__23310 = Vvar__1__hypo__proof__23311
& Vvar__0__hypo__type__23308 = Vvar__0__hypo__type__23309 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__10739,Vvar__0__C__10740] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10739) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10740)
=> Vvar__0__C__10739 = Vvar__0__C__10740 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__10737,Vvar__0__C__10738] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10737) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10738)
=> Vvar__0__C__10737 = Vvar__0__C__10738 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__10745,Vvar__0__C__10746,Vvar__1___24Anonymous__10747,Vvar__1___24Anonymous__10748] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10745,Vvar__1___24Anonymous__10747) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10746,Vvar__1___24Anonymous__10748)
=> ( Vvar__1___24Anonymous__10747 = Vvar__1___24Anonymous__10748
& Vvar__0__C__10745 = Vvar__0__C__10746 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__10749,Vvar__0__C__10750,Vvar__1___24Anonymous__10751,Vvar__1___24Anonymous__10752,Vvar__2___24Anonymous__10753,Vvar__2___24Anonymous__10754] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10749,Vvar__1___24Anonymous__10751,Vvar__2___24Anonymous__10753) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10750,Vvar__1___24Anonymous__10752,Vvar__2___24Anonymous__10754)
=> ( Vvar__2___24Anonymous__10753 = Vvar__2___24Anonymous__10754
& Vvar__1___24Anonymous__10751 = Vvar__1___24Anonymous__10752
& Vvar__0__C__10749 = Vvar__0__C__10750 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__10741,Vvar__0__C__10742,Vvar__1___24Anonymous__10743,Vvar__1___24Anonymous__10744] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10741,Vvar__1___24Anonymous__10743) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10742,Vvar__1___24Anonymous__10744)
=> ( Vvar__1___24Anonymous__10743 = Vvar__1___24Anonymous__10744
& Vvar__0__C__10741 = Vvar__0__C__10742 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__10761,Vvar__0__C__10762,Vvar__1___24Anonymous__10763,Vvar__1___24Anonymous__10764,Vvar__2___24Anonymous__10765,Vvar__2___24Anonymous__10766] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10761,Vvar__1___24Anonymous__10763,Vvar__2___24Anonymous__10765) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10762,Vvar__1___24Anonymous__10764,Vvar__2___24Anonymous__10766)
=> ( Vvar__2___24Anonymous__10765 = Vvar__2___24Anonymous__10766
& Vvar__1___24Anonymous__10763 = Vvar__1___24Anonymous__10764
& Vvar__0__C__10761 = Vvar__0__C__10762 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__10767,Vvar__0__C__10768,Vvar__1___24Anonymous__10769,Vvar__1___24Anonymous__10770] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10767,Vvar__1___24Anonymous__10769) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10768,Vvar__1___24Anonymous__10770)
=> ( Vvar__1___24Anonymous__10769 = Vvar__1___24Anonymous__10770
& Vvar__0__C__10767 = Vvar__0__C__10768 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__10771,Vvar__0__C__10772,Vvar__1___24Anonymous__10773,Vvar__1___24Anonymous__10774,Vvar__2___24Anonymous__10775,Vvar__2___24Anonymous__10776] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10771,Vvar__1___24Anonymous__10773,Vvar__2___24Anonymous__10775) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10772,Vvar__1___24Anonymous__10774,Vvar__2___24Anonymous__10776)
=> ( Vvar__2___24Anonymous__10775 = Vvar__2___24Anonymous__10776
& Vvar__1___24Anonymous__10773 = Vvar__1___24Anonymous__10774
& Vvar__0__C__10771 = Vvar__0__C__10772 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__10755,Vvar__0__C__10756,Vvar__1___24Anonymous__10757,Vvar__1___24Anonymous__10758,Vvar__2___24Anonymous__10759,Vvar__2___24Anonymous__10760] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10755,Vvar__1___24Anonymous__10757,Vvar__2___24Anonymous__10759) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10756,Vvar__1___24Anonymous__10758,Vvar__2___24Anonymous__10760)
=> ( Vvar__2___24Anonymous__10759 = Vvar__2___24Anonymous__10760
& Vvar__1___24Anonymous__10757 = Vvar__1___24Anonymous__10758
& Vvar__0__C__10755 = Vvar__0__C__10756 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__10394,Vvar__0__C__10395,Vvar__1___24Anonymous__10396,Vvar__1___24Anonymous__10397,Vvar__2___24Anonymous__10398,Vvar__2___24Anonymous__10399,Vvar__3___24Anonymous__10400,Vvar__3___24Anonymous__10401] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__10394,Vvar__1___24Anonymous__10396,Vvar__2___24Anonymous__10398,Vvar__3___24Anonymous__10400) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__10395,Vvar__1___24Anonymous__10397,Vvar__2___24Anonymous__10399,Vvar__3___24Anonymous__10401)
=> ( Vvar__3___24Anonymous__10400 = Vvar__3___24Anonymous__10401
& Vvar__2___24Anonymous__10398 = Vvar__2___24Anonymous__10399
& Vvar__1___24Anonymous__10396 = Vvar__1___24Anonymous__10397
& Vvar__0__C__10394 = Vvar__0__C__10395 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__10384,Vvar__0__C__10385,Vvar__1___24Anonymous__10386,Vvar__1___24Anonymous__10387] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__10384,Vvar__1___24Anonymous__10386) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__10385,Vvar__1___24Anonymous__10387)
=> ( Vvar__1___24Anonymous__10386 = Vvar__1___24Anonymous__10387
& Vvar__0__C__10384 = Vvar__0__C__10385 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__10388,Vvar__0__C__10389,Vvar__1___24Anonymous__10390,Vvar__1___24Anonymous__10391,Vvar__2___24Anonymous__10392,Vvar__2___24Anonymous__10393] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__10388,Vvar__1___24Anonymous__10390,Vvar__2___24Anonymous__10392) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__10389,Vvar__1___24Anonymous__10391,Vvar__2___24Anonymous__10393)
=> ( Vvar__2___24Anonymous__10392 = Vvar__2___24Anonymous__10393
& Vvar__1___24Anonymous__10390 = Vvar__1___24Anonymous__10391
& Vvar__0__C__10388 = Vvar__0__C__10389 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__10551,Vvar__0___24Anonymous__10552,Vvar__1___24Anonymous__10553,Vvar__1___24Anonymous__10554] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10551,Vvar__1___24Anonymous__10553) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10552,Vvar__1___24Anonymous__10554)
=> ( Vvar__1___24Anonymous__10553 = Vvar__1___24Anonymous__10554
& Vvar__0___24Anonymous__10551 = Vvar__0___24Anonymous__10552 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__10547,Vvar__0___24Anonymous__10548,Vvar__1___24Anonymous__10549,Vvar__1___24Anonymous__10550] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10547,Vvar__1___24Anonymous__10549) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10548,Vvar__1___24Anonymous__10550)
=> ( Vvar__1___24Anonymous__10549 = Vvar__1___24Anonymous__10550
& Vvar__0___24Anonymous__10547 = Vvar__0___24Anonymous__10548 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__22104,Vvar__0__R__22105,Vvar__1__req__22106,Vvar__1__req__22107,Vvar__2__reqb__22108,Vvar__2__reqb__22109,Vvar__3___24Anonymous__22110,Vvar__3___24Anonymous__22111] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22104,Vvar__1__req__22106,Vvar__2__reqb__22108) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22105,Vvar__1__req__22107,Vvar__2__reqb__22109)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__22108 = Vvar__2__reqb__22109
& Vvar__1__req__22106 = Vvar__1__req__22107
& Vvar__0__R__22104 = Vvar__0__R__22105 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__22112,Vvar__0__R__22113,Vvar__1__rO__22114,Vvar__1__rO__22115,Vvar__2__rI__22116,Vvar__2__rI__22117,Vvar__3__radd__22118,Vvar__3__radd__22119,Vvar__4__rmul__22120,Vvar__4__rmul__22121,Vvar__5__rsub__22122,Vvar__5__rsub__22123,Vvar__6__ropp__22124,Vvar__6__ropp__22125,Vvar__7__req__22126,Vvar__7__req__22127,Vvar__8__C__22128,Vvar__8__C__22129,Vvar__9__cO__22130,Vvar__9__cO__22131,Vvar__10__cI__22132,Vvar__10__cI__22133,Vvar__11__cadd__22134,Vvar__11__cadd__22135,Vvar__12__cmul__22136,Vvar__12__cmul__22137,Vvar__13__csub__22138,Vvar__13__csub__22139,Vvar__14__copp__22140,Vvar__14__copp__22141,Vvar__15__ceqb__22142,Vvar__15__ceqb__22143,Vvar__16__phi__22144,Vvar__16__phi__22145,Vvar__17___24Anonymous__22146,Vvar__17___24Anonymous__22147] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__22112,Vvar__1__rO__22114,Vvar__2__rI__22116,Vvar__3__radd__22118,Vvar__4__rmul__22120,Vvar__5__rsub__22122,Vvar__6__ropp__22124,Vvar__7__req__22126,Vvar__8__C__22128,Vvar__9__cO__22130,Vvar__10__cI__22132,Vvar__11__cadd__22134,Vvar__12__cmul__22136,Vvar__13__csub__22138,Vvar__14__copp__22140,Vvar__15__ceqb__22142,Vvar__16__phi__22144) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__22113,Vvar__1__rO__22115,Vvar__2__rI__22117,Vvar__3__radd__22119,Vvar__4__rmul__22121,Vvar__5__rsub__22123,Vvar__6__ropp__22125,Vvar__7__req__22127,Vvar__8__C__22129,Vvar__9__cO__22131,Vvar__10__cI__22133,Vvar__11__cadd__22135,Vvar__12__cmul__22137,Vvar__13__csub__22139,Vvar__14__copp__22141,Vvar__15__ceqb__22143,Vvar__16__phi__22145)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__22144 = Vvar__16__phi__22145
& Vvar__15__ceqb__22142 = Vvar__15__ceqb__22143
& Vvar__14__copp__22140 = Vvar__14__copp__22141
& Vvar__13__csub__22138 = Vvar__13__csub__22139
& Vvar__12__cmul__22136 = Vvar__12__cmul__22137
& Vvar__11__cadd__22134 = Vvar__11__cadd__22135
& Vvar__10__cI__22132 = Vvar__10__cI__22133
& Vvar__9__cO__22130 = Vvar__9__cO__22131
& Vvar__8__C__22128 = Vvar__8__C__22129
& Vvar__7__req__22126 = Vvar__7__req__22127
& Vvar__6__ropp__22124 = Vvar__6__ropp__22125
& Vvar__5__rsub__22122 = Vvar__5__rsub__22123
& Vvar__4__rmul__22120 = Vvar__4__rmul__22121
& Vvar__3__radd__22118 = Vvar__3__radd__22119
& Vvar__2__rI__22116 = Vvar__2__rI__22117
& Vvar__1__rO__22114 = Vvar__1__rO__22115
& Vvar__0__R__22112 = Vvar__0__R__22113 ) ) ).
fof('$_inj_Lambda.Redexes.Ap',axiom,
! [Vvar__0___24Anonymous__29,Vvar__0___24Anonymous__30,Vvar__1___24Anonymous__31,Vvar__1___24Anonymous__32,Vvar__2___24Anonymous__33,Vvar__2___24Anonymous__34] :
( cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__29,Vvar__1___24Anonymous__31,Vvar__2___24Anonymous__33) = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__30,Vvar__1___24Anonymous__32,Vvar__2___24Anonymous__34)
=> ( Vvar__2___24Anonymous__33 = Vvar__2___24Anonymous__34
& Vvar__1___24Anonymous__31 = Vvar__1___24Anonymous__32
& Vvar__0___24Anonymous__29 = Vvar__0___24Anonymous__30 ) ) ).
fof('$_inj_Lambda.Redexes.Fun',axiom,
! [Vvar__0___24Anonymous__27,Vvar__0___24Anonymous__28] :
( cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__27) = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__28)
=> Vvar__0___24Anonymous__27 = Vvar__0___24Anonymous__28 ) ).
fof('$_inj_Lambda.Redexes.Var',axiom,
! [Vvar__0___24Anonymous__25,Vvar__0___24Anonymous__26] :
( cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__25) = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__26)
=> Vvar__0___24Anonymous__25 = Vvar__0___24Anonymous__26 ) ).
fof('$_inj_Lambda.Terms.Abs',axiom,
! [Vvar__0___24Anonymous__17024,Vvar__0___24Anonymous__17025] :
( cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__17024) = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__17025)
=> Vvar__0___24Anonymous__17024 = Vvar__0___24Anonymous__17025 ) ).
fof('$_inj_Lambda.Terms.App',axiom,
! [Vvar__0___24Anonymous__17026,Vvar__0___24Anonymous__17027,Vvar__1___24Anonymous__17028,Vvar__1___24Anonymous__17029] :
( cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__17026,Vvar__1___24Anonymous__17028) = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__17027,Vvar__1___24Anonymous__17029)
=> ( Vvar__1___24Anonymous__17028 = Vvar__1___24Anonymous__17029
& Vvar__0___24Anonymous__17026 = Vvar__0___24Anonymous__17027 ) ) ).
fof('$_inj_Lambda.Terms.Ref',axiom,
! [Vvar__0___24Anonymous__17022,Vvar__0___24Anonymous__17023] :
( cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__17022) = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__17023)
=> Vvar__0___24Anonymous__17022 = Vvar__0___24Anonymous__17023 ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__23010,Vvar__1__Q__23012,Vvar__2__init__23015,Vvar__3___24Anonymous__23016,Vvar__4___24Anonymous__23017] :
( c_24__type__23043___24t(Vvar__0__P__23010,Vvar__1__Q__23012,Vvar__2__init__23015,Vvar__3___24Anonymous__23016,Vvar__4___24Anonymous__23017,Vvar__0__P__23010)
=> ( c_24__type__23051___24t(Vvar__0__P__23010,Vvar__1__Q__23012,Vvar__2__init__23015,Vvar__3___24Anonymous__23016,Vvar__4___24Anonymous__23017,Vvar__1__Q__23012)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__23015)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__23016)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__23017)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__23010,Vvar__1__Q__23012,Vvar__2__init__23015,Vvar__3___24Anonymous__23016,Vvar__4___24Anonymous__23017)
=> ( ( Vvar__4___24Anonymous__23017 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__23016 = Vvar__2__init__23015 )
| ? [Vvar__3__k__23031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__23031)
& ? [Vvar__4__l__23032] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__23032)
& ? [Vvar__5__n__23033] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__23033)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__23010,Vvar__1__Q__23012,Vvar__2__init__23015,Vvar__3__k__23031,Vvar__5__n__23033)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__23010,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__23031),Vvar__4__l__23032)
& p(happ(Vvar__1__Q__23012,Vvar__4__l__23032))
& Vvar__4___24Anonymous__23017 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__23033)
& Vvar__3___24Anonymous__23016 = Vvar__4__l__23032 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__22965,Vvar__1__k__22967,Vvar__2___24Anonymous__22968] :
( c_24__type__22982___24t(Vvar__0__P__22965,Vvar__1__k__22967,Vvar__2___24Anonymous__22968,Vvar__0__P__22965)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__22967)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__22968)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__22965,Vvar__1__k__22967,Vvar__2___24Anonymous__22968)
=> ( Vvar__2___24Anonymous__22968 = Vvar__1__k__22967
| ? [Vvar__2__l__22976] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__22976)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__22965,Vvar__1__k__22967,Vvar__2__l__22976)
& p(happ(Vvar__0__P__22965,Vvar__2__l__22976))
& Vvar__2___24Anonymous__22968 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__22976) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__22984,Vvar__1__k__22986,Vvar__2___24Anonymous__22987] :
( c_24__type__23003___24t(Vvar__0__Q__22984,Vvar__1__k__22986,Vvar__2___24Anonymous__22987,Vvar__0__Q__22984)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__22986)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__22987)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__22984,Vvar__1__k__22986,Vvar__2___24Anonymous__22987)
=> ( ? [Vvar__2__l__22992] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__22992)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__22984,Vvar__1__k__22986,Vvar__2__l__22992)
& Vvar__2___24Anonymous__22987 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__22992) )
| ? [Vvar__2__l__22997] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__22997)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__22986,Vvar__2__l__22997))
& p(happ(Vvar__0__Q__22984,Vvar__2__l__22997))
& Vvar__2___24Anonymous__22987 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__22997) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__18731] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18731)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__18731)
=> ( Vvar__0___24Anonymous__18731 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__18733] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__18733)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__18733)
& Vvar__0___24Anonymous__18731 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__18733) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__18735] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18735)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__18735)
=> ? [Vvar__0__n__18737] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__18737)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__18737)
& Vvar__0___24Anonymous__18735 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__18737) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__18581,Vvar__1___24Anonymous__18582,VX18583] :
( cProp___24t(Vvar__0__P__18581)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__18582)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__18581,Vvar__1___24Anonymous__18582,VX18583)
=> ( ( p(Vvar__0__P__18581)
& Vvar__1___24Anonymous__18582 = cCoq_2eInit_2eDatatypes_2etrue
& VX18583 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__18581) )
| ( ~ p(Vvar__0__P__18581)
& Vvar__1___24Anonymous__18582 = cCoq_2eInit_2eDatatypes_2efalse
& VX18583 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__18581) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__31989,Vvar__1___24Anonymous__31990,Vvar__2___24Anonymous__31991] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__31989)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__31990)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__31991)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__31989,Vvar__1___24Anonymous__31990,Vvar__2___24Anonymous__31991)
=> ( ? [Vvar__0__x__31993] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__31993)
& Vvar__2___24Anonymous__31991 = Vvar__0__x__31993
& Vvar__1___24Anonymous__31990 = Vvar__0__x__31993
& Vvar__0___24Anonymous__31989 = Vvar__0__x__31993 )
| ? [Vvar__0__x__31994] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__31994)
& Vvar__2___24Anonymous__31991 = Vvar__0__x__31994
& Vvar__1___24Anonymous__31990 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__31989 = Vvar__0__x__31994 )
| ? [Vvar__0__x__31995] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__31995)
& Vvar__2___24Anonymous__31991 = Vvar__0__x__31995
& Vvar__1___24Anonymous__31990 = Vvar__0__x__31995
& Vvar__0___24Anonymous__31989 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__31996] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__31996)
& Vvar__2___24Anonymous__31991 = Vvar__0__x__31996
& Vvar__1___24Anonymous__31990 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__31989 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__31997] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__31997)
& Vvar__2___24Anonymous__31991 = Vvar__0__x__31997
& Vvar__1___24Anonymous__31990 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__31989 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX3882] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX3882)
=> ( VX3882 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__3883] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__3883)
& ? [Vvar__1___24Anonymous__3884] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__3884)
& ? [Vvar__2___24Anonymous__3885] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__3885)
& VX3882 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__3883,Vvar__1___24Anonymous__3884,Vvar__2___24Anonymous__3885) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX4032] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX4032)
=> ( VX4032 = cCoq_2eInit_2eByte_2ex00
| VX4032 = cCoq_2eInit_2eByte_2ex01
| VX4032 = cCoq_2eInit_2eByte_2ex02
| VX4032 = cCoq_2eInit_2eByte_2ex03
| VX4032 = cCoq_2eInit_2eByte_2ex04
| VX4032 = cCoq_2eInit_2eByte_2ex05
| VX4032 = cCoq_2eInit_2eByte_2ex06
| VX4032 = cCoq_2eInit_2eByte_2ex07
| VX4032 = cCoq_2eInit_2eByte_2ex08
| VX4032 = cCoq_2eInit_2eByte_2ex09
| VX4032 = cCoq_2eInit_2eByte_2ex0a
| VX4032 = cCoq_2eInit_2eByte_2ex0b
| VX4032 = cCoq_2eInit_2eByte_2ex0c
| VX4032 = cCoq_2eInit_2eByte_2ex0d
| VX4032 = cCoq_2eInit_2eByte_2ex0e
| VX4032 = cCoq_2eInit_2eByte_2ex0f
| VX4032 = cCoq_2eInit_2eByte_2ex10
| VX4032 = cCoq_2eInit_2eByte_2ex11
| VX4032 = cCoq_2eInit_2eByte_2ex12
| VX4032 = cCoq_2eInit_2eByte_2ex13
| VX4032 = cCoq_2eInit_2eByte_2ex14
| VX4032 = cCoq_2eInit_2eByte_2ex15
| VX4032 = cCoq_2eInit_2eByte_2ex16
| VX4032 = cCoq_2eInit_2eByte_2ex17
| VX4032 = cCoq_2eInit_2eByte_2ex18
| VX4032 = cCoq_2eInit_2eByte_2ex19
| VX4032 = cCoq_2eInit_2eByte_2ex1a
| VX4032 = cCoq_2eInit_2eByte_2ex1b
| VX4032 = cCoq_2eInit_2eByte_2ex1c
| VX4032 = cCoq_2eInit_2eByte_2ex1d
| VX4032 = cCoq_2eInit_2eByte_2ex1e
| VX4032 = cCoq_2eInit_2eByte_2ex1f
| VX4032 = cCoq_2eInit_2eByte_2ex20
| VX4032 = cCoq_2eInit_2eByte_2ex21
| VX4032 = cCoq_2eInit_2eByte_2ex22
| VX4032 = cCoq_2eInit_2eByte_2ex23
| VX4032 = cCoq_2eInit_2eByte_2ex24
| VX4032 = cCoq_2eInit_2eByte_2ex25
| VX4032 = cCoq_2eInit_2eByte_2ex26
| VX4032 = cCoq_2eInit_2eByte_2ex27
| VX4032 = cCoq_2eInit_2eByte_2ex28
| VX4032 = cCoq_2eInit_2eByte_2ex29
| VX4032 = cCoq_2eInit_2eByte_2ex2a
| VX4032 = cCoq_2eInit_2eByte_2ex2b
| VX4032 = cCoq_2eInit_2eByte_2ex2c
| VX4032 = cCoq_2eInit_2eByte_2ex2d
| VX4032 = cCoq_2eInit_2eByte_2ex2e
| VX4032 = cCoq_2eInit_2eByte_2ex2f
| VX4032 = cCoq_2eInit_2eByte_2ex30
| VX4032 = cCoq_2eInit_2eByte_2ex31
| VX4032 = cCoq_2eInit_2eByte_2ex32
| VX4032 = cCoq_2eInit_2eByte_2ex33
| VX4032 = cCoq_2eInit_2eByte_2ex34
| VX4032 = cCoq_2eInit_2eByte_2ex35
| VX4032 = cCoq_2eInit_2eByte_2ex36
| VX4032 = cCoq_2eInit_2eByte_2ex37
| VX4032 = cCoq_2eInit_2eByte_2ex38
| VX4032 = cCoq_2eInit_2eByte_2ex39
| VX4032 = cCoq_2eInit_2eByte_2ex3a
| VX4032 = cCoq_2eInit_2eByte_2ex3b
| VX4032 = cCoq_2eInit_2eByte_2ex3c
| VX4032 = cCoq_2eInit_2eByte_2ex3d
| VX4032 = cCoq_2eInit_2eByte_2ex3e
| VX4032 = cCoq_2eInit_2eByte_2ex3f
| VX4032 = cCoq_2eInit_2eByte_2ex40
| VX4032 = cCoq_2eInit_2eByte_2ex41
| VX4032 = cCoq_2eInit_2eByte_2ex42
| VX4032 = cCoq_2eInit_2eByte_2ex43
| VX4032 = cCoq_2eInit_2eByte_2ex44
| VX4032 = cCoq_2eInit_2eByte_2ex45
| VX4032 = cCoq_2eInit_2eByte_2ex46
| VX4032 = cCoq_2eInit_2eByte_2ex47
| VX4032 = cCoq_2eInit_2eByte_2ex48
| VX4032 = cCoq_2eInit_2eByte_2ex49
| VX4032 = cCoq_2eInit_2eByte_2ex4a
| VX4032 = cCoq_2eInit_2eByte_2ex4b
| VX4032 = cCoq_2eInit_2eByte_2ex4c
| VX4032 = cCoq_2eInit_2eByte_2ex4d
| VX4032 = cCoq_2eInit_2eByte_2ex4e
| VX4032 = cCoq_2eInit_2eByte_2ex4f
| VX4032 = cCoq_2eInit_2eByte_2ex50
| VX4032 = cCoq_2eInit_2eByte_2ex51
| VX4032 = cCoq_2eInit_2eByte_2ex52
| VX4032 = cCoq_2eInit_2eByte_2ex53
| VX4032 = cCoq_2eInit_2eByte_2ex54
| VX4032 = cCoq_2eInit_2eByte_2ex55
| VX4032 = cCoq_2eInit_2eByte_2ex56
| VX4032 = cCoq_2eInit_2eByte_2ex57
| VX4032 = cCoq_2eInit_2eByte_2ex58
| VX4032 = cCoq_2eInit_2eByte_2ex59
| VX4032 = cCoq_2eInit_2eByte_2ex5a
| VX4032 = cCoq_2eInit_2eByte_2ex5b
| VX4032 = cCoq_2eInit_2eByte_2ex5c
| VX4032 = cCoq_2eInit_2eByte_2ex5d
| VX4032 = cCoq_2eInit_2eByte_2ex5e
| VX4032 = cCoq_2eInit_2eByte_2ex5f
| VX4032 = cCoq_2eInit_2eByte_2ex60
| VX4032 = cCoq_2eInit_2eByte_2ex61
| VX4032 = cCoq_2eInit_2eByte_2ex62
| VX4032 = cCoq_2eInit_2eByte_2ex63
| VX4032 = cCoq_2eInit_2eByte_2ex64
| VX4032 = cCoq_2eInit_2eByte_2ex65
| VX4032 = cCoq_2eInit_2eByte_2ex66
| VX4032 = cCoq_2eInit_2eByte_2ex67
| VX4032 = cCoq_2eInit_2eByte_2ex68
| VX4032 = cCoq_2eInit_2eByte_2ex69
| VX4032 = cCoq_2eInit_2eByte_2ex6a
| VX4032 = cCoq_2eInit_2eByte_2ex6b
| VX4032 = cCoq_2eInit_2eByte_2ex6c
| VX4032 = cCoq_2eInit_2eByte_2ex6d
| VX4032 = cCoq_2eInit_2eByte_2ex6e
| VX4032 = cCoq_2eInit_2eByte_2ex6f
| VX4032 = cCoq_2eInit_2eByte_2ex70
| VX4032 = cCoq_2eInit_2eByte_2ex71
| VX4032 = cCoq_2eInit_2eByte_2ex72
| VX4032 = cCoq_2eInit_2eByte_2ex73
| VX4032 = cCoq_2eInit_2eByte_2ex74
| VX4032 = cCoq_2eInit_2eByte_2ex75
| VX4032 = cCoq_2eInit_2eByte_2ex76
| VX4032 = cCoq_2eInit_2eByte_2ex77
| VX4032 = cCoq_2eInit_2eByte_2ex78
| VX4032 = cCoq_2eInit_2eByte_2ex79
| VX4032 = cCoq_2eInit_2eByte_2ex7a
| VX4032 = cCoq_2eInit_2eByte_2ex7b
| VX4032 = cCoq_2eInit_2eByte_2ex7c
| VX4032 = cCoq_2eInit_2eByte_2ex7d
| VX4032 = cCoq_2eInit_2eByte_2ex7e
| VX4032 = cCoq_2eInit_2eByte_2ex7f
| VX4032 = cCoq_2eInit_2eByte_2ex80
| VX4032 = cCoq_2eInit_2eByte_2ex81
| VX4032 = cCoq_2eInit_2eByte_2ex82
| VX4032 = cCoq_2eInit_2eByte_2ex83
| VX4032 = cCoq_2eInit_2eByte_2ex84
| VX4032 = cCoq_2eInit_2eByte_2ex85
| VX4032 = cCoq_2eInit_2eByte_2ex86
| VX4032 = cCoq_2eInit_2eByte_2ex87
| VX4032 = cCoq_2eInit_2eByte_2ex88
| VX4032 = cCoq_2eInit_2eByte_2ex89
| VX4032 = cCoq_2eInit_2eByte_2ex8a
| VX4032 = cCoq_2eInit_2eByte_2ex8b
| VX4032 = cCoq_2eInit_2eByte_2ex8c
| VX4032 = cCoq_2eInit_2eByte_2ex8d
| VX4032 = cCoq_2eInit_2eByte_2ex8e
| VX4032 = cCoq_2eInit_2eByte_2ex8f
| VX4032 = cCoq_2eInit_2eByte_2ex90
| VX4032 = cCoq_2eInit_2eByte_2ex91
| VX4032 = cCoq_2eInit_2eByte_2ex92
| VX4032 = cCoq_2eInit_2eByte_2ex93
| VX4032 = cCoq_2eInit_2eByte_2ex94
| VX4032 = cCoq_2eInit_2eByte_2ex95
| VX4032 = cCoq_2eInit_2eByte_2ex96
| VX4032 = cCoq_2eInit_2eByte_2ex97
| VX4032 = cCoq_2eInit_2eByte_2ex98
| VX4032 = cCoq_2eInit_2eByte_2ex99
| VX4032 = cCoq_2eInit_2eByte_2ex9a
| VX4032 = cCoq_2eInit_2eByte_2ex9b
| VX4032 = cCoq_2eInit_2eByte_2ex9c
| VX4032 = cCoq_2eInit_2eByte_2ex9d
| VX4032 = cCoq_2eInit_2eByte_2ex9e
| VX4032 = cCoq_2eInit_2eByte_2ex9f
| VX4032 = cCoq_2eInit_2eByte_2exa0
| VX4032 = cCoq_2eInit_2eByte_2exa1
| VX4032 = cCoq_2eInit_2eByte_2exa2
| VX4032 = cCoq_2eInit_2eByte_2exa3
| VX4032 = cCoq_2eInit_2eByte_2exa4
| VX4032 = cCoq_2eInit_2eByte_2exa5
| VX4032 = cCoq_2eInit_2eByte_2exa6
| VX4032 = cCoq_2eInit_2eByte_2exa7
| VX4032 = cCoq_2eInit_2eByte_2exa8
| VX4032 = cCoq_2eInit_2eByte_2exa9
| VX4032 = cCoq_2eInit_2eByte_2exaa
| VX4032 = cCoq_2eInit_2eByte_2exab
| VX4032 = cCoq_2eInit_2eByte_2exac
| VX4032 = cCoq_2eInit_2eByte_2exad
| VX4032 = cCoq_2eInit_2eByte_2exae
| VX4032 = cCoq_2eInit_2eByte_2exaf
| VX4032 = cCoq_2eInit_2eByte_2exb0
| VX4032 = cCoq_2eInit_2eByte_2exb1
| VX4032 = cCoq_2eInit_2eByte_2exb2
| VX4032 = cCoq_2eInit_2eByte_2exb3
| VX4032 = cCoq_2eInit_2eByte_2exb4
| VX4032 = cCoq_2eInit_2eByte_2exb5
| VX4032 = cCoq_2eInit_2eByte_2exb6
| VX4032 = cCoq_2eInit_2eByte_2exb7
| VX4032 = cCoq_2eInit_2eByte_2exb8
| VX4032 = cCoq_2eInit_2eByte_2exb9
| VX4032 = cCoq_2eInit_2eByte_2exba
| VX4032 = cCoq_2eInit_2eByte_2exbb
| VX4032 = cCoq_2eInit_2eByte_2exbc
| VX4032 = cCoq_2eInit_2eByte_2exbd
| VX4032 = cCoq_2eInit_2eByte_2exbe
| VX4032 = cCoq_2eInit_2eByte_2exbf
| VX4032 = cCoq_2eInit_2eByte_2exc0
| VX4032 = cCoq_2eInit_2eByte_2exc1
| VX4032 = cCoq_2eInit_2eByte_2exc2
| VX4032 = cCoq_2eInit_2eByte_2exc3
| VX4032 = cCoq_2eInit_2eByte_2exc4
| VX4032 = cCoq_2eInit_2eByte_2exc5
| VX4032 = cCoq_2eInit_2eByte_2exc6
| VX4032 = cCoq_2eInit_2eByte_2exc7
| VX4032 = cCoq_2eInit_2eByte_2exc8
| VX4032 = cCoq_2eInit_2eByte_2exc9
| VX4032 = cCoq_2eInit_2eByte_2exca
| VX4032 = cCoq_2eInit_2eByte_2excb
| VX4032 = cCoq_2eInit_2eByte_2excc
| VX4032 = cCoq_2eInit_2eByte_2excd
| VX4032 = cCoq_2eInit_2eByte_2exce
| VX4032 = cCoq_2eInit_2eByte_2excf
| VX4032 = cCoq_2eInit_2eByte_2exd0
| VX4032 = cCoq_2eInit_2eByte_2exd1
| VX4032 = cCoq_2eInit_2eByte_2exd2
| VX4032 = cCoq_2eInit_2eByte_2exd3
| VX4032 = cCoq_2eInit_2eByte_2exd4
| VX4032 = cCoq_2eInit_2eByte_2exd5
| VX4032 = cCoq_2eInit_2eByte_2exd6
| VX4032 = cCoq_2eInit_2eByte_2exd7
| VX4032 = cCoq_2eInit_2eByte_2exd8
| VX4032 = cCoq_2eInit_2eByte_2exd9
| VX4032 = cCoq_2eInit_2eByte_2exda
| VX4032 = cCoq_2eInit_2eByte_2exdb
| VX4032 = cCoq_2eInit_2eByte_2exdc
| VX4032 = cCoq_2eInit_2eByte_2exdd
| VX4032 = cCoq_2eInit_2eByte_2exde
| VX4032 = cCoq_2eInit_2eByte_2exdf
| VX4032 = cCoq_2eInit_2eByte_2exe0
| VX4032 = cCoq_2eInit_2eByte_2exe1
| VX4032 = cCoq_2eInit_2eByte_2exe2
| VX4032 = cCoq_2eInit_2eByte_2exe3
| VX4032 = cCoq_2eInit_2eByte_2exe4
| VX4032 = cCoq_2eInit_2eByte_2exe5
| VX4032 = cCoq_2eInit_2eByte_2exe6
| VX4032 = cCoq_2eInit_2eByte_2exe7
| VX4032 = cCoq_2eInit_2eByte_2exe8
| VX4032 = cCoq_2eInit_2eByte_2exe9
| VX4032 = cCoq_2eInit_2eByte_2exea
| VX4032 = cCoq_2eInit_2eByte_2exeb
| VX4032 = cCoq_2eInit_2eByte_2exec
| VX4032 = cCoq_2eInit_2eByte_2exed
| VX4032 = cCoq_2eInit_2eByte_2exee
| VX4032 = cCoq_2eInit_2eByte_2exef
| VX4032 = cCoq_2eInit_2eByte_2exf0
| VX4032 = cCoq_2eInit_2eByte_2exf1
| VX4032 = cCoq_2eInit_2eByte_2exf2
| VX4032 = cCoq_2eInit_2eByte_2exf3
| VX4032 = cCoq_2eInit_2eByte_2exf4
| VX4032 = cCoq_2eInit_2eByte_2exf5
| VX4032 = cCoq_2eInit_2eByte_2exf6
| VX4032 = cCoq_2eInit_2eByte_2exf7
| VX4032 = cCoq_2eInit_2eByte_2exf8
| VX4032 = cCoq_2eInit_2eByte_2exf9
| VX4032 = cCoq_2eInit_2eByte_2exfa
| VX4032 = cCoq_2eInit_2eByte_2exfb
| VX4032 = cCoq_2eInit_2eByte_2exfc
| VX4032 = cCoq_2eInit_2eByte_2exfd
| VX4032 = cCoq_2eInit_2eByte_2exfe
| VX4032 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__18604,Vvar__1__Q__18605,Vvar__2___24Anonymous__18606] :
( cProp___24t(Vvar__0__P__18604)
=> ( cProp___24t(Vvar__1__Q__18605)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__18606)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__18604,Vvar__1__Q__18605,Vvar__2___24Anonymous__18606)
=> ( ( p(Vvar__0__P__18604)
& Vvar__2___24Anonymous__18606 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__18605)
& Vvar__2___24Anonymous__18606 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__4884,Vvar__1__Plt__4885,Vvar__2__Pgt__4886,Vvar__3___24Anonymous__4887] :
( cProp___24t(Vvar__0__Peq__4884)
=> ( cProp___24t(Vvar__1__Plt__4885)
=> ( cProp___24t(Vvar__2__Pgt__4886)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__4887)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__4884,Vvar__1__Plt__4885,Vvar__2__Pgt__4886,Vvar__3___24Anonymous__4887)
=> ( ( p(Vvar__0__Peq__4884)
& Vvar__3___24Anonymous__4887 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__4885)
& Vvar__3___24Anonymous__4887 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__4886)
& Vvar__3___24Anonymous__4887 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__23111,Vvar__1__Plt__23112,Vvar__2__Pgt__23113,Vvar__3___24Anonymous__23114,VX23115] :
( cProp___24t(Vvar__0__Peq__23111)
=> ( cProp___24t(Vvar__1__Plt__23112)
=> ( cProp___24t(Vvar__2__Pgt__23113)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__23114)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__23111,Vvar__1__Plt__23112,Vvar__2__Pgt__23113,Vvar__3___24Anonymous__23114,VX23115)
=> ( ( p(Vvar__0__Peq__23111)
& Vvar__3___24Anonymous__23114 = cCoq_2eInit_2eDatatypes_2eEq
& VX23115 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23111,Vvar__1__Plt__23112,Vvar__2__Pgt__23113) )
| ( p(Vvar__1__Plt__23112)
& Vvar__3___24Anonymous__23114 = cCoq_2eInit_2eDatatypes_2eLt
& VX23115 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23111,Vvar__1__Plt__23112,Vvar__2__Pgt__23113) )
| ( p(Vvar__2__Pgt__23113)
& Vvar__3___24Anonymous__23114 = cCoq_2eInit_2eDatatypes_2eGt
& VX23115 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23111,Vvar__1__Plt__23112,Vvar__2__Pgt__23113) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2etrue
| VX1 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX1405] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX1405)
=> ( VX1405 = cCoq_2eInit_2eDatatypes_2eEq
| VX1405 = cCoq_2eInit_2eDatatypes_2eLt
| VX1405 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__4684] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4684)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__4684)
=> Vvar__0___24Anonymous__4684 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__18614,Vvar__1__a__18615,Vvar__2___24Anonymous__18616] :
( cType___24t(Vvar__0__A__18614)
=> ( t(Vvar__1__a__18615,Vvar__0__A__18614)
=> ( t(Vvar__2___24Anonymous__18616,Vvar__0__A__18614)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__18614,Vvar__1__a__18615,Vvar__2___24Anonymous__18616)
=> Vvar__2___24Anonymous__18616 = Vvar__1__a__18615 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__4777,VX4778] :
( cType___24t(Vvar__0__A__4777)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4777,VX4778)
=> ( VX4778 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4777)
| ? [Vvar__1___24Anonymous__4781] :
( t(Vvar__1___24Anonymous__4781,Vvar__0__A__4777)
& ? [Vvar__2___24Anonymous__4782] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4777,Vvar__2___24Anonymous__4782)
& VX4778 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4777,Vvar__1___24Anonymous__4781,Vvar__2___24Anonymous__4782) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX4)
=> ( VX4 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5)
& VX4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__4686,VX4687] :
( cType___24t(Vvar__0__A__4686)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__4686,VX4687)
=> ( ? [Vvar__1___24Anonymous__4689] :
( t(Vvar__1___24Anonymous__4689,Vvar__0__A__4686)
& VX4687 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4686,Vvar__1___24Anonymous__4689) )
| VX4687 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4686) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__4735,Vvar__1__B__4736,VX4737] :
( cType___24t(Vvar__0__A__4735)
=> ( cType___24t(Vvar__1__B__4736)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__4735,Vvar__1__B__4736,VX4737)
=> ? [Vvar__2___24Anonymous__4740] :
( t(Vvar__2___24Anonymous__4740,Vvar__0__A__4735)
& ? [Vvar__3___24Anonymous__4741] :
( t(Vvar__3___24Anonymous__4741,Vvar__1__B__4736)
& VX4737 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4735,Vvar__1__B__4736,Vvar__2___24Anonymous__4740,Vvar__3___24Anonymous__4741) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__4705,Vvar__1__B__4706,VX4707] :
( cType___24t(Vvar__0__A__4705)
=> ( cType___24t(Vvar__1__B__4706)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__4705,Vvar__1__B__4706,VX4707)
=> ( ? [Vvar__2___24Anonymous__4710] :
( t(Vvar__2___24Anonymous__4710,Vvar__0__A__4705)
& VX4707 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__4705,Vvar__1__B__4706,Vvar__2___24Anonymous__4710) )
| ? [Vvar__2___24Anonymous__4713] :
( t(Vvar__2___24Anonymous__4713,Vvar__1__B__4706)
& VX4707 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__4705,Vvar__1__B__4706,Vvar__2___24Anonymous__4713) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX4680] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX4680)
=> VX4680 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX18629] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX18629)
=> ( ? [Vvar__0__i__18630] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__18630)
& ? [Vvar__1__f__18631] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__18631)
& VX18629 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__18630,Vvar__1__f__18631) ) )
| ? [Vvar__0__i__18632] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__18632)
& ? [Vvar__1__f__18633] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__18633)
& ? [Vvar__2__e__18634] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__18634)
& VX18629 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__18632,Vvar__1__f__18633,Vvar__2__e__18634) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX18620] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX18620)
=> ( ? [Vvar__0__d__18621] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__18621)
& VX18620 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__18621) )
| ? [Vvar__0__d__18622] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__18622)
& VX18620 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__18622) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX4904] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX4904)
=> ( VX4904 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__4905] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4905)
& VX4904 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__4905) )
| ? [Vvar__0___24Anonymous__4906] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4906)
& VX4904 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__4906) )
| ? [Vvar__0___24Anonymous__4907] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4907)
& VX4904 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__4907) )
| ? [Vvar__0___24Anonymous__4908] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4908)
& VX4904 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__4908) )
| ? [Vvar__0___24Anonymous__4909] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4909)
& VX4904 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__4909) )
| ? [Vvar__0___24Anonymous__4910] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4910)
& VX4904 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__4910) )
| ? [Vvar__0___24Anonymous__4911] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4911)
& VX4904 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__4911) )
| ? [Vvar__0___24Anonymous__4912] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4912)
& VX4904 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__4912) )
| ? [Vvar__0___24Anonymous__4913] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4913)
& VX4904 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__4913) )
| ? [Vvar__0___24Anonymous__4914] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4914)
& VX4904 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__4914) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__1149,Vvar__1___24Anonymous__1150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1149)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__1150)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1149,Vvar__1___24Anonymous__1150))
=> ( Vvar__1___24Anonymous__1150 = Vvar__0__n__1149
| ? [Vvar__1__m__1154] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__1154)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1149,Vvar__1__m__1154))
& Vvar__1___24Anonymous__1150 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__1154) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__16763,Vvar__1__P__16764,VX16767] :
( cType___24t(Vvar__0__A__16763)
=> ( c_24__type__16777___24t(Vvar__0__A__16763,Vvar__1__P__16764,Vvar__1__P__16764)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__16763,Vvar__1__P__16764,VX16767)
=> ? [Vvar__2__x__16772] :
( t(Vvar__2__x__16772,Vvar__0__A__16763)
& p(happ(Vvar__1__P__16764,Vvar__2__x__16772))
& VX16767 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__16763,Vvar__1__P__16764,Vvar__2__x__16772) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__22148,Vvar__1__P__22149,Vvar__2__Q__22152,VX22155] :
( cType___24t(Vvar__0__A__22148)
=> ( c_24__type__22172___24t(Vvar__0__A__22148,Vvar__1__P__22149,Vvar__2__Q__22152,Vvar__1__P__22149)
=> ( c_24__type__22180___24t(Vvar__0__A__22148,Vvar__1__P__22149,Vvar__2__Q__22152,Vvar__2__Q__22152)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__22148,Vvar__1__P__22149,Vvar__2__Q__22152,VX22155)
=> ? [Vvar__3__x__22163] :
( t(Vvar__3__x__22163,Vvar__0__A__22148)
& p(happ(Vvar__1__P__22149,Vvar__3__x__22163))
& p(happ(Vvar__2__Q__22152,Vvar__3__x__22163))
& VX22155 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22148,Vvar__1__P__22149,Vvar__2__Q__22152,Vvar__3__x__22163) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__16802,Vvar__1__P__16803,VX16806] :
( cType___24t(Vvar__0__A__16802)
=> ( c_24__type__16816___24t(Vvar__0__A__16802,Vvar__1__P__16803,Vvar__1__P__16803)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__16802,Vvar__1__P__16803,VX16806)
=> ? [Vvar__2__x__16811] :
( t(Vvar__2__x__16811,Vvar__0__A__16802)
& ? [Vvar__3___24Anonymous__16812] :
( t(Vvar__3___24Anonymous__16812,happ(Vvar__1__P__16803,Vvar__2__x__16811))
& VX16806 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__16802,Vvar__1__P__16803,Vvar__2__x__16811,Vvar__3___24Anonymous__16812) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__22204,Vvar__1__P__22205,Vvar__2__Q__22208,VX22211] :
( cType___24t(Vvar__0__A__22204)
=> ( c_24__type__22228___24t(Vvar__0__A__22204,Vvar__1__P__22205,Vvar__2__Q__22208,Vvar__1__P__22205)
=> ( c_24__type__22236___24t(Vvar__0__A__22204,Vvar__1__P__22205,Vvar__2__Q__22208,Vvar__2__Q__22208)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__22204,Vvar__1__P__22205,Vvar__2__Q__22208,VX22211)
=> ? [Vvar__3__x__22219] :
( t(Vvar__3__x__22219,Vvar__0__A__22204)
& ? [Vvar__4___24Anonymous__22220] :
( t(Vvar__4___24Anonymous__22220,happ(Vvar__1__P__22205,Vvar__3__x__22219))
& ? [Vvar__5___24Anonymous__22221] :
( t(Vvar__5___24Anonymous__22221,happ(Vvar__2__Q__22208,Vvar__3__x__22219))
& VX22211 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22204,Vvar__1__P__22205,Vvar__2__Q__22208,Vvar__3__x__22219,Vvar__4___24Anonymous__22220,Vvar__5___24Anonymous__22221) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__983,Vvar__1__B__984,VX985] :
( cProp___24t(Vvar__0__A__983)
=> ( cProp___24t(Vvar__1__B__984)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__983,Vvar__1__B__984,VX985)
=> ( ( p(Vvar__0__A__983)
& VX985 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__983,Vvar__1__B__984) )
| ( p(Vvar__1__B__984)
& VX985 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__983,Vvar__1__B__984) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__1019,Vvar__1__B__1020,VX1021] :
( cType___24t(Vvar__0__A__1019)
=> ( cProp___24t(Vvar__1__B__1020)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__1019,Vvar__1__B__1020,VX1021)
=> ( ? [Vvar__2___24Anonymous__1024] :
( t(Vvar__2___24Anonymous__1024,Vvar__0__A__1019)
& VX1021 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__1019,Vvar__1__B__1020,Vvar__2___24Anonymous__1024) )
| ( p(Vvar__1__B__1020)
& VX1021 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__1019,Vvar__1__B__1020) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__17032,Vvar__1__R__17033,Vvar__2__x__17038] :
( cType___24t(Vvar__0__A__17032)
=> ( c_24__type__17067___24t(Vvar__0__A__17032,Vvar__1__R__17033,Vvar__2__x__17038,Vvar__1__R__17033)
=> ( t(Vvar__2__x__17038,Vvar__0__A__17032)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__17032,Vvar__1__R__17033,Vvar__2__x__17038)
=> ( ! [Vvar__var__var__var__var__3__y__17048__17050__17052__17054__17056] :
( t(Vvar__var__var__var__var__3__y__17048__17050__17052__17054__17056,Vvar__0__A__17032)
=> ( p(happ(happ(Vvar__1__R__17033,Vvar__var__var__var__var__3__y__17048__17050__17052__17054__17056),Vvar__2__x__17038))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__17032,Vvar__1__R__17033,Vvar__var__var__var__var__3__y__17048__17050__17052__17054__17056) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__23357,Vvar__1__a__23358,Vvar__2___24Anonymous__23359,Vvar__3___24Anonymous__23360] :
( cType___24t(Vvar__0__A__23357)
=> ( t(Vvar__1__a__23358,Vvar__0__A__23357)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23357,Vvar__2___24Anonymous__23359)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23357,Vvar__3___24Anonymous__23360)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__23357,Vvar__1__a__23358,Vvar__2___24Anonymous__23359,Vvar__3___24Anonymous__23360)
=> ( ? [Vvar__2__l__23364] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23357,Vvar__2__l__23364)
& Vvar__3___24Anonymous__23360 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23357,Vvar__1__a__23358,Vvar__2__l__23364)
& Vvar__2___24Anonymous__23359 = Vvar__2__l__23364 )
| ? [Vvar__2__x__23367] :
( t(Vvar__2__x__23367,Vvar__0__A__23357)
& ? [Vvar__3__l__23368] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23357,Vvar__3__l__23368)
& ? [Vvar__4__l_27__23369] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23357,Vvar__4__l_27__23369)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__23357,Vvar__1__a__23358,Vvar__3__l__23368,Vvar__4__l_27__23369)
& Vvar__3___24Anonymous__23360 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23357,Vvar__2__x__23367,Vvar__4__l_27__23369)
& Vvar__2___24Anonymous__23359 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23357,Vvar__2__x__23367,Vvar__3__l__23368) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__23380,Vvar__1__P__23381,Vvar__2___24Anonymous__23384] :
( cType___24t(Vvar__0__A__23380)
=> ( c_24__type__23404___24t(Vvar__0__A__23380,Vvar__1__P__23381,Vvar__2___24Anonymous__23384,Vvar__1__P__23381)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23380,Vvar__2___24Anonymous__23384)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__23380,Vvar__1__P__23381,Vvar__2___24Anonymous__23384)
=> ( ? [Vvar__2__x__23390] :
( t(Vvar__2__x__23390,Vvar__0__A__23380)
& ? [Vvar__3__l__23391] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23380,Vvar__3__l__23391)
& p(happ(Vvar__1__P__23381,Vvar__2__x__23390))
& Vvar__2___24Anonymous__23384 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23380,Vvar__2__x__23390,Vvar__3__l__23391) ) )
| ? [Vvar__2__x__23397] :
( t(Vvar__2__x__23397,Vvar__0__A__23380)
& ? [Vvar__3__l__23398] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23380,Vvar__3__l__23398)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__23380,Vvar__1__P__23381,Vvar__3__l__23398)
& Vvar__2___24Anonymous__23384 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23380,Vvar__2__x__23397,Vvar__3__l__23398) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__23406,Vvar__1__P__23407,Vvar__2___24Anonymous__23410] :
( cType___24t(Vvar__0__A__23406)
=> ( c_24__type__23428___24t(Vvar__0__A__23406,Vvar__1__P__23407,Vvar__2___24Anonymous__23410,Vvar__1__P__23407)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23406,Vvar__2___24Anonymous__23410)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23406,Vvar__1__P__23407,Vvar__2___24Anonymous__23410)
=> ( Vvar__2___24Anonymous__23410 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23406)
| ? [Vvar__2__x__23420] :
( t(Vvar__2__x__23420,Vvar__0__A__23406)
& ? [Vvar__3__l__23421] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23406,Vvar__3__l__23421)
& p(happ(Vvar__1__P__23407,Vvar__2__x__23420))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23406,Vvar__1__P__23407,Vvar__3__l__23421)
& Vvar__2___24Anonymous__23410 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23406,Vvar__2__x__23420,Vvar__3__l__23421) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__23430,Vvar__1__B__23431,Vvar__2__R__23432,Vvar__3___24Anonymous__23437,Vvar__4___24Anonymous__23438] :
( cType___24t(Vvar__0__A__23430)
=> ( cType___24t(Vvar__1__B__23431)
=> ( c_24__type__23475___24t(Vvar__0__A__23430,Vvar__1__B__23431,Vvar__2__R__23432,Vvar__3___24Anonymous__23437,Vvar__4___24Anonymous__23438,Vvar__2__R__23432)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23430,Vvar__3___24Anonymous__23437)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__23431,Vvar__4___24Anonymous__23438)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__23430,Vvar__1__B__23431,Vvar__2__R__23432,Vvar__3___24Anonymous__23437,Vvar__4___24Anonymous__23438)
=> ( ( Vvar__4___24Anonymous__23438 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__23431)
& Vvar__3___24Anonymous__23437 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23430) )
| ? [Vvar__3__x__23454] :
( t(Vvar__3__x__23454,Vvar__0__A__23430)
& ? [Vvar__4__y__23455] :
( t(Vvar__4__y__23455,Vvar__1__B__23431)
& ? [Vvar__5__l__23456] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23430,Vvar__5__l__23456)
& ? [Vvar__6__l_27__23457] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__23431,Vvar__6__l_27__23457)
& p(happ(happ(Vvar__2__R__23432,Vvar__3__x__23454),Vvar__4__y__23455))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__23430,Vvar__1__B__23431,Vvar__2__R__23432,Vvar__5__l__23456,Vvar__6__l_27__23457)
& Vvar__4___24Anonymous__23438 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__23431,Vvar__4__y__23455,Vvar__6__l_27__23457)
& Vvar__3___24Anonymous__23437 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23430,Vvar__3__x__23454,Vvar__5__l__23456) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__23477,Vvar__1__R__23478,Vvar__2___24Anonymous__23483] :
( cType___24t(Vvar__0__A__23477)
=> ( c_24__type__23510___24t(Vvar__0__A__23477,Vvar__1__R__23478,Vvar__2___24Anonymous__23483,Vvar__1__R__23478)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23477,Vvar__2___24Anonymous__23483)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23477,Vvar__1__R__23478,Vvar__2___24Anonymous__23483)
=> ( Vvar__2___24Anonymous__23483 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23477)
| ? [Vvar__2__a__23497] :
( t(Vvar__2__a__23497,Vvar__0__A__23477)
& ? [Vvar__3__l__23498] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23477,Vvar__3__l__23498)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__23477,happ(Vvar__1__R__23478,Vvar__2__a__23497),Vvar__3__l__23498)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__23477,Vvar__1__R__23478,Vvar__3__l__23498)
& Vvar__2___24Anonymous__23483 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23477,Vvar__2__a__23497,Vvar__3__l__23498) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__23371,Vvar__1___24Anonymous__23372] :
( cType___24t(Vvar__0__A__23371)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23371,Vvar__1___24Anonymous__23372)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__23371,Vvar__1___24Anonymous__23372)
=> ( Vvar__1___24Anonymous__23372 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__23371)
| ? [Vvar__1__x__23376] :
( t(Vvar__1__x__23376,Vvar__0__A__23371)
& ? [Vvar__2__l__23377] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__23371,Vvar__2__l__23377)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__23371,Vvar__1__x__23376,Vvar__2__l__23377)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__23371,Vvar__2__l__23377)
& Vvar__1___24Anonymous__23372 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23371,Vvar__1__x__23376,Vvar__2__l__23377) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__30977,Vvar__1__eqA__30978,Vvar__2__x__30983,Vvar__3___24Anonymous__30984] :
( cType___24t(Vvar__0__A__30977)
=> ( c_24__type__31017___24t(Vvar__0__A__30977,Vvar__1__eqA__30978,Vvar__2__x__30983,Vvar__3___24Anonymous__30984,Vvar__1__eqA__30978)
=> ( t(Vvar__2__x__30983,Vvar__0__A__30977)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30977,Vvar__3___24Anonymous__30984)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__30977,Vvar__1__eqA__30978,Vvar__2__x__30983,Vvar__3___24Anonymous__30984)
=> ( ? [Vvar__3__y__30993] :
( t(Vvar__3__y__30993,Vvar__0__A__30977)
& ? [Vvar__4__l__30994] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30977,Vvar__4__l__30994)
& p(happ(happ(Vvar__1__eqA__30978,Vvar__2__x__30983),Vvar__3__y__30993))
& Vvar__3___24Anonymous__30984 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30977,Vvar__3__y__30993,Vvar__4__l__30994) ) )
| ? [Vvar__3__y__31003] :
( t(Vvar__3__y__31003,Vvar__0__A__30977)
& ? [Vvar__4__l__31004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30977,Vvar__4__l__31004)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__30977,Vvar__1__eqA__30978,Vvar__2__x__30983,Vvar__4__l__31004)
& Vvar__3___24Anonymous__30984 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30977,Vvar__3__y__31003,Vvar__4__l__31004) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__31019,Vvar__1__eqA__31020,Vvar__2___24Anonymous__31025] :
( cType___24t(Vvar__0__A__31019)
=> ( c_24__type__31052___24t(Vvar__0__A__31019,Vvar__1__eqA__31020,Vvar__2___24Anonymous__31025,Vvar__1__eqA__31020)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31019,Vvar__2___24Anonymous__31025)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__31019,Vvar__1__eqA__31020,Vvar__2___24Anonymous__31025)
=> ( Vvar__2___24Anonymous__31025 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31019)
| ? [Vvar__2__x__31039] :
( t(Vvar__2__x__31039,Vvar__0__A__31019)
& ? [Vvar__3__l__31040] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31019,Vvar__3__l__31040)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__31019,Vvar__1__eqA__31020,Vvar__2__x__31039,Vvar__3__l__31040)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__31019,Vvar__1__eqA__31020,Vvar__3__l__31040)
& Vvar__2___24Anonymous__31025 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31019,Vvar__2__x__31039,Vvar__3__l__31040) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__31054,Vvar__1__eqA__31055,Vvar__2___24Anonymous__31060,Vvar__3___24Anonymous__31061] :
( cType___24t(Vvar__0__A__31054)
=> ( c_24__type__31092___24t(Vvar__0__A__31054,Vvar__1__eqA__31055,Vvar__2___24Anonymous__31060,Vvar__3___24Anonymous__31061,Vvar__1__eqA__31055)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31054,Vvar__2___24Anonymous__31060)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31054,Vvar__3___24Anonymous__31061)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__31054,Vvar__1__eqA__31055,Vvar__2___24Anonymous__31060,Vvar__3___24Anonymous__31061)
=> ( ( Vvar__3___24Anonymous__31061 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31054)
& Vvar__2___24Anonymous__31060 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31054) )
| ? [Vvar__2__x__31075] :
( t(Vvar__2__x__31075,Vvar__0__A__31054)
& ? [Vvar__3__x_27__31076] :
( t(Vvar__3__x_27__31076,Vvar__0__A__31054)
& ? [Vvar__4__l__31077] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31054,Vvar__4__l__31077)
& ? [Vvar__5__l_27__31078] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31054,Vvar__5__l_27__31078)
& p(happ(happ(Vvar__1__eqA__31055,Vvar__2__x__31075),Vvar__3__x_27__31076))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__31054,Vvar__1__eqA__31055,Vvar__4__l__31077,Vvar__5__l_27__31078)
& Vvar__3___24Anonymous__31061 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31054,Vvar__3__x_27__31076,Vvar__5__l_27__31078)
& Vvar__2___24Anonymous__31060 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31054,Vvar__2__x__31075,Vvar__4__l__31077) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__18679,Vvar__1__P__18680,Vvar__2__p__18683,Vvar__3__x__18684,Vvar__4__q__18685,Vvar__5___24Anonymous__18686] :
( cType___24t(Vvar__0__U__18679)
=> ( c_24__type__18701___24t(Vvar__0__U__18679,Vvar__1__P__18680,Vvar__2__p__18683,Vvar__3__x__18684,Vvar__4__q__18685,Vvar__5___24Anonymous__18686,Vvar__1__P__18680)
=> ( t(Vvar__2__p__18683,Vvar__0__U__18679)
=> ( t(Vvar__3__x__18684,happ(Vvar__1__P__18680,Vvar__2__p__18683))
=> ( t(Vvar__4__q__18685,Vvar__0__U__18679)
=> ( t(Vvar__5___24Anonymous__18686,happ(Vvar__1__P__18680,Vvar__4__q__18685))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__18679,Vvar__1__P__18680,Vvar__2__p__18683,Vvar__3__x__18684,Vvar__4__q__18685,Vvar__5___24Anonymous__18686)
=> ( Vvar__5___24Anonymous__18686 = Vvar__3__x__18684
& Vvar__4__q__18685 = Vvar__2__p__18683 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__18703,Vvar__1__P__18704,Vvar__2__p__18707,Vvar__3__x__18708,Vvar__4__q__18709,Vvar__5__y__18710] :
( cType___24t(Vvar__0__U__18703)
=> ( c_24__type__18729___24t(Vvar__0__U__18703,Vvar__1__P__18704,Vvar__2__p__18707,Vvar__3__x__18708,Vvar__4__q__18709,Vvar__5__y__18710,Vvar__1__P__18704)
=> ( t(Vvar__2__p__18707,Vvar__0__U__18703)
=> ( t(Vvar__3__x__18708,happ(Vvar__1__P__18704,Vvar__2__p__18707))
=> ( t(Vvar__4__q__18709,Vvar__0__U__18703)
=> ( t(Vvar__5__y__18710,happ(Vvar__1__P__18704,Vvar__4__q__18709))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__18703,Vvar__1__P__18704,Vvar__2__p__18707,Vvar__3__x__18708,Vvar__4__q__18709,Vvar__5__y__18710)
=> ( Vvar__4__q__18709 = Vvar__2__p__18707
& Vvar__3__x__18708 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__18703,Vvar__4__q__18709,Vvar__1__P__18704,Vvar__5__y__18710,Vvar__2__p__18707)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1386] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1386)
=> ( VX1386 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1387] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1387)
& VX1386 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1387) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1391] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1391)
=> ( VX1391 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1392] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1392)
& VX1391 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1392) )
| ? [Vvar__0___24Anonymous__1393] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1393)
& VX1391 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1393) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1367] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1367)
=> ( ? [Vvar__0___24Anonymous__1368] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1368)
& VX1367 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1368) )
| ? [Vvar__0___24Anonymous__1369] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1369)
& VX1367 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1369) )
| VX1367 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__22867,VX22868] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22867)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__22867,VX22868)
=> ( ( Vvar__0___24Anonymous__22867 = cCoq_2eNumbers_2eBinNums_2exH
& VX22868 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__22869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__22869)
& ? [Vvar__1___24Anonymous__22870] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__22869,Vvar__1___24Anonymous__22870)
& Vvar__0___24Anonymous__22867 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905___24a2(Vvar__0___24Anonymous__22867,Vvar__0__p__22869)
& VX22868 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__22869,Vvar__1___24Anonymous__22870) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__31970,Vvar__1__q__31971,Vvar__2___24Anonymous__31972] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__31970)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__31971)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__31972)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__31970,Vvar__1__q__31971,Vvar__2___24Anonymous__31972)
=> ( ( Vvar__0__p__31970 = Vvar__1__q__31971
& Vvar__2___24Anonymous__31972 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__31979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__31979)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__31971,Vvar__2__r__31979) = Vvar__0__p__31970
& Vvar__2___24Anonymous__31972 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__31979) )
| ? [Vvar__2__r__31983] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__31983)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__31970,Vvar__2__r__31983) = Vvar__1__q__31971
& Vvar__2___24Anonymous__31972 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX17582] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX17582)
=> ( VX17582 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__17583] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17583)
& VX17582 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__17583) )
| VX17582 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX9104] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX9104)
=> ? [Vvar__0__Qnum__9105] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9105)
& ? [Vvar__1__Qden__9106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9106)
& VX9104 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9105,Vvar__1__Qden__9106) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX19919] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX19919)
=> ? [Vvar__0__neg__19920] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__19920)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__19920,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX19919 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__19920) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX24155] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX24155)
=> ? [Vvar__0__nonneg__24156] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__24156)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__24156)
& VX24155 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__24156) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX9169] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX9169)
=> ? [Vvar__0__nonpos__9170] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__9170)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__9170,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX9169 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__9170) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX19926] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX19926)
=> ? [Vvar__0__nonzero__19927] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__19927)
& Vvar__0__nonzero__19927 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX19926 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__19927) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX19912] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX19912)
=> ? [Vvar__0__pos__19913] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__19913)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__19913)
& VX19912 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__19913) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__19934,Vvar__1___24Anonymous__19935,VX19936] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__19934)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__19935)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__19934,Vvar__1___24Anonymous__19935,VX19936)
=> ( ( Vvar__0__x__19934 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__19935 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX19936 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__19934) )
| ? [Vvar__1__n__19940] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__19940)
& Vvar__0__x__19934 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__19940)
& Vvar__1___24Anonymous__19935 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2419960___24a3(Vvar__0__x__19934,Vvar__1___24Anonymous__19935,Vvar__1__n__19940)
& VX19936 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__19934,Vvar__1__n__19940) )
| ? [Vvar__1__n__19945] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__19945)
& Vvar__0__x__19934 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__19945))
& Vvar__1___24Anonymous__19935 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977___24a3(Vvar__0__x__19934,Vvar__1___24Anonymous__19935,Vvar__1__n__19945)
& VX19936 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__19934,Vvar__1__n__19945) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__24553,Vvar__1__R__24554] :
( cType___24t(Vvar__0__A__24553)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24553,Vvar__1__R__24554)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__24553,Vvar__1__R__24554)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__24553,Vvar__1__R__24554)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__24553,Vvar__1__R__24554)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__24545,Vvar__1__R__24546] :
( cType___24t(Vvar__0__A__24545)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24545,Vvar__1__R__24546)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__24545,Vvar__1__R__24546)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__24545,Vvar__1__R__24546)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__24545,Vvar__1__R__24546)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__24545,Vvar__1__R__24546)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__24537,Vvar__1__R__24538] :
( cType___24t(Vvar__0__A__24537)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24537,Vvar__1__R__24538)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__24537,Vvar__1__R__24538)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__24537,Vvar__1__R__24538)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__24537,Vvar__1__R__24538)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__24537,Vvar__1__R__24538)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__24530,Vvar__1__R__24531] :
( cType___24t(Vvar__0__A__24530)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24530,Vvar__1__R__24531)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__24530,Vvar__1__R__24531)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__24530,Vvar__1__R__24531)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__24530,Vvar__1__R__24531)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__24988,Vvar__1__leA__24989,Vvar__2___24Anonymous__24994] :
( cType___24t(Vvar__0__A__24988)
=> ( c_24__type__25084___24t(Vvar__0__A__24988,Vvar__1__leA__24989,Vvar__2___24Anonymous__24994,Vvar__1__leA__24989)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24988,Vvar__2___24Anonymous__24994)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__24988,Vvar__1__leA__24989,Vvar__2___24Anonymous__24994)
=> ( Vvar__2___24Anonymous__24994 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24988)
| ? [Vvar__2__x__25008] :
( t(Vvar__2__x__25008,Vvar__0__A__24988)
& Vvar__2___24Anonymous__24994 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24988,Vvar__2__x__25008,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24988)) )
| ? [Vvar__2__x__25015] :
( t(Vvar__2__x__25015,Vvar__0__A__24988)
& ? [Vvar__3__y__25016] :
( t(Vvar__3__y__25016,Vvar__0__A__24988)
& ? [Vvar__4__l__25017] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24988,Vvar__4__l__25017)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__24988,Vvar__1__leA__24989,Vvar__2__x__25015,Vvar__3__y__25016)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__24988,Vvar__1__leA__24989,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__24988,Vvar__4__l__25017,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24988,Vvar__3__y__25016,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24988))))
& Vvar__2___24Anonymous__24994 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2425282___24a6(Vvar__0__A__24988,Vvar__1__leA__24989,Vvar__2___24Anonymous__24994,Vvar__2__x__25015,Vvar__3__y__25016,Vvar__4__l__25017) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__24937,Vvar__1__leA__24938,Vvar__2___24Anonymous__24943,Vvar__3___24Anonymous__24944] :
( cType___24t(Vvar__0__A__24937)
=> ( c_24__type__24986___24t(Vvar__0__A__24937,Vvar__1__leA__24938,Vvar__2___24Anonymous__24943,Vvar__3___24Anonymous__24944,Vvar__1__leA__24938)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__2___24Anonymous__24943)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__3___24Anonymous__24944)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__24937,Vvar__1__leA__24938,Vvar__2___24Anonymous__24943,Vvar__3___24Anonymous__24944)
=> ( ? [Vvar__2__a__24952] :
( t(Vvar__2__a__24952,Vvar__0__A__24937)
& ? [Vvar__3__x__24953] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__3__x__24953)
& Vvar__3___24Anonymous__24944 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24937,Vvar__2__a__24952,Vvar__3__x__24953)
& Vvar__2___24Anonymous__24943 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24937) ) )
| ? [Vvar__2__a__24960] :
( t(Vvar__2__a__24960,Vvar__0__A__24937)
& ? [Vvar__3__b__24961] :
( t(Vvar__3__b__24961,Vvar__0__A__24937)
& p(happ(happ(Vvar__1__leA__24938,Vvar__2__a__24960),Vvar__3__b__24961))
& ? [Vvar__5__x__24963] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__5__x__24963)
& ? [Vvar__6__y__24964] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__6__y__24964)
& Vvar__3___24Anonymous__24944 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24937,Vvar__3__b__24961,Vvar__6__y__24964)
& Vvar__2___24Anonymous__24943 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24937,Vvar__2__a__24960,Vvar__5__x__24963) ) ) ) )
| ? [Vvar__2__a__24971] :
( t(Vvar__2__a__24971,Vvar__0__A__24937)
& ? [Vvar__3__x__24972] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__3__x__24972)
& ? [Vvar__4__y__24973] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24937,Vvar__4__y__24973)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__24937,Vvar__1__leA__24938,Vvar__3__x__24972,Vvar__4__y__24973)
& Vvar__3___24Anonymous__24944 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24937,Vvar__2__a__24971,Vvar__4__y__24973)
& Vvar__2___24Anonymous__24943 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24937,Vvar__2__a__24971,Vvar__3__x__24972) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__24611,Vvar__1__R__24612,Vvar__2__x__24613,Vvar__3___24Anonymous__24614] :
( cType___24t(Vvar__0__A__24611)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24611,Vvar__1__R__24612)
=> ( t(Vvar__2__x__24613,Vvar__0__A__24611)
=> ( t(Vvar__3___24Anonymous__24614,Vvar__0__A__24611)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__24611,Vvar__1__R__24612,Vvar__2__x__24613,Vvar__3___24Anonymous__24614)
=> ( ? [Vvar__3__y__24619] :
( t(Vvar__3__y__24619,Vvar__0__A__24611)
& p(happ(happ(Vvar__1__R__24612,Vvar__2__x__24613),Vvar__3__y__24619))
& Vvar__3___24Anonymous__24614 = Vvar__3__y__24619 )
| Vvar__3___24Anonymous__24614 = Vvar__2__x__24613 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__24659,Vvar__1__R__24660,Vvar__2__x__24661,Vvar__3___24Anonymous__24662] :
( cType___24t(Vvar__0__A__24659)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24659,Vvar__1__R__24660)
=> ( t(Vvar__2__x__24661,Vvar__0__A__24659)
=> ( t(Vvar__3___24Anonymous__24662,Vvar__0__A__24659)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__24659,Vvar__1__R__24660,Vvar__2__x__24661,Vvar__3___24Anonymous__24662)
=> ( Vvar__3___24Anonymous__24662 = Vvar__2__x__24661
| ? [Vvar__3__y__24670] :
( t(Vvar__3__y__24670,Vvar__0__A__24659)
& ? [Vvar__4__z__24671] :
( t(Vvar__4__z__24671,Vvar__0__A__24659)
& ( p(happ(happ(Vvar__1__R__24660,Vvar__2__x__24661),Vvar__3__y__24670))
| p(happ(happ(Vvar__1__R__24660,Vvar__3__y__24670),Vvar__2__x__24661)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__24659,Vvar__1__R__24660,Vvar__3__y__24670,Vvar__4__z__24671)
& Vvar__3___24Anonymous__24662 = Vvar__4__z__24671 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__24674,Vvar__1__R__24675,Vvar__2__x__24676,Vvar__3___24Anonymous__24677] :
( cType___24t(Vvar__0__A__24674)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24674,Vvar__1__R__24675)
=> ( t(Vvar__2__x__24676,Vvar__0__A__24674)
=> ( t(Vvar__3___24Anonymous__24677,Vvar__0__A__24674)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__24674,Vvar__1__R__24675,Vvar__2__x__24676,Vvar__3___24Anonymous__24677)
=> ( Vvar__3___24Anonymous__24677 = Vvar__2__x__24676
| ? [Vvar__3__y__24685] :
( t(Vvar__3__y__24685,Vvar__0__A__24674)
& ? [Vvar__4__z__24686] :
( t(Vvar__4__z__24686,Vvar__0__A__24674)
& ( p(happ(happ(Vvar__1__R__24675,Vvar__3__y__24685),Vvar__4__z__24686))
| p(happ(happ(Vvar__1__R__24675,Vvar__4__z__24686),Vvar__3__y__24685)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__24674,Vvar__1__R__24675,Vvar__2__x__24676,Vvar__3__y__24685)
& Vvar__3___24Anonymous__24677 = Vvar__4__z__24686 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__24624,Vvar__1__R__24625,Vvar__2__x__24626,Vvar__3___24Anonymous__24627] :
( cType___24t(Vvar__0__A__24624)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24624,Vvar__1__R__24625)
=> ( t(Vvar__2__x__24626,Vvar__0__A__24624)
=> ( t(Vvar__3___24Anonymous__24627,Vvar__0__A__24624)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__24624,Vvar__1__R__24625,Vvar__2__x__24626,Vvar__3___24Anonymous__24627)
=> ( ? [Vvar__3__y__24632] :
( t(Vvar__3__y__24632,Vvar__0__A__24624)
& p(happ(happ(Vvar__1__R__24625,Vvar__2__x__24626),Vvar__3__y__24632))
& Vvar__3___24Anonymous__24627 = Vvar__3__y__24632 )
| Vvar__3___24Anonymous__24627 = Vvar__2__x__24626
| ? [Vvar__3__y__24640] :
( t(Vvar__3__y__24640,Vvar__0__A__24624)
& ? [Vvar__4__z__24641] :
( t(Vvar__4__z__24641,Vvar__0__A__24624)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__24624,Vvar__1__R__24625,Vvar__2__x__24626,Vvar__3__y__24640)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__24624,Vvar__1__R__24625,Vvar__3__y__24640,Vvar__4__z__24641)
& Vvar__3___24Anonymous__24627 = Vvar__4__z__24641 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__24644,Vvar__1__R__24645,Vvar__2__x__24646,Vvar__3___24Anonymous__24647] :
( cType___24t(Vvar__0__A__24644)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24644,Vvar__1__R__24645)
=> ( t(Vvar__2__x__24646,Vvar__0__A__24644)
=> ( t(Vvar__3___24Anonymous__24647,Vvar__0__A__24644)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__24644,Vvar__1__R__24645,Vvar__2__x__24646,Vvar__3___24Anonymous__24647)
=> ( Vvar__3___24Anonymous__24647 = Vvar__2__x__24646
| ? [Vvar__3__y__24655] :
( t(Vvar__3__y__24655,Vvar__0__A__24644)
& ? [Vvar__4__z__24656] :
( t(Vvar__4__z__24656,Vvar__0__A__24644)
& p(happ(happ(Vvar__1__R__24645,Vvar__2__x__24646),Vvar__3__y__24655))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__24644,Vvar__1__R__24645,Vvar__3__y__24655,Vvar__4__z__24656)
& Vvar__3___24Anonymous__24647 = Vvar__4__z__24656 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__9980,Vvar__1__R__9981,Vvar__2__x__9982,Vvar__3___24Anonymous__9983] :
( cType___24t(Vvar__0__A__9980)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__9980,Vvar__1__R__9981)
=> ( t(Vvar__2__x__9982,Vvar__0__A__9980)
=> ( t(Vvar__3___24Anonymous__9983,Vvar__0__A__9980)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__9980,Vvar__1__R__9981,Vvar__2__x__9982,Vvar__3___24Anonymous__9983)
=> ( Vvar__3___24Anonymous__9983 = Vvar__2__x__9982
| ? [Vvar__3__y__9991] :
( t(Vvar__3__y__9991,Vvar__0__A__9980)
& ? [Vvar__4__z__9992] :
( t(Vvar__4__z__9992,Vvar__0__A__9980)
& p(happ(happ(Vvar__1__R__9981,Vvar__3__y__9991),Vvar__4__z__9992))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__9980,Vvar__1__R__9981,Vvar__2__x__9982,Vvar__3__y__9991)
& Vvar__3___24Anonymous__9983 = Vvar__4__z__9992 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__24560,Vvar__1__R__24561,Vvar__2__x__24562,Vvar__3___24Anonymous__24563] :
( cType___24t(Vvar__0__A__24560)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24560,Vvar__1__R__24561)
=> ( t(Vvar__2__x__24562,Vvar__0__A__24560)
=> ( t(Vvar__3___24Anonymous__24563,Vvar__0__A__24560)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__24560,Vvar__1__R__24561,Vvar__2__x__24562,Vvar__3___24Anonymous__24563)
=> ( ? [Vvar__3__y__24568] :
( t(Vvar__3__y__24568,Vvar__0__A__24560)
& p(happ(happ(Vvar__1__R__24561,Vvar__2__x__24562),Vvar__3__y__24568))
& Vvar__3___24Anonymous__24563 = Vvar__3__y__24568 )
| ? [Vvar__3__y__24573] :
( t(Vvar__3__y__24573,Vvar__0__A__24560)
& ? [Vvar__4__z__24574] :
( t(Vvar__4__z__24574,Vvar__0__A__24560)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__24560,Vvar__1__R__24561,Vvar__2__x__24562,Vvar__3__y__24573)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__24560,Vvar__1__R__24561,Vvar__3__y__24573,Vvar__4__z__24574)
& Vvar__3___24Anonymous__24563 = Vvar__4__z__24574 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__24577,Vvar__1__R__24578,Vvar__2__x__24579,Vvar__3___24Anonymous__24580] :
( cType___24t(Vvar__0__A__24577)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24577,Vvar__1__R__24578)
=> ( t(Vvar__2__x__24579,Vvar__0__A__24577)
=> ( t(Vvar__3___24Anonymous__24580,Vvar__0__A__24577)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__24577,Vvar__1__R__24578,Vvar__2__x__24579,Vvar__3___24Anonymous__24580)
=> ( ? [Vvar__3__y__24585] :
( t(Vvar__3__y__24585,Vvar__0__A__24577)
& p(happ(happ(Vvar__1__R__24578,Vvar__2__x__24579),Vvar__3__y__24585))
& Vvar__3___24Anonymous__24580 = Vvar__3__y__24585 )
| ? [Vvar__3__y__24590] :
( t(Vvar__3__y__24590,Vvar__0__A__24577)
& ? [Vvar__4__z__24591] :
( t(Vvar__4__z__24591,Vvar__0__A__24577)
& p(happ(happ(Vvar__1__R__24578,Vvar__2__x__24579),Vvar__3__y__24590))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__24577,Vvar__1__R__24578,Vvar__3__y__24590,Vvar__4__z__24591)
& Vvar__3___24Anonymous__24580 = Vvar__4__z__24591 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__24594,Vvar__1__R__24595,Vvar__2__x__24596,Vvar__3___24Anonymous__24597] :
( cType___24t(Vvar__0__A__24594)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__24594,Vvar__1__R__24595)
=> ( t(Vvar__2__x__24596,Vvar__0__A__24594)
=> ( t(Vvar__3___24Anonymous__24597,Vvar__0__A__24594)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__24594,Vvar__1__R__24595,Vvar__2__x__24596,Vvar__3___24Anonymous__24597)
=> ( ? [Vvar__3__y__24602] :
( t(Vvar__3__y__24602,Vvar__0__A__24594)
& p(happ(happ(Vvar__1__R__24595,Vvar__2__x__24596),Vvar__3__y__24602))
& Vvar__3___24Anonymous__24597 = Vvar__3__y__24602 )
| ? [Vvar__3__y__24607] :
( t(Vvar__3__y__24607,Vvar__0__A__24594)
& ? [Vvar__4__z__24608] :
( t(Vvar__4__z__24608,Vvar__0__A__24594)
& p(happ(happ(Vvar__1__R__24595,Vvar__3__y__24607),Vvar__4__z__24608))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__24594,Vvar__1__R__24595,Vvar__2__x__24596,Vvar__3__y__24607)
& Vvar__3___24Anonymous__24597 = Vvar__4__z__24608 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.le_AsB',axiom,
! [Vvar__0__A__24689,Vvar__1__B__24690,Vvar__2__leA__24691,Vvar__3__leB__24696,Vvar__4___24Anonymous__24701,Vvar__5___24Anonymous__24702] :
( cType___24t(Vvar__0__A__24689)
=> ( cType___24t(Vvar__1__B__24690)
=> ( c_24__type__24771___24t(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__2__leA__24691,Vvar__3__leB__24696,Vvar__4___24Anonymous__24701,Vvar__5___24Anonymous__24702,Vvar__2__leA__24691)
=> ( c_24__type__24796___24t(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__2__leA__24691,Vvar__3__leB__24696,Vvar__4___24Anonymous__24701,Vvar__5___24Anonymous__24702,Vvar__3__leB__24696)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__4___24Anonymous__24701)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__5___24Anonymous__24702)
=> ( cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__2__leA__24691,Vvar__3__leB__24696,Vvar__4___24Anonymous__24701,Vvar__5___24Anonymous__24702)
=> ( ? [Vvar__4__x__24716] :
( t(Vvar__4__x__24716,Vvar__0__A__24689)
& ? [Vvar__5__y__24717] :
( t(Vvar__5__y__24717,Vvar__0__A__24689)
& p(happ(happ(Vvar__2__leA__24691,Vvar__4__x__24716),Vvar__5__y__24717))
& Vvar__5___24Anonymous__24702 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__5__y__24717)
& Vvar__4___24Anonymous__24701 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__4__x__24716) ) )
| ? [Vvar__4__x__24731] :
( t(Vvar__4__x__24731,Vvar__0__A__24689)
& ? [Vvar__5__y__24732] :
( t(Vvar__5__y__24732,Vvar__1__B__24690)
& Vvar__5___24Anonymous__24702 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__5__y__24732)
& Vvar__4___24Anonymous__24701 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__4__x__24731) ) )
| ? [Vvar__4__x__24745] :
( t(Vvar__4__x__24745,Vvar__1__B__24690)
& ? [Vvar__5__y__24746] :
( t(Vvar__5__y__24746,Vvar__1__B__24690)
& p(happ(happ(Vvar__3__leB__24696,Vvar__4__x__24745),Vvar__5__y__24746))
& Vvar__5___24Anonymous__24702 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__5__y__24746)
& Vvar__4___24Anonymous__24701 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__24689,Vvar__1__B__24690,Vvar__4__x__24745) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
! [Vvar__0__A__9995,Vvar__1__B__9996,Vvar__2__leA__9999,Vvar__3__leB__10004,Vvar__4___24Anonymous__10011,Vvar__5___24Anonymous__10012] :
( cType___24t(Vvar__0__A__9995)
=> ( c_24__type__10075___24t(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__2__leA__9999,Vvar__3__leB__10004,Vvar__4___24Anonymous__10011,Vvar__5___24Anonymous__10012,Vvar__1__B__9996)
=> ( c_24__type__10104___24t(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__2__leA__9999,Vvar__3__leB__10004,Vvar__4___24Anonymous__10011,Vvar__5___24Anonymous__10012,Vvar__2__leA__9999)
=> ( c_24__type__10141___24t(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__2__leA__9999,Vvar__3__leB__10004,Vvar__4___24Anonymous__10011,Vvar__5___24Anonymous__10012,Vvar__3__leB__10004)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__4___24Anonymous__10011)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__5___24Anonymous__10012)
=> ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__2__leA__9999,Vvar__3__leB__10004,Vvar__4___24Anonymous__10011,Vvar__5___24Anonymous__10012)
=> ( ? [Vvar__4__x__10030] :
( t(Vvar__4__x__10030,Vvar__0__A__9995)
& ? [Vvar__5__x_27__10031] :
( t(Vvar__5__x_27__10031,Vvar__0__A__9995)
& ? [Vvar__6__y__10032] :
( t(Vvar__6__y__10032,happ(Vvar__1__B__9996,Vvar__4__x__10030))
& ? [Vvar__7__y_27__10033] :
( t(Vvar__7__y_27__10033,happ(Vvar__1__B__9996,Vvar__5__x_27__10031))
& p(happ(happ(Vvar__2__leA__9999,Vvar__4__x__10030),Vvar__5__x_27__10031))
& Vvar__5___24Anonymous__10012 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__5__x_27__10031,Vvar__7__y_27__10033)
& Vvar__4___24Anonymous__10011 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__4__x__10030,Vvar__6__y__10032) ) ) ) )
| ? [Vvar__4__x__10051] :
( t(Vvar__4__x__10051,Vvar__0__A__9995)
& ? [Vvar__5__y__10052] :
( t(Vvar__5__y__10052,happ(Vvar__1__B__9996,Vvar__4__x__10051))
& ? [Vvar__6__y_27__10053] :
( t(Vvar__6__y_27__10053,happ(Vvar__1__B__9996,Vvar__4__x__10051))
& p(happ(happ(happ(Vvar__3__leB__10004,Vvar__4__x__10051),Vvar__5__y__10052),Vvar__6__y_27__10053))
& Vvar__5___24Anonymous__10012 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__4__x__10051,Vvar__6__y_27__10053)
& Vvar__4___24Anonymous__10011 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__9995,Vvar__1__B__9996,Vvar__4__x__10051,Vvar__5__y__10052) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
! [Vvar__0__A__24895,Vvar__1__R__24896,Vvar__2___24Anonymous__24901,Vvar__3___24Anonymous__24902] :
( cType___24t(Vvar__0__A__24895)
=> ( c_24__type__24935___24t(Vvar__0__A__24895,Vvar__1__R__24896,Vvar__2___24Anonymous__24901,Vvar__3___24Anonymous__24902,Vvar__1__R__24896)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__2___24Anonymous__24901)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__3___24Anonymous__24902)
=> ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__24895,Vvar__1__R__24896,Vvar__2___24Anonymous__24901,Vvar__3___24Anonymous__24902)
=> ( ? [Vvar__2__x__24910] :
( t(Vvar__2__x__24910,Vvar__0__A__24895)
& ? [Vvar__3__y__24911] :
( t(Vvar__3__y__24911,Vvar__0__A__24895)
& ? [Vvar__4__p__24912] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__4__p__24912)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__1__R__24896,Vvar__1__R__24896,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__2__x__24910,Vvar__3__y__24911),Vvar__4__p__24912)
& Vvar__3___24Anonymous__24902 = Vvar__4__p__24912
& Vvar__2___24Anonymous__24901 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__2__x__24910,Vvar__3__y__24911) ) ) )
| ? [Vvar__2__x__24920] :
( t(Vvar__2__x__24920,Vvar__0__A__24895)
& ? [Vvar__3__y__24921] :
( t(Vvar__3__y__24921,Vvar__0__A__24895)
& ? [Vvar__4__p__24922] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__4__p__24922)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__1__R__24896,Vvar__1__R__24896,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__2__x__24920,Vvar__3__y__24921),Vvar__4__p__24922)
& Vvar__3___24Anonymous__24902 = Vvar__4__p__24922
& Vvar__2___24Anonymous__24901 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24895,Vvar__0__A__24895,Vvar__3__y__24921,Vvar__2__x__24920) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__24798,Vvar__1__B__24799,Vvar__2__leA__24800,Vvar__3__leB__24805,Vvar__4___24Anonymous__24810,Vvar__5___24Anonymous__24811] :
( cType___24t(Vvar__0__A__24798)
=> ( cType___24t(Vvar__1__B__24799)
=> ( c_24__type__24868___24t(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__2__leA__24800,Vvar__3__leB__24805,Vvar__4___24Anonymous__24810,Vvar__5___24Anonymous__24811,Vvar__2__leA__24800)
=> ( c_24__type__24893___24t(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__2__leA__24800,Vvar__3__leB__24805,Vvar__4___24Anonymous__24810,Vvar__5___24Anonymous__24811,Vvar__3__leB__24805)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__4___24Anonymous__24810)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__5___24Anonymous__24811)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__2__leA__24800,Vvar__3__leB__24805,Vvar__4___24Anonymous__24810,Vvar__5___24Anonymous__24811)
=> ( ? [Vvar__4__x__24825] :
( t(Vvar__4__x__24825,Vvar__0__A__24798)
& ? [Vvar__5__x_27__24826] :
( t(Vvar__5__x_27__24826,Vvar__0__A__24798)
& p(happ(happ(Vvar__2__leA__24800,Vvar__4__x__24825),Vvar__5__x_27__24826))
& ? [Vvar__7__y__24828] :
( t(Vvar__7__y__24828,Vvar__1__B__24799)
& Vvar__5___24Anonymous__24811 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__5__x_27__24826,Vvar__7__y__24828)
& Vvar__4___24Anonymous__24810 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__4__x__24825,Vvar__7__y__24828) ) ) )
| ? [Vvar__4__y__24841] :
( t(Vvar__4__y__24841,Vvar__1__B__24799)
& ? [Vvar__5__y_27__24842] :
( t(Vvar__5__y_27__24842,Vvar__1__B__24799)
& p(happ(happ(Vvar__3__leB__24805,Vvar__4__y__24841),Vvar__5__y_27__24842))
& ? [Vvar__7__x__24844] :
( t(Vvar__7__x__24844,Vvar__0__A__24798)
& Vvar__5___24Anonymous__24811 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__7__x__24844,Vvar__5__y_27__24842)
& Vvar__4___24Anonymous__24810 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24798,Vvar__1__B__24799,Vvar__7__x__24844,Vvar__4__y__24841) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__31234,Vvar__1__R__31235,Vvar__2__a__31240,Vvar__3___24Anonymous__31241] :
( cType___24t(Vvar__0__A__31234)
=> ( c_24__type__31271___24t(Vvar__0__A__31234,Vvar__1__R__31235,Vvar__2__a__31240,Vvar__3___24Anonymous__31241,Vvar__1__R__31235)
=> ( t(Vvar__2__a__31240,Vvar__0__A__31234)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31234,Vvar__3___24Anonymous__31241)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__31234,Vvar__1__R__31235,Vvar__2__a__31240,Vvar__3___24Anonymous__31241)
=> ( Vvar__3___24Anonymous__31241 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31234)
| ? [Vvar__3__b__31257] :
( t(Vvar__3__b__31257,Vvar__0__A__31234)
& ? [Vvar__4__l__31258] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31234,Vvar__4__l__31258)
& p(happ(happ(Vvar__1__R__31235,Vvar__2__a__31240),Vvar__3__b__31257))
& Vvar__3___24Anonymous__31241 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31234,Vvar__3__b__31257,Vvar__4__l__31258) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__31191,Vvar__1__R__31192,Vvar__2___24Anonymous__31197] :
( cType___24t(Vvar__0__A__31191)
=> ( c_24__type__31232___24t(Vvar__0__A__31191,Vvar__1__R__31192,Vvar__2___24Anonymous__31197,Vvar__1__R__31192)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31191,Vvar__2___24Anonymous__31197)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__31191,Vvar__1__R__31192,Vvar__2___24Anonymous__31197)
=> ( Vvar__2___24Anonymous__31197 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31191)
| ? [Vvar__2__a__31211] :
( t(Vvar__2__a__31211,Vvar__0__A__31191)
& Vvar__2___24Anonymous__31197 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31191,Vvar__2__a__31211,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31191)) )
| ? [Vvar__2__a__31218] :
( t(Vvar__2__a__31218,Vvar__0__A__31191)
& ? [Vvar__3__b__31219] :
( t(Vvar__3__b__31219,Vvar__0__A__31191)
& ? [Vvar__4__l__31220] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31191,Vvar__4__l__31220)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__31191,Vvar__1__R__31192,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31191,Vvar__3__b__31219,Vvar__4__l__31220))
& p(happ(happ(Vvar__1__R__31192,Vvar__2__a__31218),Vvar__3__b__31219))
& Vvar__2___24Anonymous__31197 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31191,Vvar__2__a__31218,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31191,Vvar__3__b__31219,Vvar__4__l__31220)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__31273,Vvar__1__R__31274,Vvar__2___24Anonymous__31279] :
( cType___24t(Vvar__0__A__31273)
=> ( c_24__type__31306___24t(Vvar__0__A__31273,Vvar__1__R__31274,Vvar__2___24Anonymous__31279,Vvar__1__R__31274)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31273,Vvar__2___24Anonymous__31279)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__31273,Vvar__1__R__31274,Vvar__2___24Anonymous__31279)
=> ( Vvar__2___24Anonymous__31279 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31273)
| ? [Vvar__2__a__31293] :
( t(Vvar__2__a__31293,Vvar__0__A__31273)
& ? [Vvar__3__l__31294] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31273,Vvar__3__l__31294)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__31273,Vvar__1__R__31274,Vvar__3__l__31294)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__31273,Vvar__1__R__31274,Vvar__2__a__31293,Vvar__3__l__31294)
& Vvar__2___24Anonymous__31279 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31273,Vvar__2__a__31293,Vvar__3__l__31294) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__31308,Vvar__1__R__31309,Vvar__2___24Anonymous__31314] :
( cType___24t(Vvar__0__A__31308)
=> ( c_24__type__31341___24t(Vvar__0__A__31308,Vvar__1__R__31309,Vvar__2___24Anonymous__31314,Vvar__1__R__31309)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31308,Vvar__2___24Anonymous__31314)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__31308,Vvar__1__R__31309,Vvar__2___24Anonymous__31314)
=> ( Vvar__2___24Anonymous__31314 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31308)
| ? [Vvar__2__a__31328] :
( t(Vvar__2__a__31328,Vvar__0__A__31308)
& ? [Vvar__3__l__31329] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31308,Vvar__3__l__31329)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__31308,Vvar__1__R__31309,Vvar__3__l__31329)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__31308,happ(Vvar__1__R__31309,Vvar__2__a__31328),Vvar__3__l__31329)
& Vvar__2___24Anonymous__31314 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31308,Vvar__2__a__31328,Vvar__3__l__31329) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX4003] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX4003)
=> ? [Vvar__0___24Anonymous__4004] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__4004)
& ? [Vvar__1___24Anonymous__4005] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__4005)
& ? [Vvar__2___24Anonymous__4006] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4006)
& ? [Vvar__3___24Anonymous__4007] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__4007)
& ? [Vvar__4___24Anonymous__4008] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__4008)
& ? [Vvar__5___24Anonymous__4009] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__4009)
& ? [Vvar__6___24Anonymous__4010] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__4010)
& ? [Vvar__7___24Anonymous__4011] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__4011)
& VX4003 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__4004,Vvar__1___24Anonymous__4005,Vvar__2___24Anonymous__4006,Vvar__3___24Anonymous__4007,Vvar__4___24Anonymous__4008,Vvar__5___24Anonymous__4009,Vvar__6___24Anonymous__4010,Vvar__7___24Anonymous__4011) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX16841] :
( cCoq_2eStrings_2eString_2estring___24t(VX16841)
=> ( VX16841 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__16842] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__16842)
& ? [Vvar__1___24Anonymous__16843] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__16843)
& VX16841 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__16842,Vvar__1___24Anonymous__16843) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890,VX8891] :
( cType___24t(Vvar__0__X__8878)
=> ( c_24__type__8951___24t(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890,Vvar__1__lt__8879)
=> ( c_24__type__8970___24t(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890,Vvar__2__eq__8884)
=> ( t(Vvar__3__x__8889,Vvar__0__X__8878)
=> ( t(Vvar__4__y__8890,Vvar__0__X__8878)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890,VX8891)
=> ( ( p(happ(happ(Vvar__1__lt__8879,Vvar__3__x__8889),Vvar__4__y__8890))
& VX8891 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890) )
| ( p(happ(happ(Vvar__2__eq__8884,Vvar__3__x__8889),Vvar__4__y__8890))
& VX8891 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890) )
| ( p(happ(happ(Vvar__1__lt__8879,Vvar__4__y__8890),Vvar__3__x__8889))
& VX8891 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__8878,Vvar__1__lt__8879,Vvar__2__eq__8884,Vvar__3__x__8889,Vvar__4__y__8890) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__32002,Vvar__1___24Anonymous__32003] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__32002)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__32003)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__32002,Vvar__1___24Anonymous__32003)
=> ( ? [Vvar__0__a__32005] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__32005)
& ? [Vvar__1__s__32006] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__32006)
& Vvar__1___24Anonymous__32003 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__32005,Vvar__1__s__32006)
& Vvar__0___24Anonymous__32002 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__32007] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__32007)
& ? [Vvar__1__s1__32008] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__32008)
& ? [Vvar__2__s2__32009] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__32009)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__32008,Vvar__2__s2__32009)
& Vvar__1___24Anonymous__32003 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__32007,Vvar__2__s2__32009)
& Vvar__0___24Anonymous__32002 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__32007,Vvar__1__s1__32008) ) ) )
| ? [Vvar__0__a__32011] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__32011)
& ? [Vvar__1__b__32012] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__32012)
& ? [Vvar__2__s1__32013] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__32013)
& ? [Vvar__3__s2__32014] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__32014)
& p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__32011),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__32012)))
& Vvar__1___24Anonymous__32003 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__32012,Vvar__3__s2__32014)
& Vvar__0___24Anonymous__32002 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__32011,Vvar__2__s1__32013) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX2547] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX2547)
=> ( VX2547 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX2547 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX2547 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__8412,VX8413] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8412)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__8412,VX8413)
=> ( ? [Vvar__0__n__8414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__8414)
& Vvar__0___24Anonymous__8412 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__8414)
& VX8413 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8414) )
| ? [Vvar__0__n__8415] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__8415)
& ? [Vvar__1___24Anonymous__8416] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__8415,Vvar__1___24Anonymous__8416)
& Vvar__0___24Anonymous__8412 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__8415)
& VX8413 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8415,Vvar__1___24Anonymous__8416) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
! [Vvar__0__A__31460,Vvar__1__P__31461,Vvar__2__n__31464,Vvar__3___24Anonymous__31465] :
( cType___24t(Vvar__0__A__31460)
=> ( c_24__type__31488___24t(Vvar__0__A__31460,Vvar__1__P__31461,Vvar__2__n__31464,Vvar__3___24Anonymous__31465,Vvar__1__P__31461)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__31464)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31460,Vvar__2__n__31464,Vvar__3___24Anonymous__31465)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__31460,Vvar__1__P__31461,Vvar__2__n__31464,Vvar__3___24Anonymous__31465)
=> ( ? [Vvar__2__m__31471] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__31471)
& ? [Vvar__3__x__31472] :
( t(Vvar__3__x__31472,Vvar__0__A__31460)
& ? [Vvar__4__v__31473] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31460,Vvar__2__m__31471,Vvar__4__v__31473)
& p(happ(Vvar__1__P__31461,Vvar__3__x__31472))
& Vvar__3___24Anonymous__31465 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31460,Vvar__3__x__31472,Vvar__2__m__31471,Vvar__4__v__31473)
& Vvar__2__n__31464 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__31471) ) ) )
| ? [Vvar__2__m__31479] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__31479)
& ? [Vvar__3__x__31480] :
( t(Vvar__3__x__31480,Vvar__0__A__31460)
& ? [Vvar__4__v__31481] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31460,Vvar__2__m__31479,Vvar__4__v__31481)
& cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__31460,Vvar__1__P__31461,Vvar__2__m__31479,Vvar__4__v__31481)
& Vvar__3___24Anonymous__31465 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31460,Vvar__3__x__31480,Vvar__2__m__31479,Vvar__4__v__31481)
& Vvar__2__n__31464 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__31479) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
! [Vvar__0__A__31556,Vvar__1__B__31557,Vvar__2__P__31558,Vvar__3__n__31563,Vvar__4___24Anonymous__31564,Vvar__5___24Anonymous__31565] :
( cType___24t(Vvar__0__A__31556)
=> ( cType___24t(Vvar__1__B__31557)
=> ( c_24__type__31610___24t(Vvar__0__A__31556,Vvar__1__B__31557,Vvar__2__P__31558,Vvar__3__n__31563,Vvar__4___24Anonymous__31564,Vvar__5___24Anonymous__31565,Vvar__2__P__31558)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__31563)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31556,Vvar__3__n__31563,Vvar__4___24Anonymous__31564)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__31557,Vvar__3__n__31563,Vvar__5___24Anonymous__31565)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__31556,Vvar__1__B__31557,Vvar__2__P__31558,Vvar__3__n__31563,Vvar__4___24Anonymous__31564,Vvar__5___24Anonymous__31565)
=> ( ? [Vvar__3__m__31574] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__31574)
& ? [Vvar__4__x1__31575] :
( t(Vvar__4__x1__31575,Vvar__0__A__31556)
& ? [Vvar__5__x2__31576] :
( t(Vvar__5__x2__31576,Vvar__1__B__31557)
& ? [Vvar__6__v1__31577] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31556,Vvar__3__m__31574,Vvar__6__v1__31577)
& ? [Vvar__7__v2__31578] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__31557,Vvar__3__m__31574,Vvar__7__v2__31578)
& p(happ(happ(Vvar__2__P__31558,Vvar__4__x1__31575),Vvar__5__x2__31576))
& Vvar__5___24Anonymous__31565 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__31557,Vvar__5__x2__31576,Vvar__3__m__31574,Vvar__7__v2__31578)
& Vvar__4___24Anonymous__31564 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31556,Vvar__4__x1__31575,Vvar__3__m__31574,Vvar__6__v1__31577)
& Vvar__3__n__31563 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__31574) ) ) ) ) )
| ? [Vvar__3__m__31587] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__31587)
& ? [Vvar__4__x1__31588] :
( t(Vvar__4__x1__31588,Vvar__0__A__31556)
& ? [Vvar__5__x2__31589] :
( t(Vvar__5__x2__31589,Vvar__1__B__31557)
& ? [Vvar__6__v1__31590] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31556,Vvar__3__m__31587,Vvar__6__v1__31590)
& ? [Vvar__7__v2__31591] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__31557,Vvar__3__m__31587,Vvar__7__v2__31591)
& cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__31556,Vvar__1__B__31557,Vvar__2__P__31558,Vvar__3__m__31587,Vvar__6__v1__31590,Vvar__7__v2__31591)
& Vvar__5___24Anonymous__31565 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__31557,Vvar__5__x2__31589,Vvar__3__m__31587,Vvar__7__v2__31591)
& Vvar__4___24Anonymous__31564 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31556,Vvar__4__x1__31588,Vvar__3__m__31587,Vvar__6__v1__31590)
& Vvar__3__n__31563 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__31587) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
! [Vvar__0__A__3136,Vvar__1__P__3137,Vvar__2__n__3140,Vvar__3__v__3141] :
( cType___24t(Vvar__0__A__3136)
=> ( c_24__type__3161___24t(Vvar__0__A__3136,Vvar__1__P__3137,Vvar__2__n__3140,Vvar__3__v__3141,Vvar__1__P__3137)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__3140)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3136,Vvar__2__n__3140,Vvar__3__v__3141)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__3136,Vvar__1__P__3137,Vvar__2__n__3140,Vvar__3__v__3141)
=> ( ( Vvar__3__v__3141 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3136)
& Vvar__2__n__3140 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__n__3151] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__3151)
& ? [Vvar__3__x__3152] :
( t(Vvar__3__x__3152,Vvar__0__A__3136)
& ? [Vvar__4__v__3153] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3136,Vvar__2__n__3151,Vvar__4__v__3153)
& p(happ(Vvar__1__P__3137,Vvar__3__x__3152))
& cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__3136,Vvar__1__P__3137,Vvar__2__n__3151,Vvar__4__v__3153)
& Vvar__3__v__3141 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3136,Vvar__3__x__3152,Vvar__2__n__3151,Vvar__4__v__3153)
& Vvar__2__n__3140 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__3151) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
! [Vvar__0__A__31505,Vvar__1__B__31506,Vvar__2__P__31507,Vvar__3__n__31512,Vvar__4___24Anonymous__31513,Vvar__5___24Anonymous__31514] :
( cType___24t(Vvar__0__A__31505)
=> ( cType___24t(Vvar__1__B__31506)
=> ( c_24__type__31554___24t(Vvar__0__A__31505,Vvar__1__B__31506,Vvar__2__P__31507,Vvar__3__n__31512,Vvar__4___24Anonymous__31513,Vvar__5___24Anonymous__31514,Vvar__2__P__31507)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__31512)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31505,Vvar__3__n__31512,Vvar__4___24Anonymous__31513)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__31506,Vvar__3__n__31512,Vvar__5___24Anonymous__31514)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__31505,Vvar__1__B__31506,Vvar__2__P__31507,Vvar__3__n__31512,Vvar__4___24Anonymous__31513,Vvar__5___24Anonymous__31514)
=> ( ( Vvar__5___24Anonymous__31514 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__31506)
& Vvar__4___24Anonymous__31513 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__31505)
& Vvar__3__n__31512 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__3__m__31530] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__31530)
& ? [Vvar__4__x1__31531] :
( t(Vvar__4__x1__31531,Vvar__0__A__31505)
& ? [Vvar__5__x2__31532] :
( t(Vvar__5__x2__31532,Vvar__1__B__31506)
& ? [Vvar__6__v1__31533] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31505,Vvar__3__m__31530,Vvar__6__v1__31533)
& ? [Vvar__7__v2__31534] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__31506,Vvar__3__m__31530,Vvar__7__v2__31534)
& p(happ(happ(Vvar__2__P__31507,Vvar__4__x1__31531),Vvar__5__x2__31532))
& cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__31505,Vvar__1__B__31506,Vvar__2__P__31507,Vvar__3__m__31530,Vvar__6__v1__31533,Vvar__7__v2__31534)
& Vvar__5___24Anonymous__31514 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__31506,Vvar__5__x2__31532,Vvar__3__m__31530,Vvar__7__v2__31534)
& Vvar__4___24Anonymous__31513 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31505,Vvar__4__x1__31531,Vvar__3__m__31530,Vvar__6__v1__31533)
& Vvar__3__n__31512 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__31530) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
! [Vvar__0__A__31490,Vvar__1__a__31491,Vvar__2__n__31492,Vvar__3___24Anonymous__31493] :
( cType___24t(Vvar__0__A__31490)
=> ( t(Vvar__1__a__31491,Vvar__0__A__31490)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__31492)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31490,Vvar__2__n__31492,Vvar__3___24Anonymous__31493)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__31490,Vvar__1__a__31491,Vvar__2__n__31492,Vvar__3___24Anonymous__31493)
=> ( ? [Vvar__2__m__31497] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__31497)
& ? [Vvar__3__v__31498] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31490,Vvar__2__m__31497,Vvar__3__v__31498)
& Vvar__3___24Anonymous__31493 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31490,Vvar__1__a__31491,Vvar__2__m__31497,Vvar__3__v__31498)
& Vvar__2__n__31492 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__31497) ) )
| ? [Vvar__2__m__31501] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__31501)
& ? [Vvar__3__x__31502] :
( t(Vvar__3__x__31502,Vvar__0__A__31490)
& ? [Vvar__4__v__31503] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__31490,Vvar__2__m__31501,Vvar__4__v__31503)
& cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__31490,Vvar__1__a__31491,Vvar__2__m__31501,Vvar__4__v__31503)
& Vvar__3___24Anonymous__31493 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__31490,Vvar__3__x__31502,Vvar__2__m__31501,Vvar__4__v__31503)
& Vvar__2__n__31492 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__31501) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__3110,Vvar__1___24Anonymous__3111,VX3112] :
( cType___24t(Vvar__0__A__3110)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__3111)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3110,Vvar__1___24Anonymous__3111,VX3112)
=> ( ( Vvar__1___24Anonymous__3111 = cCoq_2eInit_2eDatatypes_2eO
& VX3112 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3110) )
| ? [Vvar__1__h__3115] :
( t(Vvar__1__h__3115,Vvar__0__A__3110)
& ? [Vvar__2__n__3116] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__3116)
& ? [Vvar__3___24Anonymous__3117] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3110,Vvar__2__n__3116,Vvar__3___24Anonymous__3117)
& Vvar__1___24Anonymous__3111 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__3116)
& VX3112 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3110,Vvar__1__h__3115,Vvar__2__n__3116,Vvar__3___24Anonymous__3117) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__22793,Vvar__1__b__22794,Vvar__2__d__22795] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__22793)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__22794)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__22795)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__22793,Vvar__1__b__22794,Vvar__2__d__22795)
=> ? [Vvar__3__u__22800] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__22800)
& ? [Vvar__4__v__22801] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__22801)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__22800,Vvar__0__a__22793),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__22801,Vvar__1__b__22794)) = Vvar__2__d__22795
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__22768,Vvar__1__b__22769,VX22770] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__22768)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__22769)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__22768,Vvar__1__b__22769,VX22770)
=> ? [Vvar__2__u__22773] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__22773)
& ? [Vvar__3__v__22774] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__22774)
& ? [Vvar__4__d__22775] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__22775)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__22773,Vvar__0__a__22768),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__22774,Vvar__1__b__22769)) = Vvar__4__d__22775
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__22768,Vvar__1__b__22769,Vvar__4__d__22775)
& VX22770 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__22768,Vvar__1__b__22769,Vvar__2__u__22773,Vvar__3__v__22774,Vvar__4__d__22775) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__22740,Vvar__1__b__22741,Vvar__2__g__22742] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__22740)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__22741)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__22742)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__22740,Vvar__1__b__22741,Vvar__2__g__22742)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__22742,Vvar__0__a__22740)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__22742,Vvar__1__b__22741)
& ! [Vvar__var__var__var__var__5__x__22750__22753__22756__22759__22762] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__22750__22753__22756__22759__22762)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__22750__22753__22756__22759__22762,Vvar__0__a__22740)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__22750__22753__22756__22759__22762,Vvar__1__b__22741)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__22750__22753__22756__22759__22762,Vvar__2__g__22742) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__17243] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__17243)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__17243)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__17243))
& ! [Vvar__var__var__2__n__17248__17250__17252] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__17248__17250__17252)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__17248__17250__17252))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__17248__17250__17252,Vvar__0__p__17243)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__17248__17250__17252,Vvar__0__p__17243) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__31775,Vvar__1__p__31776,VX31777] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__31775)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__31776)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__31775,Vvar__1__p__31776,VX31777)
=> ? [Vvar__2__q__31780] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__31780)
& ? [Vvar__3__r__31781] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__31781)
& Vvar__0__x__31775 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__31780,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__31776)),Vvar__3__r__31781)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__31781))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__31781,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__31776)))
& VX31777 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__31775,Vvar__1__p__31776,Vvar__2__q__31780,Vvar__3__r__31781) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__5037,Vvar__1__F__5038] :
( cType___24t(Vvar__0__T__5037)
=> ( t(Vvar__1__F__5038,Vvar__0__T__5037)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__5037,Vvar__1__F__5038)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__18650,Vvar__1__F__18651] :
( cType___24t(Vvar__0__T__18650)
=> ( t(Vvar__1__F__18651,Vvar__0__T__18650)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__18650,Vvar__1__F__18651)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX18658] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX18658)
=> ( VX18658 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__18659] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18659)
& ? [Vvar__1___24Anonymous__18660] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__18660)
& VX18658 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__18659,Vvar__1___24Anonymous__18660) ) )
| ? [Vvar__0___24Anonymous__18661] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18661)
& ? [Vvar__1___24Anonymous__18662] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__18662)
& VX18658 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__18661,Vvar__1___24Anonymous__18662) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__5042,VX5043] :
( cType___24t(Vvar__0__C__5042)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,VX5043)
=> ( ? [Vvar__1___24Anonymous__5045] :
( t(Vvar__1___24Anonymous__5045,Vvar__0__C__5042)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__5042,Vvar__1___24Anonymous__5045) )
| ? [Vvar__1___24Anonymous__5047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5047)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__5042,Vvar__1___24Anonymous__5047) )
| ? [Vvar__1___24Anonymous__5049] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__1___24Anonymous__5049)
& ? [Vvar__2___24Anonymous__5050] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__2___24Anonymous__5050)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__5042,Vvar__1___24Anonymous__5049,Vvar__2___24Anonymous__5050) ) )
| ? [Vvar__1___24Anonymous__5052] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__1___24Anonymous__5052)
& ? [Vvar__2___24Anonymous__5053] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__2___24Anonymous__5053)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__5042,Vvar__1___24Anonymous__5052,Vvar__2___24Anonymous__5053) ) )
| ? [Vvar__1___24Anonymous__5055] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__1___24Anonymous__5055)
& ? [Vvar__2___24Anonymous__5056] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__2___24Anonymous__5056)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__5042,Vvar__1___24Anonymous__5055,Vvar__2___24Anonymous__5056) ) )
| ? [Vvar__1___24Anonymous__5058] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__1___24Anonymous__5058)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__5042,Vvar__1___24Anonymous__5058) )
| ? [Vvar__1___24Anonymous__5060] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__5042,Vvar__1___24Anonymous__5060)
& ? [Vvar__2___24Anonymous__5061] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5061)
& VX5043 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__5042,Vvar__1___24Anonymous__5060,Vvar__2___24Anonymous__5061) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__5206,VX5207] :
( cType___24t(Vvar__0__C__5206)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5206,VX5207)
=> ( ? [Vvar__1___24Anonymous__5209] :
( t(Vvar__1___24Anonymous__5209,Vvar__0__C__5206)
& VX5207 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__5206,Vvar__1___24Anonymous__5209) )
| ? [Vvar__1___24Anonymous__5211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5211)
& ? [Vvar__2___24Anonymous__5212] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5206,Vvar__2___24Anonymous__5212)
& VX5207 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__5206,Vvar__1___24Anonymous__5211,Vvar__2___24Anonymous__5212) ) )
| ? [Vvar__1___24Anonymous__5214] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5206,Vvar__1___24Anonymous__5214)
& ? [Vvar__2___24Anonymous__5215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5215)
& ? [Vvar__3___24Anonymous__5216] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__5206,Vvar__3___24Anonymous__5216)
& VX5207 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__5206,Vvar__1___24Anonymous__5214,Vvar__2___24Anonymous__5215,Vvar__3___24Anonymous__5216) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456] :
( cType___24t(Vvar__0__R__1425)
=> ( t(Vvar__1__rO__1426,Vvar__0__R__1425)
=> ( t(Vvar__2__rI__1427,Vvar__0__R__1425)
=> ( c_24__type__1857___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__3__rplus__1428)
=> ( c_24__type__1958___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__4__rtimes__1433)
=> ( c_24__type__2059___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__5__rminus__1438)
=> ( c_24__type__2149___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__6__ropp__1443)
=> ( c_24__type__2250___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__7__req__1446)
=> ( c_24__type__2351___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__8__rle__1451)
=> ( c_24__type__2452___24t(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456,Vvar__9__rlt__1456)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446,Vvar__8__rle__1451,Vvar__9__rlt__1456)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__1425,Vvar__7__req__1446)
& ! [Vvar__var__var__var__var__11__x1__1500__1506__1611__1617__1623] :
( t(Vvar__var__var__var__var__11__x1__1500__1506__1611__1617__1623,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__12__x2__1501__1507__1612__1618__1624] :
( t(Vvar__var__var__var__var__12__x2__1501__1507__1612__1618__1624,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__11__x1__1500__1506__1611__1617__1623),Vvar__var__var__var__var__12__x2__1501__1507__1612__1618__1624))
=> ! [Vvar__var__var__var__var__14__y1__1502__1508__1613__1619__1625] :
( t(Vvar__var__var__var__var__14__y1__1502__1508__1613__1619__1625,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__15__y2__1503__1509__1614__1620__1626] :
( t(Vvar__var__var__var__var__15__y2__1503__1509__1614__1620__1626,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__14__y1__1502__1508__1613__1619__1625),Vvar__var__var__var__var__15__y2__1503__1509__1614__1620__1626))
=> p(happ(happ(Vvar__7__req__1446,happ(happ(Vvar__3__rplus__1428,Vvar__var__var__var__var__11__x1__1500__1506__1611__1617__1623),Vvar__var__var__var__var__14__y1__1502__1508__1613__1619__1625)),happ(happ(Vvar__3__rplus__1428,Vvar__var__var__var__var__12__x2__1501__1507__1612__1618__1624),Vvar__var__var__var__var__15__y2__1503__1509__1614__1620__1626))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__1513__1519__1629__1635__1641] :
( t(Vvar__var__var__var__var__12__x1__1513__1519__1629__1635__1641,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__13__x2__1514__1520__1630__1636__1642] :
( t(Vvar__var__var__var__var__13__x2__1514__1520__1630__1636__1642,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__12__x1__1513__1519__1629__1635__1641),Vvar__var__var__var__var__13__x2__1514__1520__1630__1636__1642))
=> ! [Vvar__var__var__var__var__15__y1__1515__1521__1631__1637__1643] :
( t(Vvar__var__var__var__var__15__y1__1515__1521__1631__1637__1643,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__16__y2__1516__1522__1632__1638__1644] :
( t(Vvar__var__var__var__var__16__y2__1516__1522__1632__1638__1644,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__15__y1__1515__1521__1631__1637__1643),Vvar__var__var__var__var__16__y2__1516__1522__1632__1638__1644))
=> p(happ(happ(Vvar__7__req__1446,happ(happ(Vvar__4__rtimes__1433,Vvar__var__var__var__var__12__x1__1513__1519__1629__1635__1641),Vvar__var__var__var__var__15__y1__1515__1521__1631__1637__1643)),happ(happ(Vvar__4__rtimes__1433,Vvar__var__var__var__var__13__x2__1514__1520__1630__1636__1642),Vvar__var__var__var__var__16__y2__1516__1522__1632__1638__1644))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__1526__1529__1647__1650__1653] :
( t(Vvar__var__var__var__var__13__x1__1526__1529__1647__1650__1653,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__14__x2__1527__1530__1648__1651__1654] :
( t(Vvar__var__var__var__var__14__x2__1527__1530__1648__1651__1654,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__13__x1__1526__1529__1647__1650__1653),Vvar__var__var__var__var__14__x2__1527__1530__1648__1651__1654))
=> p(happ(happ(Vvar__7__req__1446,happ(Vvar__6__ropp__1443,Vvar__var__var__var__var__13__x1__1526__1529__1647__1650__1653)),happ(Vvar__6__ropp__1443,Vvar__var__var__var__var__14__x2__1527__1530__1648__1651__1654))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__1533__1539__1656__1662__1668] :
( t(Vvar__var__var__var__var__14__x1__1533__1539__1656__1662__1668,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__15__x2__1534__1540__1657__1663__1669] :
( t(Vvar__var__var__var__var__15__x2__1534__1540__1657__1663__1669,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__14__x1__1533__1539__1656__1662__1668),Vvar__var__var__var__var__15__x2__1534__1540__1657__1663__1669))
=> ! [Vvar__var__var__var__var__17__y1__1535__1541__1658__1664__1670] :
( t(Vvar__var__var__var__var__17__y1__1535__1541__1658__1664__1670,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__18__y2__1536__1542__1659__1665__1671] :
( t(Vvar__var__var__var__var__18__y2__1536__1542__1659__1665__1671,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__17__y1__1535__1541__1658__1664__1670),Vvar__var__var__var__var__18__y2__1536__1542__1659__1665__1671))
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__14__x1__1533__1539__1656__1662__1668),Vvar__var__var__var__var__17__y1__1535__1541__1658__1664__1670))
<=> p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__15__x2__1534__1540__1657__1663__1669),Vvar__var__var__var__var__18__y2__1536__1542__1659__1665__1671)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__1546__1552__1674__1680__1686] :
( t(Vvar__var__var__var__var__15__x1__1546__1552__1674__1680__1686,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__16__x2__1547__1553__1675__1681__1687] :
( t(Vvar__var__var__var__var__16__x2__1547__1553__1675__1681__1687,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__15__x1__1546__1552__1674__1680__1686),Vvar__var__var__var__var__16__x2__1547__1553__1675__1681__1687))
=> ! [Vvar__var__var__var__var__18__y1__1548__1554__1676__1682__1688] :
( t(Vvar__var__var__var__var__18__y1__1548__1554__1676__1682__1688,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__19__y2__1549__1555__1677__1683__1689] :
( t(Vvar__var__var__var__var__19__y2__1549__1555__1677__1683__1689,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__18__y1__1548__1554__1676__1682__1688),Vvar__var__var__var__var__19__y2__1549__1555__1677__1683__1689))
=> ( p(happ(happ(Vvar__9__rlt__1456,Vvar__var__var__var__var__15__x1__1546__1552__1674__1680__1686),Vvar__var__var__var__var__18__y1__1548__1554__1676__1682__1688))
<=> p(happ(happ(Vvar__9__rlt__1456,Vvar__var__var__var__var__16__x2__1547__1553__1675__1681__1687),Vvar__var__var__var__var__19__y2__1549__1555__1677__1683__1689)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__1425,Vvar__1__rO__1426,Vvar__2__rI__1427,Vvar__3__rplus__1428,Vvar__4__rtimes__1433,Vvar__5__rminus__1438,Vvar__6__ropp__1443,Vvar__7__req__1446)
& ! [Vvar__var__var__var__17__n__1560__1561__1692__1693] :
( t(Vvar__var__var__var__17__n__1560__1561__1692__1693,Vvar__0__R__1425)
=> p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__17__n__1560__1561__1692__1693),Vvar__var__var__var__17__n__1560__1561__1692__1693)) )
& ! [Vvar__var__var__var__var__18__n__1563__1567__1694__1698__1702] :
( t(Vvar__var__var__var__var__18__n__1563__1567__1694__1698__1702,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__19__m__1564__1568__1695__1699__1703] :
( t(Vvar__var__var__var__var__19__m__1564__1568__1695__1699__1703,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__18__n__1563__1567__1694__1698__1702),Vvar__var__var__var__var__19__m__1564__1568__1695__1699__1703))
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__19__m__1564__1568__1695__1699__1703),Vvar__var__var__var__var__18__n__1563__1567__1694__1698__1702))
=> p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__18__n__1563__1567__1694__1698__1702),Vvar__var__var__var__var__19__m__1564__1568__1695__1699__1703)) ) ) ) )
& ! [Vvar__var__var__var__19__n__1572__1577__1706__1711] :
( t(Vvar__var__var__var__19__n__1572__1577__1706__1711,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__20__m__1573__1578__1707__1712] :
( t(Vvar__var__var__var__20__m__1573__1578__1707__1712,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__21__p__1574__1579__1708__1713] :
( t(Vvar__var__var__var__21__p__1574__1579__1708__1713,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__19__n__1572__1577__1706__1711),Vvar__var__var__var__20__m__1573__1578__1707__1712))
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__20__m__1573__1578__1707__1712),Vvar__var__var__var__21__p__1574__1579__1708__1713))
=> p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__19__n__1572__1577__1706__1711),Vvar__var__var__var__21__p__1574__1579__1708__1713)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__1583__1585__1716__1718__1720__1722] :
( t(Vvar__var__var__var__var__var__20__n__1583__1585__1716__1718__1720__1722,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__var__21__m__1584__1586__1717__1719__1721__1723] :
( t(Vvar__var__var__var__var__var__21__m__1584__1586__1717__1719__1721__1723,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__9__rlt__1456,Vvar__var__var__var__var__var__20__n__1583__1585__1716__1718__1720__1722),Vvar__var__var__var__var__var__21__m__1584__1586__1717__1719__1721__1723))
<=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__var__20__n__1583__1585__1716__1718__1720__1722),Vvar__var__var__var__var__var__21__m__1584__1586__1717__1719__1721__1723))
& ~ p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__var__20__n__1583__1585__1716__1718__1720__1722),Vvar__var__var__var__var__var__21__m__1584__1586__1717__1719__1721__1723)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__1588__1590__1724__1726__1728] :
( t(Vvar__var__var__var__var__21__n__1588__1590__1724__1726__1728,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__22__m__1589__1591__1725__1727__1729] :
( t(Vvar__var__var__var__var__22__m__1589__1591__1725__1727__1729,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__9__rlt__1456,Vvar__var__var__var__var__21__n__1588__1590__1724__1726__1728),Vvar__var__var__var__var__22__m__1589__1591__1725__1727__1729))
| p(happ(happ(Vvar__7__req__1446,Vvar__var__var__var__var__21__n__1588__1590__1724__1726__1728),Vvar__var__var__var__var__22__m__1589__1591__1725__1727__1729))
| p(happ(happ(Vvar__9__rlt__1456,Vvar__var__var__var__var__22__m__1589__1591__1725__1727__1729),Vvar__var__var__var__var__21__n__1588__1590__1724__1726__1728)) ) ) )
& ! [Vvar__var__var__var__var__22__n__1593__1597__1730__1734__1738] :
( t(Vvar__var__var__var__var__22__n__1593__1597__1730__1734__1738,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__23__m__1594__1598__1731__1735__1739] :
( t(Vvar__var__var__var__var__23__m__1594__1598__1731__1735__1739,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__24__p__1595__1599__1732__1736__1740] :
( t(Vvar__var__var__var__var__24__p__1595__1599__1732__1736__1740,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__8__rle__1451,Vvar__var__var__var__var__22__n__1593__1597__1730__1734__1738),Vvar__var__var__var__var__23__m__1594__1598__1731__1735__1739))
=> p(happ(happ(Vvar__8__rle__1451,happ(happ(Vvar__3__rplus__1428,Vvar__var__var__var__var__24__p__1595__1599__1732__1736__1740),Vvar__var__var__var__var__22__n__1593__1597__1730__1734__1738)),happ(happ(Vvar__3__rplus__1428,Vvar__var__var__var__var__24__p__1595__1599__1732__1736__1740),Vvar__var__var__var__var__23__m__1594__1598__1731__1735__1739))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__1602__1606__1742__1746__1750__1754] :
( t(Vvar__var__var__var__var__var__23__n__1602__1606__1742__1746__1750__1754,Vvar__0__R__1425)
=> ! [Vvar__var__var__var__var__var__24__m__1603__1607__1743__1747__1751__1755] :
( t(Vvar__var__var__var__var__var__24__m__1603__1607__1743__1747__1751__1755,Vvar__0__R__1425)
=> ( p(happ(happ(Vvar__9__rlt__1456,Vvar__1__rO__1426),Vvar__var__var__var__var__var__23__n__1602__1606__1742__1746__1750__1754))
=> ( p(happ(happ(Vvar__9__rlt__1456,Vvar__1__rO__1426),Vvar__var__var__var__var__var__24__m__1603__1607__1743__1747__1751__1755))
=> p(happ(happ(Vvar__9__rlt__1456,Vvar__1__rO__1426),happ(happ(Vvar__4__rtimes__1433,Vvar__var__var__var__var__var__23__n__1602__1606__1742__1746__1750__1754),Vvar__var__var__var__var__var__24__m__1603__1607__1743__1747__1751__1755))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__1446,Vvar__1__rO__1426),Vvar__2__rI__1427))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX9181] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX9181)
=> ( VX9181 = cCoq_2emicromega_2eRMicromega_2eC0
| VX9181 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__9182] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__9182)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__9182) )
| ? [Vvar__0__r__9183] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__9183)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__9183) )
| ? [Vvar__0__r1__9184] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9184)
& ? [Vvar__1__r2__9185] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9185)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__9184,Vvar__1__r2__9185) ) )
| ? [Vvar__0__r1__9186] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9186)
& ? [Vvar__1__r2__9187] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9187)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__9186,Vvar__1__r2__9187) ) )
| ? [Vvar__0__r1__9188] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9188)
& ? [Vvar__1__r2__9189] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9189)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__9188,Vvar__1__r2__9189) ) )
| ? [Vvar__0__r1__9190] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9190)
& ? [Vvar__1__z__9191] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__9191)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__9190,Vvar__1__z__9191) ) )
| ? [Vvar__0__r__9192] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__9192)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__9192) )
| ? [Vvar__0__r__9193] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__9193)
& VX9181 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__9193) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__2810,VX2811] :
( cType___24t(Vvar__0__T__2810)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__2810,VX2811)
=> ? [Vvar__1__Flhs__2813] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__2810,Vvar__1__Flhs__2813)
& ? [Vvar__2__Fop__2814] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__2814)
& ? [Vvar__3__Frhs__2815] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__2810,Vvar__3__Frhs__2815)
& VX2811 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__2810,Vvar__1__Flhs__2813,Vvar__2__Fop__2814,Vvar__3__Frhs__2815) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX10210] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX10210)
=> ( VX10210 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX10210 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX10210 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX10210 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX10354] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX10354)
=> ( VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX10354 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__20023,VX20024] :
( cType___24t(Vvar__0__C__20023)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,VX20024)
=> ( ? [Vvar__1___24Anonymous__20026] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__20026)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20023,Vvar__1___24Anonymous__20026) )
| ? [Vvar__1___24Anonymous__20028] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20023,Vvar__1___24Anonymous__20028)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20023,Vvar__1___24Anonymous__20028) )
| ? [Vvar__1___24Anonymous__20030] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20023,Vvar__1___24Anonymous__20030)
& ? [Vvar__2___24Anonymous__20031] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,Vvar__2___24Anonymous__20031)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20023,Vvar__1___24Anonymous__20030,Vvar__2___24Anonymous__20031) ) )
| ? [Vvar__1___24Anonymous__20033] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,Vvar__1___24Anonymous__20033)
& ? [Vvar__2___24Anonymous__20034] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,Vvar__2___24Anonymous__20034)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20023,Vvar__1___24Anonymous__20033,Vvar__2___24Anonymous__20034) ) )
| ? [Vvar__1___24Anonymous__20036] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,Vvar__1___24Anonymous__20036)
& ? [Vvar__2___24Anonymous__20037] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20023,Vvar__2___24Anonymous__20037)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20023,Vvar__1___24Anonymous__20036,Vvar__2___24Anonymous__20037) ) )
| ? [Vvar__1___24Anonymous__20039] :
( t(Vvar__1___24Anonymous__20039,Vvar__0__C__20023)
& VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20023,Vvar__1___24Anonymous__20039) )
| VX20024 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20023) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576] :
( cType___24t(Vvar__0__R__25507)
=> ( t(Vvar__1__rO__25508,Vvar__0__R__25507)
=> ( t(Vvar__2__rI__25509,Vvar__0__R__25507)
=> ( c_24__type__26040___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__3__rplus__25510)
=> ( c_24__type__26386___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__4__rtimes__25515)
=> ( c_24__type__26732___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__5__rminus__25520)
=> ( c_24__type__27055___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__6__ropp__25525)
=> ( c_24__type__27401___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__7__req__25528)
=> ( c_24__type__27747___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__8__rle__25533)
=> ( cType___24t(Vvar__9__C__25538)
=> ( t(Vvar__10__cO__25539,Vvar__9__C__25538)
=> ( t(Vvar__11__cI__25540,Vvar__9__C__25538)
=> ( c_24__type__28093___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__12__cplus__25541)
=> ( c_24__type__28439___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__13__ctimes__25546)
=> ( c_24__type__28785___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__14__cminus__25551)
=> ( c_24__type__29108___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__15__copp__25556)
=> ( c_24__type__29454___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__16__ceqb__25559)
=> ( c_24__type__29800___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__17__cleb__25564)
=> ( c_24__type__30123___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__18__phi__25569)
=> ( cType___24t(Vvar__19__E__25572)
=> ( c_24__type__30446___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__20__pow__phi__25573)
=> ( c_24__type__30792___24t(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576,Vvar__21__rpow__25576)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__8__rle__25533,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__17__cleb__25564,Vvar__18__phi__25569,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__25507,Vvar__1__rO__25508,Vvar__2__rI__25509,Vvar__3__rplus__25510,Vvar__4__rtimes__25515,Vvar__5__rminus__25520,Vvar__6__ropp__25525,Vvar__7__req__25528,Vvar__9__C__25538,Vvar__10__cO__25539,Vvar__11__cI__25540,Vvar__12__cplus__25541,Vvar__13__ctimes__25546,Vvar__14__cminus__25551,Vvar__15__copp__25556,Vvar__16__ceqb__25559,Vvar__18__phi__25569)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__25507,Vvar__2__rI__25509,Vvar__4__rtimes__25515,Vvar__7__req__25528,Vvar__19__E__25572,Vvar__20__pow__phi__25573,Vvar__21__rpow__25576)
& ! [Vvar__var__var__var__var__var__24__x__25659__25662__25672__25675__25678__25681] :
( t(Vvar__var__var__var__var__var__24__x__25659__25662__25672__25675__25678__25681,Vvar__9__C__25538)
=> ! [Vvar__var__var__var__var__var__25__y__25660__25663__25673__25676__25679__25682] :
( t(Vvar__var__var__var__var__var__25__y__25660__25663__25673__25676__25679__25682,Vvar__9__C__25538)
=> ( happ(happ(Vvar__16__ceqb__25559,Vvar__var__var__var__var__var__24__x__25659__25662__25672__25675__25678__25681),Vvar__var__var__var__var__var__25__y__25660__25663__25673__25676__25679__25682) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__25528,happ(Vvar__18__phi__25569,Vvar__var__var__var__var__var__24__x__25659__25662__25672__25675__25678__25681)),happ(Vvar__18__phi__25569,Vvar__var__var__var__var__var__25__y__25660__25663__25673__25676__25679__25682))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__25666__25669__25684__25687__25690__25693] :
( t(Vvar__var__var__var__var__var__25__x__25666__25669__25684__25687__25690__25693,Vvar__9__C__25538)
=> ! [Vvar__var__var__var__var__var__26__y__25667__25670__25685__25688__25691__25694] :
( t(Vvar__var__var__var__var__var__26__y__25667__25670__25685__25688__25691__25694,Vvar__9__C__25538)
=> ( happ(happ(Vvar__17__cleb__25564,Vvar__var__var__var__var__var__25__x__25666__25669__25684__25687__25690__25693),Vvar__var__var__var__var__var__26__y__25667__25670__25685__25688__25691__25694) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__25533,happ(Vvar__18__phi__25569,Vvar__var__var__var__var__var__25__x__25666__25669__25684__25687__25690__25693)),happ(Vvar__18__phi__25569,Vvar__var__var__var__var__var__26__y__25667__25670__25685__25688__25691__25694))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,VX22264] :
( cType___24t(Vvar__0__TA__22260)
=> ( cType___24t(Vvar__1__TX__22261)
=> ( cType___24t(Vvar__2__AA__22262)
=> ( cType___24t(Vvar__3__AF__22263)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,VX22264)
=> ( VX22264 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263)
| VX22264 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263)
| ? [Vvar__4___24Anonymous__22277] :
( t(Vvar__4___24Anonymous__22277,Vvar__1__TX__22261)
& VX22264 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22277) )
| ? [Vvar__4___24Anonymous__22282] :
( t(Vvar__4___24Anonymous__22282,Vvar__0__TA__22260)
& ? [Vvar__5___24Anonymous__22283] :
( t(Vvar__5___24Anonymous__22283,Vvar__2__AA__22262)
& VX22264 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22282,Vvar__5___24Anonymous__22283) ) )
| ? [Vvar__4___24Anonymous__22288] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22288)
& ? [Vvar__5___24Anonymous__22289] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__5___24Anonymous__22289)
& VX22264 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22288,Vvar__5___24Anonymous__22289) ) )
| ? [Vvar__4___24Anonymous__22294] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22294)
& ? [Vvar__5___24Anonymous__22295] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__5___24Anonymous__22295)
& VX22264 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22294,Vvar__5___24Anonymous__22295) ) )
| ? [Vvar__4___24Anonymous__22300] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22300)
& VX22264 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22300) )
| ? [Vvar__4___24Anonymous__22305] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22305)
& ? [Vvar__5___24Anonymous__22306] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__22263,Vvar__5___24Anonymous__22306)
& ? [Vvar__6___24Anonymous__22307] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__6___24Anonymous__22307)
& VX22264 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22260,Vvar__1__TX__22261,Vvar__2__AA__22262,Vvar__3__AF__22263,Vvar__4___24Anonymous__22305,Vvar__5___24Anonymous__22306,Vvar__6___24Anonymous__22307) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__22703,VX22704] :
( cType___24t(Vvar__0__A__22703)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__22703,VX22704)
=> ( VX22704 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__22703)
| ? [Vvar__1___24Anonymous__22707] :
( t(Vvar__1___24Anonymous__22707,Vvar__0__A__22703)
& VX22704 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__22703,Vvar__1___24Anonymous__22707) )
| ? [Vvar__1___24Anonymous__22709] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__22703,Vvar__1___24Anonymous__22709)
& ? [Vvar__2___24Anonymous__22710] :
( t(Vvar__2___24Anonymous__22710,Vvar__0__A__22703)
& ? [Vvar__3___24Anonymous__22711] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__22703,Vvar__3___24Anonymous__22711)
& VX22704 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__22703,Vvar__1___24Anonymous__22709,Vvar__2___24Anonymous__22710,Vvar__3___24Anonymous__22711) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__22835] :
( cProp___24t(Vvar__0___24Anonymous__22835)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__22835)
=> ( ? [Vvar__0__P__22837] :
( cProp___24t(Vvar__0__P__22837)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__22837)
& Vvar__0___24Anonymous__22835 = Vvar__0__P__22837 )
| ? [Vvar__0__s__22839] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__22839)
& Vvar__0___24Anonymous__22835 = c_24__prop__22848___24a2(Vvar__0___24Anonymous__22835,Vvar__0__s__22839) )
| ? [Vvar__0__s1__22841] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__22841)
& ? [Vvar__1__s2__22842] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__22842)
& Vvar__0___24Anonymous__22835 = c_24__prop__22849___24a3(Vvar__0___24Anonymous__22835,Vvar__0__s1__22841,Vvar__1__s2__22842) ) )
| ? [Vvar__0__s1__22845] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__22845)
& ? [Vvar__1__s2__22846] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__22846)
& Vvar__0___24Anonymous__22835 = c_24__prop__22850___24a3(Vvar__0___24Anonymous__22835,Vvar__0__s1__22845,Vvar__1__s2__22846) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__22804] :
( cProp___24t(Vvar__0___24Anonymous__22804)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__22804)
=> ( ? [Vvar__0__S__22806] :
( cType___24t(Vvar__0__S__22806)
& ? [Vvar__1__x__22807] :
( t(Vvar__1__x__22807,Vvar__0__S__22806)
& ? [Vvar__2__y__22808] :
( t(Vvar__2__y__22808,Vvar__0__S__22806)
& Vvar__0___24Anonymous__22804 = c_24__prop__22828___24a4(Vvar__0___24Anonymous__22804,Vvar__0__S__22806,Vvar__1__x__22807,Vvar__2__y__22808) ) ) )
| ? [Vvar__0__x__22809] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__22809)
& ? [Vvar__1__y__22810] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__22810)
& Vvar__0___24Anonymous__22804 = c_24__prop__22829___24a3(Vvar__0___24Anonymous__22804,Vvar__0__x__22809,Vvar__1__y__22810) ) )
| ? [Vvar__0__x__22811] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__22811)
& ? [Vvar__1__s__22812] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__22812)
& Vvar__0___24Anonymous__22804 = c_24__prop__22830___24a3(Vvar__0___24Anonymous__22804,Vvar__0__x__22811,Vvar__1__s__22812) ) )
| Vvar__0___24Anonymous__22804 = c_24True
| Vvar__0___24Anonymous__22804 = c_24False
| ? [Vvar__0__P__22813] :
( cProp___24t(Vvar__0__P__22813)
& ? [Vvar__1__Q__22814] :
( cProp___24t(Vvar__1__Q__22814)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__22813)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__22814)
& Vvar__0___24Anonymous__22804 = c_24__prop__22831___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22813,Vvar__1__Q__22814) ) )
| ? [Vvar__0__P__22817] :
( cProp___24t(Vvar__0__P__22817)
& ? [Vvar__1__Q__22818] :
( cProp___24t(Vvar__1__Q__22818)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__22817)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__22818)
& Vvar__0___24Anonymous__22804 = c_24__prop__22832___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22817,Vvar__1__Q__22818) ) )
| ? [Vvar__0__P__22821] :
( cProp___24t(Vvar__0__P__22821)
& ? [Vvar__1__Q__22822] :
( cProp___24t(Vvar__1__Q__22822)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__22821)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__22822)
& Vvar__0___24Anonymous__22804 = c_24__prop__22833___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22821,Vvar__1__Q__22822) ) )
| ? [Vvar__0__P__22826] :
( cProp___24t(Vvar__0__P__22826)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__22826)
& Vvar__0___24Anonymous__22804 = c_24__prop__22834___24a2(Vvar__0___24Anonymous__22804,Vvar__0__P__22826) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX3325] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX3325)
=> ( VX3325 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__3326] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__3326)
& ? [Vvar__1___24Anonymous__3327] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__3327)
& VX3325 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__3326,Vvar__1___24Anonymous__3327) ) )
| ? [Vvar__0___24Anonymous__3328] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__3328)
& ? [Vvar__1___24Anonymous__3329] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__3329)
& VX3325 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__3328,Vvar__1___24Anonymous__3329) ) )
| ? [Vvar__0___24Anonymous__3330] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__3330)
& ? [Vvar__1___24Anonymous__3331] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__3331)
& ? [Vvar__2___24Anonymous__3332] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__3332)
& VX3325 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__3330,Vvar__1___24Anonymous__3331,Vvar__2___24Anonymous__3332) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
! [Vvar__0__x__31712,Vvar__1___24Anonymous__31713] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__31712)
=> ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__31713)
=> ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__31712,Vvar__1___24Anonymous__31713)
=> ( ? [Vvar__1__c__31716] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__31716)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__31712,Vvar__1__c__31716)
& Vvar__1___24Anonymous__31713 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__31716) )
| ? [Vvar__1__p__31719] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__31719)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__31712,Vvar__1__p__31719)
& ? [Vvar__3__j__31721] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__31721)
& Vvar__1___24Anonymous__31713 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__31721,Vvar__1__p__31719) ) )
| ? [Vvar__1__p__31723] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__31723)
& ? [Vvar__2__q__31724] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__31724)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__31712,Vvar__1__p__31723)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__31712,Vvar__2__q__31724)
& ? [Vvar__5__j__31727] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__31727)
& Vvar__1___24Anonymous__31713 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__31723,Vvar__5__j__31727,Vvar__2__q__31724) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__31728,Vvar__1__env__31729,Vvar__2__env_27__31732,Vvar__3__x__31735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__31728)
=> ( c_24__type__31756___24t(Vvar__0__fr__31728,Vvar__1__env__31729,Vvar__2__env_27__31732,Vvar__3__x__31735,Vvar__1__env__31729)
=> ( c_24__type__31765___24t(Vvar__0__fr__31728,Vvar__1__env__31729,Vvar__2__env_27__31732,Vvar__3__x__31735,Vvar__2__env_27__31732)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__31735)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__31728,Vvar__1__env__31729,Vvar__2__env_27__31732,Vvar__3__x__31735)
=> ( happ(Vvar__1__env__31729,Vvar__3__x__31735) = happ(Vvar__2__env_27__31732,Vvar__3__x__31735)
& happ(Vvar__1__env__31729,Vvar__3__x__31735) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__31732,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__31728,Vvar__3__x__31735))),happ(Vvar__2__env_27__31732,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__31728,Vvar__3__x__31735))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__31732,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__31728,Vvar__3__x__31735))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__31732,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__31728,Vvar__3__x__31735))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__6796,VX6797] :
( cType___24t(Vvar__0__C__6796)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,VX6797)
=> ( VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__6796)
| VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__6796)
| ? [Vvar__1___24Anonymous__6801] :
( t(Vvar__1___24Anonymous__6801,Vvar__0__C__6796)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__6796,Vvar__1___24Anonymous__6801) )
| ? [Vvar__1___24Anonymous__6803] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6803)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__6796,Vvar__1___24Anonymous__6803) )
| ? [Vvar__1___24Anonymous__6805] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6805)
& ? [Vvar__2___24Anonymous__6806] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__2___24Anonymous__6806)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__6796,Vvar__1___24Anonymous__6805,Vvar__2___24Anonymous__6806) ) )
| ? [Vvar__1___24Anonymous__6808] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6808)
& ? [Vvar__2___24Anonymous__6809] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__2___24Anonymous__6809)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__6796,Vvar__1___24Anonymous__6808,Vvar__2___24Anonymous__6809) ) )
| ? [Vvar__1___24Anonymous__6811] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6811)
& ? [Vvar__2___24Anonymous__6812] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__2___24Anonymous__6812)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__6796,Vvar__1___24Anonymous__6811,Vvar__2___24Anonymous__6812) ) )
| ? [Vvar__1___24Anonymous__6814] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6814)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__6796,Vvar__1___24Anonymous__6814) )
| ? [Vvar__1___24Anonymous__6816] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6816)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__6796,Vvar__1___24Anonymous__6816) )
| ? [Vvar__1___24Anonymous__6818] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6818)
& ? [Vvar__2___24Anonymous__6819] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__2___24Anonymous__6819)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__6796,Vvar__1___24Anonymous__6818,Vvar__2___24Anonymous__6819) ) )
| ? [Vvar__1___24Anonymous__6821] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__6796,Vvar__1___24Anonymous__6821)
& ? [Vvar__2___24Anonymous__6822] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6822)
& VX6797 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__6796,Vvar__1___24Anonymous__6821,Vvar__2___24Anonymous__6822) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301] :
( cType___24t(Vvar__0__R__5272)
=> ( t(Vvar__1__rO__5273,Vvar__0__R__5272)
=> ( t(Vvar__2__rI__5274,Vvar__0__R__5272)
=> ( c_24__type__5466___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__3__radd__5275)
=> ( c_24__type__5559___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__4__rmul__5280)
=> ( c_24__type__5652___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__5__rsub__5285)
=> ( c_24__type__5734___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__6__ropp__5290)
=> ( c_24__type__5827___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__7__rdiv__5293)
=> ( c_24__type__5909___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__8__rinv__5298)
=> ( c_24__type__6002___24t(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301,Vvar__9__req__5301)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__7__rdiv__5293,Vvar__8__rinv__5298,Vvar__9__req__5301)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__5272,Vvar__1__rO__5273,Vvar__2__rI__5274,Vvar__3__radd__5275,Vvar__4__rmul__5280,Vvar__5__rsub__5285,Vvar__6__ropp__5290,Vvar__9__req__5301)
& ~ p(happ(happ(Vvar__9__req__5301,Vvar__2__rI__5274),Vvar__1__rO__5273))
& ! [Vvar__var__var__var__var__var__var__12__p__5344__5346__5353__5355__5357__5359__5361] :
( t(Vvar__var__var__var__var__var__var__12__p__5344__5346__5353__5355__5357__5359__5361,Vvar__0__R__5272)
=> ! [Vvar__var__var__var__var__var__var__13__q__5345__5347__5354__5356__5358__5360__5362] :
( t(Vvar__var__var__var__var__var__var__13__q__5345__5347__5354__5356__5358__5360__5362,Vvar__0__R__5272)
=> p(happ(happ(Vvar__9__req__5301,happ(happ(Vvar__7__rdiv__5293,Vvar__var__var__var__var__var__var__12__p__5344__5346__5353__5355__5357__5359__5361),Vvar__var__var__var__var__var__var__13__q__5345__5347__5354__5356__5358__5360__5362)),happ(happ(Vvar__4__rmul__5280,Vvar__var__var__var__var__var__var__12__p__5344__5346__5353__5355__5357__5359__5361),happ(Vvar__8__rinv__5298,Vvar__var__var__var__var__var__var__13__q__5345__5347__5354__5356__5358__5360__5362)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__5349__5351__5363__5365__5367__5369__5371__5373] :
( t(Vvar__var__var__var__var__var__var__var__13__p__5349__5351__5363__5365__5367__5369__5371__5373,Vvar__0__R__5272)
=> ( ~ p(happ(happ(Vvar__9__req__5301,Vvar__var__var__var__var__var__var__var__13__p__5349__5351__5363__5365__5367__5369__5371__5373),Vvar__1__rO__5273))
=> p(happ(happ(Vvar__9__req__5301,happ(happ(Vvar__4__rmul__5280,happ(Vvar__8__rinv__5298,Vvar__var__var__var__var__var__var__var__13__p__5349__5351__5363__5365__5367__5369__5371__5373)),Vvar__var__var__var__var__var__var__var__13__p__5349__5351__5363__5365__5367__5369__5371__5373)),Vvar__2__rI__5274)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768] :
( cType___24t(Vvar__0__R__18739)
=> ( t(Vvar__1__rO__18740,Vvar__0__R__18739)
=> ( t(Vvar__2__rI__18741,Vvar__0__R__18739)
=> ( c_24__type__18933___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__3__radd__18742)
=> ( c_24__type__19026___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__4__rmul__18747)
=> ( c_24__type__19119___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__5__rsub__18752)
=> ( c_24__type__19201___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__6__ropp__18757)
=> ( c_24__type__19294___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__7__rdiv__18760)
=> ( c_24__type__19376___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__8__rinv__18765)
=> ( c_24__type__19469___24t(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768,Vvar__9__req__18768)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__7__rdiv__18760,Vvar__8__rinv__18765,Vvar__9__req__18768)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__18739,Vvar__1__rO__18740,Vvar__2__rI__18741,Vvar__3__radd__18742,Vvar__4__rmul__18747,Vvar__5__rsub__18752,Vvar__6__ropp__18757,Vvar__9__req__18768)
& ~ p(happ(happ(Vvar__9__req__18768,Vvar__2__rI__18741),Vvar__1__rO__18740))
& ! [Vvar__var__var__var__var__var__var__12__p__18811__18813__18820__18822__18824__18826__18828] :
( t(Vvar__var__var__var__var__var__var__12__p__18811__18813__18820__18822__18824__18826__18828,Vvar__0__R__18739)
=> ! [Vvar__var__var__var__var__var__var__13__q__18812__18814__18821__18823__18825__18827__18829] :
( t(Vvar__var__var__var__var__var__var__13__q__18812__18814__18821__18823__18825__18827__18829,Vvar__0__R__18739)
=> p(happ(happ(Vvar__9__req__18768,happ(happ(Vvar__7__rdiv__18760,Vvar__var__var__var__var__var__var__12__p__18811__18813__18820__18822__18824__18826__18828),Vvar__var__var__var__var__var__var__13__q__18812__18814__18821__18823__18825__18827__18829)),happ(happ(Vvar__4__rmul__18747,Vvar__var__var__var__var__var__var__12__p__18811__18813__18820__18822__18824__18826__18828),happ(Vvar__8__rinv__18765,Vvar__var__var__var__var__var__var__13__q__18812__18814__18821__18823__18825__18827__18829)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__18816__18818__18830__18832__18834__18836__18838__18840] :
( t(Vvar__var__var__var__var__var__var__var__13__p__18816__18818__18830__18832__18834__18836__18838__18840,Vvar__0__R__18739)
=> ( ~ p(happ(happ(Vvar__9__req__18768,Vvar__var__var__var__var__var__var__var__13__p__18816__18818__18830__18832__18834__18836__18838__18840),Vvar__1__rO__18740))
=> p(happ(happ(Vvar__9__req__18768,happ(happ(Vvar__4__rmul__18747,happ(Vvar__8__rinv__18765,Vvar__var__var__var__var__var__var__var__13__p__18816__18818__18830__18832__18834__18836__18838__18840)),Vvar__var__var__var__var__var__var__var__13__p__18816__18818__18830__18832__18834__18836__18838__18840)),Vvar__2__rI__18741)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__7422,VX7423] :
( cType___24t(Vvar__0__C__7422)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__7422,VX7423)
=> ? [Vvar__1__num__7425] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7422,Vvar__1__num__7425)
& ? [Vvar__2__denum__7426] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7422,Vvar__2__denum__7426)
& ? [Vvar__3__condition__7427] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__7422),Vvar__3__condition__7427)
& VX7423 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7422,Vvar__1__num__7425,Vvar__2__denum__7426,Vvar__3__condition__7427) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__7719,VX7720] :
( cType___24t(Vvar__0__C__7719)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__7719,VX7720)
=> ? [Vvar__1__rsplit__left__7722] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7719,Vvar__1__rsplit__left__7722)
& ? [Vvar__2__rsplit__common__7723] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7719,Vvar__2__rsplit__common__7723)
& ? [Vvar__3__rsplit__right__7724] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7719,Vvar__3__rsplit__right__7724)
& VX7720 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7719,Vvar__1__rsplit__left__7722,Vvar__2__rsplit__common__7723,Vvar__3__rsplit__right__7724) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496] :
( cType___24t(Vvar__0__R__19475)
=> ( t(Vvar__1__rO__19476,Vvar__0__R__19475)
=> ( t(Vvar__2__rI__19477,Vvar__0__R__19475)
=> ( c_24__type__19623___24t(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496,Vvar__3__radd__19478)
=> ( c_24__type__19686___24t(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496,Vvar__4__rmul__19483)
=> ( c_24__type__19749___24t(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496,Vvar__5__rdiv__19488)
=> ( c_24__type__19803___24t(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496,Vvar__6__rinv__19493)
=> ( c_24__type__19866___24t(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496,Vvar__7__req__19496)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__5__rdiv__19488,Vvar__6__rinv__19493,Vvar__7__req__19496)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__19475,Vvar__1__rO__19476,Vvar__2__rI__19477,Vvar__3__radd__19478,Vvar__4__rmul__19483,Vvar__7__req__19496)
& ~ p(happ(happ(Vvar__7__req__19496,Vvar__2__rI__19477),Vvar__1__rO__19476))
& ! [Vvar__var__var__var__var__var__var__10__p__19531__19533__19540__19542__19544__19546__19548] :
( t(Vvar__var__var__var__var__var__var__10__p__19531__19533__19540__19542__19544__19546__19548,Vvar__0__R__19475)
=> ! [Vvar__var__var__var__var__var__var__11__q__19532__19534__19541__19543__19545__19547__19549] :
( t(Vvar__var__var__var__var__var__var__11__q__19532__19534__19541__19543__19545__19547__19549,Vvar__0__R__19475)
=> p(happ(happ(Vvar__7__req__19496,happ(happ(Vvar__5__rdiv__19488,Vvar__var__var__var__var__var__var__10__p__19531__19533__19540__19542__19544__19546__19548),Vvar__var__var__var__var__var__var__11__q__19532__19534__19541__19543__19545__19547__19549)),happ(happ(Vvar__4__rmul__19483,Vvar__var__var__var__var__var__var__10__p__19531__19533__19540__19542__19544__19546__19548),happ(Vvar__6__rinv__19493,Vvar__var__var__var__var__var__var__11__q__19532__19534__19541__19543__19545__19547__19549)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__19536__19538__19550__19552__19554__19556__19558__19560] :
( t(Vvar__var__var__var__var__var__var__var__11__p__19536__19538__19550__19552__19554__19556__19558__19560,Vvar__0__R__19475)
=> ( ~ p(happ(happ(Vvar__7__req__19496,Vvar__var__var__var__var__var__var__var__11__p__19536__19538__19550__19552__19554__19556__19558__19560),Vvar__1__rO__19476))
=> p(happ(happ(Vvar__7__req__19496,happ(happ(Vvar__4__rmul__19483,happ(Vvar__6__rinv__19493,Vvar__var__var__var__var__var__var__var__11__p__19536__19538__19550__19552__19554__19556__19558__19560)),Vvar__var__var__var__var__var__var__var__11__p__19536__19538__19550__19552__19554__19556__19558__19560)),Vvar__2__rI__19477)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX23305] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX23305)
=> ? [Vvar__0__hypo__type__23306] :
( cType___24t(Vvar__0__hypo__type__23306)
& ? [Vvar__1__hypo__proof__23307] :
( t(Vvar__1__hypo__proof__23307,Vvar__0__hypo__type__23306)
& VX23305 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__23306,Vvar__1__hypo__proof__23307) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX10534] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX10534)
=> ( VX10534 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__10535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10535)
& ? [Vvar__1___24Anonymous__10536] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__10536)
& VX10534 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__10535,Vvar__1___24Anonymous__10536) ) )
| ? [Vvar__0___24Anonymous__10537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10537)
& ? [Vvar__1___24Anonymous__10538] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__10538)
& VX10534 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__10537,Vvar__1___24Anonymous__10538) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__10555,VX10556] :
( cType___24t(Vvar__0__C__10555)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,VX10556)
=> ( VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10555)
| VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10555)
| ? [Vvar__1___24Anonymous__10560] :
( t(Vvar__1___24Anonymous__10560,Vvar__0__C__10555)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10555,Vvar__1___24Anonymous__10560) )
| ? [Vvar__1___24Anonymous__10562] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10562)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10555,Vvar__1___24Anonymous__10562) )
| ? [Vvar__1___24Anonymous__10564] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__1___24Anonymous__10564)
& ? [Vvar__2___24Anonymous__10565] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__2___24Anonymous__10565)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10555,Vvar__1___24Anonymous__10564,Vvar__2___24Anonymous__10565) ) )
| ? [Vvar__1___24Anonymous__10567] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__1___24Anonymous__10567)
& ? [Vvar__2___24Anonymous__10568] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__2___24Anonymous__10568)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10555,Vvar__1___24Anonymous__10567,Vvar__2___24Anonymous__10568) ) )
| ? [Vvar__1___24Anonymous__10570] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__1___24Anonymous__10570)
& ? [Vvar__2___24Anonymous__10571] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__2___24Anonymous__10571)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10555,Vvar__1___24Anonymous__10570,Vvar__2___24Anonymous__10571) ) )
| ? [Vvar__1___24Anonymous__10573] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__1___24Anonymous__10573)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10555,Vvar__1___24Anonymous__10573) )
| ? [Vvar__1___24Anonymous__10575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__10555,Vvar__1___24Anonymous__10575)
& ? [Vvar__2___24Anonymous__10576] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10576)
& VX10556 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10555,Vvar__1___24Anonymous__10575,Vvar__2___24Anonymous__10576) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__10355,VX10356] :
( cType___24t(Vvar__0__C__10355)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__10355,VX10356)
=> ( ? [Vvar__1___24Anonymous__10358] :
( t(Vvar__1___24Anonymous__10358,Vvar__0__C__10355)
& VX10356 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__10355,Vvar__1___24Anonymous__10358) )
| ? [Vvar__1___24Anonymous__10360] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10360)
& ? [Vvar__2___24Anonymous__10361] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__10355,Vvar__2___24Anonymous__10361)
& VX10356 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__10355,Vvar__1___24Anonymous__10360,Vvar__2___24Anonymous__10361) ) )
| ? [Vvar__1___24Anonymous__10363] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__10355,Vvar__1___24Anonymous__10363)
& ? [Vvar__2___24Anonymous__10364] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10364)
& ? [Vvar__3___24Anonymous__10365] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__10355,Vvar__3___24Anonymous__10365)
& VX10356 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__10355,Vvar__1___24Anonymous__10363,Vvar__2___24Anonymous__10364,Vvar__3___24Anonymous__10365) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164] :
( cType___24t(Vvar__0__R__12143)
=> ( t(Vvar__1__rO__12144,Vvar__0__R__12143)
=> ( t(Vvar__2__rI__12145,Vvar__0__R__12143)
=> ( c_24__type__12392___24t(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164,Vvar__3__radd__12146)
=> ( c_24__type__12455___24t(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164,Vvar__4__rmul__12151)
=> ( c_24__type__12518___24t(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164,Vvar__5__rsub__12156)
=> ( c_24__type__12572___24t(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164,Vvar__6__ropp__12161)
=> ( c_24__type__12635___24t(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164,Vvar__7__req__12164)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__12143,Vvar__1__rO__12144,Vvar__2__rI__12145,Vvar__3__radd__12146,Vvar__4__rmul__12151,Vvar__5__rsub__12156,Vvar__6__ropp__12161,Vvar__7__req__12164)
=> ( ! [Vvar__var__var__var__var__var__8__x__12197__12198__12251__12252__12253__12254] :
( t(Vvar__var__var__var__var__var__8__x__12197__12198__12251__12252__12253__12254,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__3__radd__12146,Vvar__1__rO__12144),Vvar__var__var__var__var__var__8__x__12197__12198__12251__12252__12253__12254)),Vvar__var__var__var__var__var__8__x__12197__12198__12251__12252__12253__12254)) )
& ! [Vvar__var__var__var__var__9__x__12200__12202__12255__12257__12259] :
( t(Vvar__var__var__var__var__9__x__12200__12202__12255__12257__12259,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__10__y__12201__12203__12256__12258__12260] :
( t(Vvar__var__var__var__var__10__y__12201__12203__12256__12258__12260,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__9__x__12200__12202__12255__12257__12259),Vvar__var__var__var__var__10__y__12201__12203__12256__12258__12260)),happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__10__y__12201__12203__12256__12258__12260),Vvar__var__var__var__var__9__x__12200__12202__12255__12257__12259))) ) )
& ! [Vvar__var__var__var__var__10__x__12205__12208__12261__12264__12267] :
( t(Vvar__var__var__var__var__10__x__12205__12208__12261__12264__12267,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__11__y__12206__12209__12262__12265__12268] :
( t(Vvar__var__var__var__var__11__y__12206__12209__12262__12265__12268,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__12__z__12207__12210__12263__12266__12269] :
( t(Vvar__var__var__var__var__12__z__12207__12210__12263__12266__12269,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__10__x__12205__12208__12261__12264__12267),happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__11__y__12206__12209__12262__12265__12268),Vvar__var__var__var__var__12__z__12207__12210__12263__12266__12269))),happ(happ(Vvar__3__radd__12146,happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__10__x__12205__12208__12261__12264__12267),Vvar__var__var__var__var__11__y__12206__12209__12262__12265__12268)),Vvar__var__var__var__var__12__z__12207__12210__12263__12266__12269))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__12212__12213__12270__12271__12272__12273] :
( t(Vvar__var__var__var__var__var__11__x__12212__12213__12270__12271__12272__12273,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__4__rmul__12151,Vvar__2__rI__12145),Vvar__var__var__var__var__var__11__x__12212__12213__12270__12271__12272__12273)),Vvar__var__var__var__var__var__11__x__12212__12213__12270__12271__12272__12273)) )
& ! [Vvar__var__var__var__var__var__12__x__12215__12216__12274__12275__12276__12277] :
( t(Vvar__var__var__var__var__var__12__x__12215__12216__12274__12275__12276__12277,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__4__rmul__12151,Vvar__1__rO__12144),Vvar__var__var__var__var__var__12__x__12215__12216__12274__12275__12276__12277)),Vvar__1__rO__12144)) )
& ! [Vvar__var__var__var__var__13__x__12218__12220__12278__12280__12282] :
( t(Vvar__var__var__var__var__13__x__12218__12220__12278__12280__12282,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__14__y__12219__12221__12279__12281__12283] :
( t(Vvar__var__var__var__var__14__y__12219__12221__12279__12281__12283,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__13__x__12218__12220__12278__12280__12282),Vvar__var__var__var__var__14__y__12219__12221__12279__12281__12283)),happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__14__y__12219__12221__12279__12281__12283),Vvar__var__var__var__var__13__x__12218__12220__12278__12280__12282))) ) )
& ! [Vvar__var__var__var__var__14__x__12223__12226__12284__12287__12290] :
( t(Vvar__var__var__var__var__14__x__12223__12226__12284__12287__12290,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__15__y__12224__12227__12285__12288__12291] :
( t(Vvar__var__var__var__var__15__y__12224__12227__12285__12288__12291,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__16__z__12225__12228__12286__12289__12292] :
( t(Vvar__var__var__var__var__16__z__12225__12228__12286__12289__12292,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__14__x__12223__12226__12284__12287__12290),happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__15__y__12224__12227__12285__12288__12291),Vvar__var__var__var__var__16__z__12225__12228__12286__12289__12292))),happ(happ(Vvar__4__rmul__12151,happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__14__x__12223__12226__12284__12287__12290),Vvar__var__var__var__var__15__y__12224__12227__12285__12288__12291)),Vvar__var__var__var__var__16__z__12225__12228__12286__12289__12292))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__12230__12233__12293__12296__12299__12302] :
( t(Vvar__var__var__var__var__var__15__x__12230__12233__12293__12296__12299__12302,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__var__16__y__12231__12234__12294__12297__12300__12303] :
( t(Vvar__var__var__var__var__var__16__y__12231__12234__12294__12297__12300__12303,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__var__17__z__12232__12235__12295__12298__12301__12304] :
( t(Vvar__var__var__var__var__var__17__z__12232__12235__12295__12298__12301__12304,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__4__rmul__12151,happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__var__15__x__12230__12233__12293__12296__12299__12302),Vvar__var__var__var__var__var__16__y__12231__12234__12294__12297__12300__12303)),Vvar__var__var__var__var__var__17__z__12232__12235__12295__12298__12301__12304)),happ(happ(Vvar__3__radd__12146,happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__var__15__x__12230__12233__12293__12296__12299__12302),Vvar__var__var__var__var__var__17__z__12232__12235__12295__12298__12301__12304)),happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__var__16__y__12231__12234__12294__12297__12300__12303),Vvar__var__var__var__var__var__17__z__12232__12235__12295__12298__12301__12304)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__12237__12239__12305__12307__12309__12311] :
( t(Vvar__var__var__var__var__var__16__x__12237__12239__12305__12307__12309__12311,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__var__17__y__12238__12240__12306__12308__12310__12312] :
( t(Vvar__var__var__var__var__var__17__y__12238__12240__12306__12308__12310__12312,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(Vvar__6__ropp__12161,happ(happ(Vvar__4__rmul__12151,Vvar__var__var__var__var__var__16__x__12237__12239__12305__12307__12309__12311),Vvar__var__var__var__var__var__17__y__12238__12240__12306__12308__12310__12312))),happ(happ(Vvar__4__rmul__12151,happ(Vvar__6__ropp__12161,Vvar__var__var__var__var__var__16__x__12237__12239__12305__12307__12309__12311)),Vvar__var__var__var__var__var__17__y__12238__12240__12306__12308__12310__12312))) ) )
& ! [Vvar__var__var__var__var__var__17__x__12242__12244__12313__12315__12317__12319] :
( t(Vvar__var__var__var__var__var__17__x__12242__12244__12313__12315__12317__12319,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__var__18__y__12243__12245__12314__12316__12318__12320] :
( t(Vvar__var__var__var__var__var__18__y__12243__12245__12314__12316__12318__12320,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(Vvar__6__ropp__12161,happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__var__17__x__12242__12244__12313__12315__12317__12319),Vvar__var__var__var__var__var__18__y__12243__12245__12314__12316__12318__12320))),happ(happ(Vvar__3__radd__12146,happ(Vvar__6__ropp__12161,Vvar__var__var__var__var__var__17__x__12242__12244__12313__12315__12317__12319)),happ(Vvar__6__ropp__12161,Vvar__var__var__var__var__var__18__y__12243__12245__12314__12316__12318__12320)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__12247__12249__12321__12323__12325__12327__12329] :
( t(Vvar__var__var__var__var__var__var__18__x__12247__12249__12321__12323__12325__12327__12329,Vvar__0__R__12143)
=> ! [Vvar__var__var__var__var__var__var__19__y__12248__12250__12322__12324__12326__12328__12330] :
( t(Vvar__var__var__var__var__var__var__19__y__12248__12250__12322__12324__12326__12328__12330,Vvar__0__R__12143)
=> p(happ(happ(Vvar__7__req__12164,happ(happ(Vvar__5__rsub__12156,Vvar__var__var__var__var__var__var__18__x__12247__12249__12321__12323__12325__12327__12329),Vvar__var__var__var__var__var__var__19__y__12248__12250__12322__12324__12326__12328__12330)),happ(happ(Vvar__3__radd__12146,Vvar__var__var__var__var__var__var__18__x__12247__12249__12321__12323__12325__12327__12329),happ(Vvar__6__ropp__12161,Vvar__var__var__var__var__var__var__19__y__12248__12250__12322__12324__12326__12328__12330)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971] :
( cType___24t(Vvar__0__R__15951)
=> ( c_24__type__16091___24t(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__1__req__15952)
=> ( cType___24t(Vvar__2__C__15957)
=> ( c_24__type__16141___24t(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__3__cadd__15958)
=> ( c_24__type__16191___24t(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__4__cmul__15963)
=> ( c_24__type__16233___24t(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__5__phi__15968)
=> ( c_24__type__16283___24t(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__6__cdiv__15971)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__16003__16008__16013__16018__16023__16028__16033__16038] :
( t(Vvar__var__var__var__var__var__var__var__7__a__16003__16008__16013__16018__16023__16028__16033__16038,Vvar__2__C__15957)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__16004__16009__16014__16019__16024__16029__16034__16039] :
( t(Vvar__var__var__var__var__var__var__var__8__b__16004__16009__16014__16019__16024__16029__16034__16039,Vvar__2__C__15957)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416346___24a9(Vvar__0__R__15951,Vvar__1__req__15952,Vvar__2__C__15957,Vvar__3__cadd__15958,Vvar__4__cmul__15963,Vvar__5__phi__15968,Vvar__6__cdiv__15971,Vvar__var__var__var__var__var__var__var__7__a__16003__16008__16013__16018__16023__16028__16033__16038,Vvar__var__var__var__var__var__var__var__8__b__16004__16009__16014__16019__16024__16029__16034__16039) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382] :
( cType___24t(Vvar__0__R__16366)
=> ( t(Vvar__1__rI__16367,Vvar__0__R__16366)
=> ( c_24__type__16468___24t(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382,Vvar__2__rmul__16368)
=> ( c_24__type__16512___24t(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382,Vvar__3__req__16373)
=> ( cType___24t(Vvar__4__Cpow__16378)
=> ( c_24__type__16548___24t(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382,Vvar__5__Cp__phi__16379)
=> ( c_24__type__16592___24t(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382,Vvar__6__rpow__16382)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__3__req__16373,Vvar__4__Cpow__16378,Vvar__5__Cp__phi__16379,Vvar__6__rpow__16382)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__16410__16412__16414__16416__16418__16420__16422__16424] :
( t(Vvar__var__var__var__var__var__var__var__7__r__16410__16412__16414__16416__16418__16420__16422__16424,Vvar__0__R__16366)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__16411__16413__16415__16417__16419__16421__16423__16425] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__16411__16413__16415__16417__16419__16421__16423__16425)
=> p(happ(happ(Vvar__3__req__16373,happ(happ(Vvar__6__rpow__16382,Vvar__var__var__var__var__var__var__var__7__r__16410__16412__16414__16416__16418__16420__16422__16424),happ(Vvar__5__Cp__phi__16379,Vvar__var__var__var__var__var__var__var__8__n__16411__16413__16415__16417__16419__16421__16423__16425))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__16366,Vvar__1__rI__16367,Vvar__2__rmul__16368,Vvar__var__var__var__var__var__var__var__7__r__16410__16412__16414__16416__16418__16420__16422__16424,Vvar__var__var__var__var__var__var__var__8__n__16411__16413__16415__16417__16419__16421__16423__16425))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973] :
( cType___24t(Vvar__0__R__12959)
=> ( c_24__type__13064___24t(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973,Vvar__1__radd__12960)
=> ( c_24__type__13094___24t(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973,Vvar__2__rmul__12965)
=> ( c_24__type__13118___24t(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973,Vvar__3__ropp__12970)
=> ( c_24__type__13148___24t(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973,Vvar__4__req__12973)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13178___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12959,c_24__type__13202___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973),Vvar__4__req__12973,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12959,Vvar__0__R__12959,Vvar__4__req__12973,Vvar__4__req__12973)),Vvar__1__radd__12960)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13235___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12959,c_24__type__13259___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973),Vvar__4__req__12973,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12959,Vvar__0__R__12959,Vvar__4__req__12973,Vvar__4__req__12973)),Vvar__2__rmul__12965)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13286___24a5(Vvar__0__R__12959,Vvar__1__radd__12960,Vvar__2__rmul__12965,Vvar__3__ropp__12970,Vvar__4__req__12973),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12959,Vvar__0__R__12959,Vvar__4__req__12973,Vvar__4__req__12973),Vvar__3__ropp__12970)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX21939] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX21939)
=> ( VX21939 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__21940] :
( cType___24t(Vvar__0__R__21940)
& ? [Vvar__1__req__21941] :
( c_24__type__1412___24t(Vvar__0__R__21940,Vvar__1__req__21941)
& ? [Vvar__2__reqb__21946] :
( c_24__type__6146___24t(Vvar__0__R__21940,Vvar__2__reqb__21946)
& ! [Vvar__var__3__x__21952__21955] :
( t(Vvar__var__3__x__21952__21955,Vvar__0__R__21940)
=> ! [Vvar__var__4__y__21953__21956] :
( t(Vvar__var__4__y__21953__21956,Vvar__0__R__21940)
=> ( happ(happ(Vvar__2__reqb__21946,Vvar__var__3__x__21952__21955),Vvar__var__4__y__21953__21956) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__21941,Vvar__var__3__x__21952__21955),Vvar__var__4__y__21953__21956)) ) ) )
& VX21939 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__21940,Vvar__1__req__21941,Vvar__2__reqb__21946) ) ) )
| ? [Vvar__0__R__21958] :
( cType___24t(Vvar__0__R__21958)
& ? [Vvar__1__rO__21959] :
( t(Vvar__1__rO__21959,Vvar__0__R__21958)
& ? [Vvar__2__rI__21960] :
( t(Vvar__2__rI__21960,Vvar__0__R__21958)
& ? [Vvar__3__radd__21961] :
( c_24__type__2506___24t(Vvar__0__R__21958,Vvar__3__radd__21961)
& ? [Vvar__4__rmul__21966] :
( c_24__type__2506___24t(Vvar__0__R__21958,Vvar__4__rmul__21966)
& ? [Vvar__5__rsub__21971] :
( c_24__type__2506___24t(Vvar__0__R__21958,Vvar__5__rsub__21971)
& ? [Vvar__6__ropp__21976] :
( c_24__type__1407___24t(Vvar__0__R__21958,Vvar__6__ropp__21976)
& ? [Vvar__7__req__21979] :
( c_24__type__1412___24t(Vvar__0__R__21958,Vvar__7__req__21979)
& ? [Vvar__8__C__21984] :
( cType___24t(Vvar__8__C__21984)
& ? [Vvar__9__cO__21985] :
( t(Vvar__9__cO__21985,Vvar__8__C__21984)
& ? [Vvar__10__cI__21986] :
( t(Vvar__10__cI__21986,Vvar__8__C__21984)
& ? [Vvar__11__cadd__21987] :
( c_24__type__2708___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__11__cadd__21987)
& ? [Vvar__12__cmul__21992] :
( c_24__type__2708___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__12__cmul__21992)
& ? [Vvar__13__csub__21997] :
( c_24__type__2708___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__13__csub__21997)
& ? [Vvar__14__copp__22002] :
( c_24__type__2722___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__14__copp__22002)
& ? [Vvar__15__ceqb__22005] :
( c_24__type__2729___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__15__ceqb__22005)
& ? [Vvar__16__phi__22010] :
( c_24__type__2682___24t(Vvar__0__R__21958,Vvar__8__C__21984,Vvar__16__phi__22010)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__21958,Vvar__1__rO__21959,Vvar__2__rI__21960,Vvar__3__radd__21961,Vvar__4__rmul__21966,Vvar__5__rsub__21971,Vvar__6__ropp__21976,Vvar__7__req__21979,Vvar__8__C__21984,Vvar__9__cO__21985,Vvar__10__cI__21986,Vvar__11__cadd__21987,Vvar__12__cmul__21992,Vvar__13__csub__21997,Vvar__14__copp__22002,Vvar__15__ceqb__22005,Vvar__16__phi__22010)
& VX21939 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__21958,Vvar__1__rO__21959,Vvar__2__rI__21960,Vvar__3__radd__21961,Vvar__4__rmul__21966,Vvar__5__rsub__21971,Vvar__6__ropp__21976,Vvar__7__req__21979,Vvar__8__C__21984,Vvar__9__cO__21985,Vvar__10__cI__21986,Vvar__11__cadd__21987,Vvar__12__cmul__21992,Vvar__13__csub__21997,Vvar__14__copp__22002,Vvar__15__ceqb__22005,Vvar__16__phi__22010) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341] :
( cType___24t(Vvar__0__R__13289)
=> ( t(Vvar__1__rO__13290,Vvar__0__R__13289)
=> ( t(Vvar__2__rI__13291,Vvar__0__R__13289)
=> ( c_24__type__13685___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__3__radd__13292)
=> ( c_24__type__13898___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__4__rmul__13297)
=> ( c_24__type__14111___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__5__rsub__13302)
=> ( c_24__type__14306___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__6__ropp__13307)
=> ( c_24__type__14519___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__7__req__13310)
=> ( cType___24t(Vvar__8__C__13315)
=> ( t(Vvar__9__cO__13316,Vvar__8__C__13315)
=> ( t(Vvar__10__cI__13317,Vvar__8__C__13315)
=> ( c_24__type__14732___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__11__cadd__13318)
=> ( c_24__type__14945___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__12__cmul__13323)
=> ( c_24__type__15158___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__13__csub__13328)
=> ( c_24__type__15353___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__14__copp__13333)
=> ( c_24__type__15566___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__15__ceqb__13336)
=> ( c_24__type__15761___24t(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341,Vvar__16__phi__13341)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__13289,Vvar__1__rO__13290,Vvar__2__rI__13291,Vvar__3__radd__13292,Vvar__4__rmul__13297,Vvar__5__rsub__13302,Vvar__6__ropp__13307,Vvar__7__req__13310,Vvar__8__C__13315,Vvar__9__cO__13316,Vvar__10__cI__13317,Vvar__11__cadd__13318,Vvar__12__cmul__13323,Vvar__13__csub__13328,Vvar__14__copp__13333,Vvar__15__ceqb__13336,Vvar__16__phi__13341)
=> ( p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,Vvar__9__cO__13316)),Vvar__1__rO__13290))
& p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,Vvar__10__cI__13317)),Vvar__2__rI__13291))
& ! [Vvar__var__var__var__var__var__var__19__x__13403__13405__13427__13429__13431__13433__13435] :
( t(Vvar__var__var__var__var__var__var__19__x__13403__13405__13427__13429__13431__13433__13435,Vvar__8__C__13315)
=> ! [Vvar__var__var__var__var__var__var__20__y__13404__13406__13428__13430__13432__13434__13436] :
( t(Vvar__var__var__var__var__var__var__20__y__13404__13406__13428__13430__13432__13434__13436,Vvar__8__C__13315)
=> p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,happ(happ(Vvar__11__cadd__13318,Vvar__var__var__var__var__var__var__19__x__13403__13405__13427__13429__13431__13433__13435),Vvar__var__var__var__var__var__var__20__y__13404__13406__13428__13430__13432__13434__13436))),happ(happ(Vvar__3__radd__13292,happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__19__x__13403__13405__13427__13429__13431__13433__13435)),happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__20__y__13404__13406__13428__13430__13432__13434__13436)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__13408__13410__13437__13439__13441__13443__13445] :
( t(Vvar__var__var__var__var__var__var__20__x__13408__13410__13437__13439__13441__13443__13445,Vvar__8__C__13315)
=> ! [Vvar__var__var__var__var__var__var__21__y__13409__13411__13438__13440__13442__13444__13446] :
( t(Vvar__var__var__var__var__var__var__21__y__13409__13411__13438__13440__13442__13444__13446,Vvar__8__C__13315)
=> p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,happ(happ(Vvar__13__csub__13328,Vvar__var__var__var__var__var__var__20__x__13408__13410__13437__13439__13441__13443__13445),Vvar__var__var__var__var__var__var__21__y__13409__13411__13438__13440__13442__13444__13446))),happ(happ(Vvar__5__rsub__13302,happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__20__x__13408__13410__13437__13439__13441__13443__13445)),happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__21__y__13409__13411__13438__13440__13442__13444__13446)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__13413__13415__13447__13449__13451__13453__13455] :
( t(Vvar__var__var__var__var__var__var__21__x__13413__13415__13447__13449__13451__13453__13455,Vvar__8__C__13315)
=> ! [Vvar__var__var__var__var__var__var__22__y__13414__13416__13448__13450__13452__13454__13456] :
( t(Vvar__var__var__var__var__var__var__22__y__13414__13416__13448__13450__13452__13454__13456,Vvar__8__C__13315)
=> p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,happ(happ(Vvar__12__cmul__13323,Vvar__var__var__var__var__var__var__21__x__13413__13415__13447__13449__13451__13453__13455),Vvar__var__var__var__var__var__var__22__y__13414__13416__13448__13450__13452__13454__13456))),happ(happ(Vvar__4__rmul__13297,happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__21__x__13413__13415__13447__13449__13451__13453__13455)),happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__22__y__13414__13416__13448__13450__13452__13454__13456)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__13418__13419__13457__13458__13459__13460__13461] :
( t(Vvar__var__var__var__var__var__var__22__x__13418__13419__13457__13458__13459__13460__13461,Vvar__8__C__13315)
=> p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,happ(Vvar__14__copp__13333,Vvar__var__var__var__var__var__var__22__x__13418__13419__13457__13458__13459__13460__13461))),happ(Vvar__6__ropp__13307,happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__var__22__x__13418__13419__13457__13458__13459__13460__13461)))) )
& ! [Vvar__var__var__var__var__var__23__x__13421__13424__13462__13465__13468__13471] :
( t(Vvar__var__var__var__var__var__23__x__13421__13424__13462__13465__13468__13471,Vvar__8__C__13315)
=> ! [Vvar__var__var__var__var__var__24__y__13422__13425__13463__13466__13469__13472] :
( t(Vvar__var__var__var__var__var__24__y__13422__13425__13463__13466__13469__13472,Vvar__8__C__13315)
=> ( happ(happ(Vvar__15__ceqb__13336,Vvar__var__var__var__var__var__23__x__13421__13424__13462__13465__13468__13471),Vvar__var__var__var__var__var__24__y__13422__13425__13463__13466__13469__13472) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__13310,happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__23__x__13421__13424__13462__13465__13468__13471)),happ(Vvar__16__phi__13341,Vvar__var__var__var__var__var__24__y__13422__13425__13463__13466__13469__13472))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475] :
( cType___24t(Vvar__0__R__20454)
=> ( t(Vvar__1__rO__20455,Vvar__0__R__20454)
=> ( t(Vvar__2__rI__20456,Vvar__0__R__20454)
=> ( c_24__type__20678___24t(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475,Vvar__3__radd__20457)
=> ( c_24__type__20741___24t(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475,Vvar__4__rmul__20462)
=> ( c_24__type__20804___24t(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475,Vvar__5__rsub__20467)
=> ( c_24__type__20858___24t(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475,Vvar__6__ropp__20472)
=> ( c_24__type__20921___24t(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475,Vvar__7__req__20475)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__20454,Vvar__1__rO__20455,Vvar__2__rI__20456,Vvar__3__radd__20457,Vvar__4__rmul__20462,Vvar__5__rsub__20467,Vvar__6__ropp__20472,Vvar__7__req__20475)
=> ( ! [Vvar__var__var__var__var__var__8__x__20508__20509__20552__20553__20554__20555] :
( t(Vvar__var__var__var__var__var__8__x__20508__20509__20552__20553__20554__20555,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__3__radd__20457,Vvar__1__rO__20455),Vvar__var__var__var__var__var__8__x__20508__20509__20552__20553__20554__20555)),Vvar__var__var__var__var__var__8__x__20508__20509__20552__20553__20554__20555)) )
& ! [Vvar__var__var__var__var__9__x__20511__20513__20556__20558__20560] :
( t(Vvar__var__var__var__var__9__x__20511__20513__20556__20558__20560,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__10__y__20512__20514__20557__20559__20561] :
( t(Vvar__var__var__var__var__10__y__20512__20514__20557__20559__20561,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__9__x__20511__20513__20556__20558__20560),Vvar__var__var__var__var__10__y__20512__20514__20557__20559__20561)),happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__10__y__20512__20514__20557__20559__20561),Vvar__var__var__var__var__9__x__20511__20513__20556__20558__20560))) ) )
& ! [Vvar__var__var__var__var__10__x__20516__20519__20562__20565__20568] :
( t(Vvar__var__var__var__var__10__x__20516__20519__20562__20565__20568,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__11__y__20517__20520__20563__20566__20569] :
( t(Vvar__var__var__var__var__11__y__20517__20520__20563__20566__20569,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__12__z__20518__20521__20564__20567__20570] :
( t(Vvar__var__var__var__var__12__z__20518__20521__20564__20567__20570,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__10__x__20516__20519__20562__20565__20568),happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__11__y__20517__20520__20563__20566__20569),Vvar__var__var__var__var__12__z__20518__20521__20564__20567__20570))),happ(happ(Vvar__3__radd__20457,happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__10__x__20516__20519__20562__20565__20568),Vvar__var__var__var__var__11__y__20517__20520__20563__20566__20569)),Vvar__var__var__var__var__12__z__20518__20521__20564__20567__20570))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__20523__20524__20571__20572__20573__20574] :
( t(Vvar__var__var__var__var__var__11__x__20523__20524__20571__20572__20573__20574,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__4__rmul__20462,Vvar__2__rI__20456),Vvar__var__var__var__var__var__11__x__20523__20524__20571__20572__20573__20574)),Vvar__var__var__var__var__var__11__x__20523__20524__20571__20572__20573__20574)) )
& ! [Vvar__var__var__var__var__12__x__20526__20528__20575__20577__20579] :
( t(Vvar__var__var__var__var__12__x__20526__20528__20575__20577__20579,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__13__y__20527__20529__20576__20578__20580] :
( t(Vvar__var__var__var__var__13__y__20527__20529__20576__20578__20580,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__12__x__20526__20528__20575__20577__20579),Vvar__var__var__var__var__13__y__20527__20529__20576__20578__20580)),happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__13__y__20527__20529__20576__20578__20580),Vvar__var__var__var__var__12__x__20526__20528__20575__20577__20579))) ) )
& ! [Vvar__var__var__var__var__13__x__20531__20534__20581__20584__20587] :
( t(Vvar__var__var__var__var__13__x__20531__20534__20581__20584__20587,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__14__y__20532__20535__20582__20585__20588] :
( t(Vvar__var__var__var__var__14__y__20532__20535__20582__20585__20588,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__15__z__20533__20536__20583__20586__20589] :
( t(Vvar__var__var__var__var__15__z__20533__20536__20583__20586__20589,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__13__x__20531__20534__20581__20584__20587),happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__14__y__20532__20535__20582__20585__20588),Vvar__var__var__var__var__15__z__20533__20536__20583__20586__20589))),happ(happ(Vvar__4__rmul__20462,happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__13__x__20531__20534__20581__20584__20587),Vvar__var__var__var__var__14__y__20532__20535__20582__20585__20588)),Vvar__var__var__var__var__15__z__20533__20536__20583__20586__20589))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__20538__20541__20590__20593__20596__20599] :
( t(Vvar__var__var__var__var__var__14__x__20538__20541__20590__20593__20596__20599,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__var__15__y__20539__20542__20591__20594__20597__20600] :
( t(Vvar__var__var__var__var__var__15__y__20539__20542__20591__20594__20597__20600,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__var__16__z__20540__20543__20592__20595__20598__20601] :
( t(Vvar__var__var__var__var__var__16__z__20540__20543__20592__20595__20598__20601,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__4__rmul__20462,happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__var__14__x__20538__20541__20590__20593__20596__20599),Vvar__var__var__var__var__var__15__y__20539__20542__20591__20594__20597__20600)),Vvar__var__var__var__var__var__16__z__20540__20543__20592__20595__20598__20601)),happ(happ(Vvar__3__radd__20457,happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__var__14__x__20538__20541__20590__20593__20596__20599),Vvar__var__var__var__var__var__16__z__20540__20543__20592__20595__20598__20601)),happ(happ(Vvar__4__rmul__20462,Vvar__var__var__var__var__var__15__y__20539__20542__20591__20594__20597__20600),Vvar__var__var__var__var__var__16__z__20540__20543__20592__20595__20598__20601)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__20545__20547__20602__20604__20606__20608__20610] :
( t(Vvar__var__var__var__var__var__var__15__x__20545__20547__20602__20604__20606__20608__20610,Vvar__0__R__20454)
=> ! [Vvar__var__var__var__var__var__var__16__y__20546__20548__20603__20605__20607__20609__20611] :
( t(Vvar__var__var__var__var__var__var__16__y__20546__20548__20603__20605__20607__20609__20611,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__5__rsub__20467,Vvar__var__var__var__var__var__var__15__x__20545__20547__20602__20604__20606__20608__20610),Vvar__var__var__var__var__var__var__16__y__20546__20548__20603__20605__20607__20609__20611)),happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__var__var__15__x__20545__20547__20602__20604__20606__20608__20610),happ(Vvar__6__ropp__20472,Vvar__var__var__var__var__var__var__16__y__20546__20548__20603__20605__20607__20609__20611)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__20550__20551__20612__20613__20614__20615__20616] :
( t(Vvar__var__var__var__var__var__var__16__x__20550__20551__20612__20613__20614__20615__20616,Vvar__0__R__20454)
=> p(happ(happ(Vvar__7__req__20475,happ(happ(Vvar__3__radd__20457,Vvar__var__var__var__var__var__var__16__x__20550__20551__20612__20613__20614__20615__20616),happ(Vvar__6__ropp__20472,Vvar__var__var__var__var__var__var__16__x__20550__20551__20612__20613__20614__20615__20616))),Vvar__1__rO__20455)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977] :
( cType___24t(Vvar__0__R__20941)
=> ( t(Vvar__1__rO__20942,Vvar__0__R__20941)
=> ( t(Vvar__2__rI__20943,Vvar__0__R__20941)
=> ( c_24__type__21194___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__3__radd__20944)
=> ( c_24__type__21319___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__4__rmul__20949)
=> ( c_24__type__21444___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__5__req__20954)
=> ( cType___24t(Vvar__6__C__20959)
=> ( t(Vvar__7__cO__20960,Vvar__6__C__20959)
=> ( t(Vvar__8__cI__20961,Vvar__6__C__20959)
=> ( c_24__type__21569___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__9__cadd__20962)
=> ( c_24__type__21694___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__10__cmul__20967)
=> ( c_24__type__21819___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__11__ceqb__20972)
=> ( c_24__type__21930___24t(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977,Vvar__12__phi__20977)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__20941,Vvar__1__rO__20942,Vvar__2__rI__20943,Vvar__3__radd__20944,Vvar__4__rmul__20949,Vvar__5__req__20954,Vvar__6__C__20959,Vvar__7__cO__20960,Vvar__8__cI__20961,Vvar__9__cadd__20962,Vvar__10__cmul__20967,Vvar__11__ceqb__20972,Vvar__12__phi__20977)
=> ( p(happ(happ(Vvar__5__req__20954,happ(Vvar__12__phi__20977,Vvar__7__cO__20960)),Vvar__1__rO__20942))
& p(happ(happ(Vvar__5__req__20954,happ(Vvar__12__phi__20977,Vvar__8__cI__20961)),Vvar__2__rI__20943))
& ! [Vvar__var__var__var__var__var__var__15__x__21023__21025__21039__21041__21043__21045__21047] :
( t(Vvar__var__var__var__var__var__var__15__x__21023__21025__21039__21041__21043__21045__21047,Vvar__6__C__20959)
=> ! [Vvar__var__var__var__var__var__var__16__y__21024__21026__21040__21042__21044__21046__21048] :
( t(Vvar__var__var__var__var__var__var__16__y__21024__21026__21040__21042__21044__21046__21048,Vvar__6__C__20959)
=> p(happ(happ(Vvar__5__req__20954,happ(Vvar__12__phi__20977,happ(happ(Vvar__9__cadd__20962,Vvar__var__var__var__var__var__var__15__x__21023__21025__21039__21041__21043__21045__21047),Vvar__var__var__var__var__var__var__16__y__21024__21026__21040__21042__21044__21046__21048))),happ(happ(Vvar__3__radd__20944,happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__var__15__x__21023__21025__21039__21041__21043__21045__21047)),happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__var__16__y__21024__21026__21040__21042__21044__21046__21048)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__21028__21030__21049__21051__21053__21055__21057] :
( t(Vvar__var__var__var__var__var__var__16__x__21028__21030__21049__21051__21053__21055__21057,Vvar__6__C__20959)
=> ! [Vvar__var__var__var__var__var__var__17__y__21029__21031__21050__21052__21054__21056__21058] :
( t(Vvar__var__var__var__var__var__var__17__y__21029__21031__21050__21052__21054__21056__21058,Vvar__6__C__20959)
=> p(happ(happ(Vvar__5__req__20954,happ(Vvar__12__phi__20977,happ(happ(Vvar__10__cmul__20967,Vvar__var__var__var__var__var__var__16__x__21028__21030__21049__21051__21053__21055__21057),Vvar__var__var__var__var__var__var__17__y__21029__21031__21050__21052__21054__21056__21058))),happ(happ(Vvar__4__rmul__20949,happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__var__16__x__21028__21030__21049__21051__21053__21055__21057)),happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__var__17__y__21029__21031__21050__21052__21054__21056__21058)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__21033__21036__21059__21062__21065__21068] :
( t(Vvar__var__var__var__var__var__17__x__21033__21036__21059__21062__21065__21068,Vvar__6__C__20959)
=> ! [Vvar__var__var__var__var__var__18__y__21034__21037__21060__21063__21066__21069] :
( t(Vvar__var__var__var__var__var__18__y__21034__21037__21060__21063__21066__21069,Vvar__6__C__20959)
=> ( happ(happ(Vvar__11__ceqb__20972,Vvar__var__var__var__var__var__17__x__21033__21036__21059__21062__21065__21068),Vvar__var__var__var__var__var__18__y__21034__21037__21060__21063__21066__21069) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__20954,happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__17__x__21033__21036__21059__21062__21065__21068)),happ(Vvar__12__phi__20977,Vvar__var__var__var__var__var__18__y__21034__21037__21060__21063__21066__21069))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__20190,Vvar__1__rO__20191,Vvar__2__rI__20192,Vvar__3__radd__20193,Vvar__4__rmul__20198,Vvar__5__req__20203] :
( cType___24t(Vvar__0__R__20190)
=> ( t(Vvar__1__rO__20191,Vvar__0__R__20190)
=> ( t(Vvar__2__rI__20192,Vvar__0__R__20190)
=> ( c_24__type__20358___24t(Vvar__0__R__20190,Vvar__1__rO__20191,Vvar__2__rI__20192,Vvar__3__radd__20193,Vvar__4__rmul__20198,Vvar__5__req__20203,Vvar__3__radd__20193)
=> ( c_24__type__20397___24t(Vvar__0__R__20190,Vvar__1__rO__20191,Vvar__2__rI__20192,Vvar__3__radd__20193,Vvar__4__rmul__20198,Vvar__5__req__20203,Vvar__4__rmul__20198)
=> ( c_24__type__20436___24t(Vvar__0__R__20190,Vvar__1__rO__20191,Vvar__2__rI__20192,Vvar__3__radd__20193,Vvar__4__rmul__20198,Vvar__5__req__20203,Vvar__5__req__20203)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__20190,Vvar__1__rO__20191,Vvar__2__rI__20192,Vvar__3__radd__20193,Vvar__4__rmul__20198,Vvar__5__req__20203)
=> ( ! [Vvar__var__var__var__var__var__6__n__20228__20229__20267__20268__20269__20270] :
( t(Vvar__var__var__var__var__var__6__n__20228__20229__20267__20268__20269__20270,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__3__radd__20193,Vvar__1__rO__20191),Vvar__var__var__var__var__var__6__n__20228__20229__20267__20268__20269__20270)),Vvar__var__var__var__var__var__6__n__20228__20229__20267__20268__20269__20270)) )
& ! [Vvar__var__var__var__var__7__n__20231__20233__20271__20273__20275] :
( t(Vvar__var__var__var__var__7__n__20231__20233__20271__20273__20275,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__8__m__20232__20234__20272__20274__20276] :
( t(Vvar__var__var__var__var__8__m__20232__20234__20272__20274__20276,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__7__n__20231__20233__20271__20273__20275),Vvar__var__var__var__var__8__m__20232__20234__20272__20274__20276)),happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__8__m__20232__20234__20272__20274__20276),Vvar__var__var__var__var__7__n__20231__20233__20271__20273__20275))) ) )
& ! [Vvar__var__var__var__var__8__n__20236__20239__20277__20280__20283] :
( t(Vvar__var__var__var__var__8__n__20236__20239__20277__20280__20283,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__9__m__20237__20240__20278__20281__20284] :
( t(Vvar__var__var__var__var__9__m__20237__20240__20278__20281__20284,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__10__p__20238__20241__20279__20282__20285] :
( t(Vvar__var__var__var__var__10__p__20238__20241__20279__20282__20285,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__8__n__20236__20239__20277__20280__20283),happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__9__m__20237__20240__20278__20281__20284),Vvar__var__var__var__var__10__p__20238__20241__20279__20282__20285))),happ(happ(Vvar__3__radd__20193,happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__8__n__20236__20239__20277__20280__20283),Vvar__var__var__var__var__9__m__20237__20240__20278__20281__20284)),Vvar__var__var__var__var__10__p__20238__20241__20279__20282__20285))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__20243__20244__20286__20287__20288__20289] :
( t(Vvar__var__var__var__var__var__9__n__20243__20244__20286__20287__20288__20289,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__4__rmul__20198,Vvar__2__rI__20192),Vvar__var__var__var__var__var__9__n__20243__20244__20286__20287__20288__20289)),Vvar__var__var__var__var__var__9__n__20243__20244__20286__20287__20288__20289)) )
& ! [Vvar__var__var__var__var__var__10__n__20246__20247__20290__20291__20292__20293] :
( t(Vvar__var__var__var__var__var__10__n__20246__20247__20290__20291__20292__20293,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__4__rmul__20198,Vvar__1__rO__20191),Vvar__var__var__var__var__var__10__n__20246__20247__20290__20291__20292__20293)),Vvar__1__rO__20191)) )
& ! [Vvar__var__var__var__var__11__n__20249__20251__20294__20296__20298] :
( t(Vvar__var__var__var__var__11__n__20249__20251__20294__20296__20298,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__12__m__20250__20252__20295__20297__20299] :
( t(Vvar__var__var__var__var__12__m__20250__20252__20295__20297__20299,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__11__n__20249__20251__20294__20296__20298),Vvar__var__var__var__var__12__m__20250__20252__20295__20297__20299)),happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__12__m__20250__20252__20295__20297__20299),Vvar__var__var__var__var__11__n__20249__20251__20294__20296__20298))) ) )
& ! [Vvar__var__var__var__var__12__n__20254__20257__20300__20303__20306] :
( t(Vvar__var__var__var__var__12__n__20254__20257__20300__20303__20306,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__13__m__20255__20258__20301__20304__20307] :
( t(Vvar__var__var__var__var__13__m__20255__20258__20301__20304__20307,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__14__p__20256__20259__20302__20305__20308] :
( t(Vvar__var__var__var__var__14__p__20256__20259__20302__20305__20308,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__12__n__20254__20257__20300__20303__20306),happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__13__m__20255__20258__20301__20304__20307),Vvar__var__var__var__var__14__p__20256__20259__20302__20305__20308))),happ(happ(Vvar__4__rmul__20198,happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__12__n__20254__20257__20300__20303__20306),Vvar__var__var__var__var__13__m__20255__20258__20301__20304__20307)),Vvar__var__var__var__var__14__p__20256__20259__20302__20305__20308))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__20261__20264__20309__20312__20315__20318] :
( t(Vvar__var__var__var__var__var__13__n__20261__20264__20309__20312__20315__20318,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__var__14__m__20262__20265__20310__20313__20316__20319] :
( t(Vvar__var__var__var__var__var__14__m__20262__20265__20310__20313__20316__20319,Vvar__0__R__20190)
=> ! [Vvar__var__var__var__var__var__15__p__20263__20266__20311__20314__20317__20320] :
( t(Vvar__var__var__var__var__var__15__p__20263__20266__20311__20314__20317__20320,Vvar__0__R__20190)
=> p(happ(happ(Vvar__5__req__20203,happ(happ(Vvar__4__rmul__20198,happ(happ(Vvar__3__radd__20193,Vvar__var__var__var__var__var__13__n__20261__20264__20309__20312__20315__20318),Vvar__var__var__var__var__var__14__m__20262__20265__20310__20313__20316__20319)),Vvar__var__var__var__var__var__15__p__20263__20266__20311__20314__20317__20320)),happ(happ(Vvar__3__radd__20193,happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__var__13__n__20261__20264__20309__20312__20315__20318),Vvar__var__var__var__var__var__15__p__20263__20266__20311__20314__20317__20320)),happ(happ(Vvar__4__rmul__20198,Vvar__var__var__var__var__var__14__m__20262__20265__20310__20313__20316__20319),Vvar__var__var__var__var__var__15__p__20263__20266__20311__20314__20317__20320)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__15847,Vvar__1__copp__15848,Vvar__2__ceqb__15851,Vvar__3__get__sign__15856] :
( cType___24t(Vvar__0__C__15847)
=> ( c_24__type__15903___24t(Vvar__0__C__15847,Vvar__1__copp__15848,Vvar__2__ceqb__15851,Vvar__3__get__sign__15856,Vvar__1__copp__15848)
=> ( c_24__type__15922___24t(Vvar__0__C__15847,Vvar__1__copp__15848,Vvar__2__ceqb__15851,Vvar__3__get__sign__15856,Vvar__2__ceqb__15851)
=> ( c_24__type__15936___24t(Vvar__0__C__15847,Vvar__1__copp__15848,Vvar__2__ceqb__15851,Vvar__3__get__sign__15856,Vvar__3__get__sign__15856)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__15847,Vvar__1__copp__15848,Vvar__2__ceqb__15851,Vvar__3__get__sign__15856)
=> ( ! [Vvar__var__var__var__var__var__4__c__15873__15876__15879__15882__15885__15888] :
( t(Vvar__var__var__var__var__var__4__c__15873__15876__15879__15882__15885__15888,Vvar__0__C__15847)
=> ! [Vvar__var__var__var__var__var__5__c_27__15874__15877__15880__15883__15886__15889] :
( t(Vvar__var__var__var__var__var__5__c_27__15874__15877__15880__15883__15886__15889,Vvar__0__C__15847)
=> ( happ(Vvar__3__get__sign__15856,Vvar__var__var__var__var__var__4__c__15873__15876__15879__15882__15885__15888) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__15847,Vvar__var__var__var__var__var__5__c_27__15874__15877__15880__15883__15886__15889)
=> happ(happ(Vvar__2__ceqb__15851,Vvar__var__var__var__var__var__4__c__15873__15876__15879__15882__15885__15888),happ(Vvar__1__copp__15848,Vvar__var__var__var__var__var__5__c_27__15874__15877__15880__15883__15886__15889)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748] :
( cType___24t(Vvar__0__R__12737)
=> ( c_24__type__12823___24t(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748,Vvar__1__radd__12738)
=> ( c_24__type__12846___24t(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748,Vvar__2__rmul__12743)
=> ( c_24__type__12869___24t(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748,Vvar__3__req__12748)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12892___24a4(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12737,c_24__type__12910___24a4(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748),Vvar__3__req__12748,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12737,Vvar__0__R__12737,Vvar__3__req__12748,Vvar__3__req__12748)),Vvar__1__radd__12738)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12936___24a4(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12737,c_24__type__12954___24a4(Vvar__0__R__12737,Vvar__1__radd__12738,Vvar__2__rmul__12743,Vvar__3__req__12748),Vvar__3__req__12748,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12737,Vvar__0__R__12737,Vvar__3__req__12748,Vvar__3__req__12748)),Vvar__2__rmul__12743)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Cube.compat',axiom,
! [Vvar__0___24Anonymous__209,Vvar__1___24Anonymous__210,Vvar__2___24Anonymous__211] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__209)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__210)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__211)
=> ( cCube_2ecompat___24a3(Vvar__0___24Anonymous__209,Vvar__1___24Anonymous__210,Vvar__2___24Anonymous__211)
=> ( ? [Vvar__0__n__213] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__213)
& Vvar__2___24Anonymous__211 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__213)
& Vvar__1___24Anonymous__210 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__213)
& Vvar__0___24Anonymous__209 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__213) )
| ? [Vvar__0__U__214] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U__214)
& ? [Vvar__1__V__215] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V__215)
& ? [Vvar__2__W__216] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W__216)
& cCube_2ecompat___24a3(Vvar__0__U__214,Vvar__1__V__215,Vvar__2__W__216)
& Vvar__2___24Anonymous__211 = cLambda_2eRedexes_2eFun___24a1(Vvar__2__W__216)
& Vvar__1___24Anonymous__210 = cLambda_2eRedexes_2eFun___24a1(Vvar__1__V__215)
& Vvar__0___24Anonymous__209 = cLambda_2eRedexes_2eFun___24a1(Vvar__0__U__214) ) ) )
| ? [Vvar__0__U1__218] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__218)
& ? [Vvar__1__V1__219] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__219)
& ? [Vvar__2__W1__220] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W1__220)
& cCube_2ecompat___24a3(Vvar__0__U1__218,Vvar__1__V1__219,Vvar__2__W1__220)
& ? [Vvar__4__U2__222] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__U2__222)
& ? [Vvar__5__V2__223] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__5__V2__223)
& ? [Vvar__6__W2__224] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__6__W2__224)
& cCube_2ecompat___24a3(Vvar__4__U2__222,Vvar__5__V2__223,Vvar__6__W2__224)
& ? [Vvar__8__b__226] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__8__b__226)
& Vvar__2___24Anonymous__211 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b__226,Vvar__2__W1__220,Vvar__6__W2__224)
& Vvar__1___24Anonymous__210 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,Vvar__1__V1__219,Vvar__5__V2__223)
& Vvar__0___24Anonymous__209 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,Vvar__0__U1__218,Vvar__4__U2__222) ) ) ) ) ) ) )
| ? [Vvar__0__U1__227] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__227)
& ? [Vvar__1__V1__228] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__228)
& ? [Vvar__2__W1__229] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W1__229)
& cCube_2ecompat___24a3(Vvar__0__U1__227,Vvar__1__V1__228,Vvar__2__W1__229)
& ? [Vvar__4__U2__231] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__U2__231)
& ? [Vvar__5__V2__232] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__5__V2__232)
& ? [Vvar__6__W2__233] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__6__W2__233)
& cCube_2ecompat___24a3(Vvar__4__U2__231,Vvar__5__V2__232,Vvar__6__W2__233)
& ? [Vvar__8__b__235] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__8__b__235)
& ? [Vvar__9__b_27__236] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__9__b_27__236)
& Vvar__2___24Anonymous__211 = cLambda_2eRedexes_2eAp___24a3(Vvar__9__b_27__236,cLambda_2eRedexes_2eFun___24a1(Vvar__2__W1__229),Vvar__6__W2__233)
& Vvar__1___24Anonymous__210 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b__235,cLambda_2eRedexes_2eFun___24a1(Vvar__1__V1__228),Vvar__5__V2__232)
& Vvar__0___24Anonymous__209 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(Vvar__0__U1__227),Vvar__4__U2__231) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX19933] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX19933)
=> ( VX19933 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX19933 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_Lambda.Redexes.comp',axiom,
! [Vvar__0___24Anonymous__253,Vvar__1___24Anonymous__254] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__253)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__254)
=> ( cLambda_2eRedexes_2ecomp___24a2(Vvar__0___24Anonymous__253,Vvar__1___24Anonymous__254)
=> ( ? [Vvar__0__n__256] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__256)
& Vvar__1___24Anonymous__254 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__256)
& Vvar__0___24Anonymous__253 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__256) )
| ? [Vvar__0__U__257] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U__257)
& ? [Vvar__1__V__258] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V__258)
& cLambda_2eRedexes_2ecomp___24a2(Vvar__0__U__257,Vvar__1__V__258)
& Vvar__1___24Anonymous__254 = cLambda_2eRedexes_2eFun___24a1(Vvar__1__V__258)
& Vvar__0___24Anonymous__253 = cLambda_2eRedexes_2eFun___24a1(Vvar__0__U__257) ) )
| ? [Vvar__0__U1__260] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__260)
& ? [Vvar__1__V1__261] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__261)
& cLambda_2eRedexes_2ecomp___24a2(Vvar__0__U1__260,Vvar__1__V1__261)
& ? [Vvar__3__U2__263] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__3__U2__263)
& ? [Vvar__4__V2__264] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__V2__264)
& cLambda_2eRedexes_2ecomp___24a2(Vvar__3__U2__263,Vvar__4__V2__264)
& ? [Vvar__6__b1__266] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6__b1__266)
& ? [Vvar__7__b2__267] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7__b2__267)
& Vvar__1___24Anonymous__254 = cLambda_2eRedexes_2eAp___24a3(Vvar__7__b2__267,Vvar__1__V1__261,Vvar__4__V2__264)
& Vvar__0___24Anonymous__253 = cLambda_2eRedexes_2eAp___24a3(Vvar__6__b1__266,Vvar__0__U1__260,Vvar__3__U2__263) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Redexes.redexes',axiom,
! [VX9] :
( cLambda_2eRedexes_2eredexes___24t(VX9)
=> ( ? [Vvar__0___24Anonymous__10] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10)
& VX9 = cLambda_2eRedexes_2eVar___24a1(Vvar__0___24Anonymous__10) )
| ? [Vvar__0___24Anonymous__11] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__11)
& VX9 = cLambda_2eRedexes_2eFun___24a1(Vvar__0___24Anonymous__11) )
| ? [Vvar__0___24Anonymous__12] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__12)
& ? [Vvar__1___24Anonymous__13] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__13)
& ? [Vvar__2___24Anonymous__14] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__14)
& VX9 = cLambda_2eRedexes_2eAp___24a3(Vvar__0___24Anonymous__12,Vvar__1___24Anonymous__13,Vvar__2___24Anonymous__14) ) ) ) ) ) ).
fof('$_inversion_Lambda.Redexes.sub',axiom,
! [Vvar__0___24Anonymous__44,Vvar__1___24Anonymous__45] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__44)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__45)
=> ( cLambda_2eRedexes_2esub___24a2(Vvar__0___24Anonymous__44,Vvar__1___24Anonymous__45)
=> ( ? [Vvar__0__n__47] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__47)
& Vvar__1___24Anonymous__45 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__47)
& Vvar__0___24Anonymous__44 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__47) )
| ? [Vvar__0__U__48] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U__48)
& ? [Vvar__1__V__49] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V__49)
& cLambda_2eRedexes_2esub___24a2(Vvar__0__U__48,Vvar__1__V__49)
& Vvar__1___24Anonymous__45 = cLambda_2eRedexes_2eFun___24a1(Vvar__1__V__49)
& Vvar__0___24Anonymous__44 = cLambda_2eRedexes_2eFun___24a1(Vvar__0__U__48) ) )
| ? [Vvar__0__U1__51] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__51)
& ? [Vvar__1__V1__52] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__52)
& cLambda_2eRedexes_2esub___24a2(Vvar__0__U1__51,Vvar__1__V1__52)
& ? [Vvar__3__U2__54] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__3__U2__54)
& ? [Vvar__4__V2__55] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__V2__55)
& cLambda_2eRedexes_2esub___24a2(Vvar__3__U2__54,Vvar__4__V2__55)
& ? [Vvar__6__b__57] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6__b__57)
& Vvar__1___24Anonymous__45 = cLambda_2eRedexes_2eAp___24a3(Vvar__6__b__57,Vvar__1__V1__52,Vvar__4__V2__55)
& Vvar__0___24Anonymous__44 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,Vvar__0__U1__51,Vvar__3__U2__54) ) ) ) ) )
| ? [Vvar__0__U1__58] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__58)
& ? [Vvar__1__V1__59] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__59)
& cLambda_2eRedexes_2esub___24a2(Vvar__0__U1__58,Vvar__1__V1__59)
& ? [Vvar__3__U2__61] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__3__U2__61)
& ? [Vvar__4__V2__62] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__V2__62)
& cLambda_2eRedexes_2esub___24a2(Vvar__3__U2__61,Vvar__4__V2__62)
& ? [Vvar__6__b__64] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6__b__64)
& Vvar__1___24Anonymous__45 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,Vvar__1__V1__59,Vvar__4__V2__62)
& Vvar__0___24Anonymous__44 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,Vvar__0__U1__58,Vvar__3__U2__61) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Redexes.union',axiom,
! [Vvar__0___24Anonymous__94,Vvar__1___24Anonymous__95,Vvar__2___24Anonymous__96] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__94)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__95)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__96)
=> ( cLambda_2eRedexes_2eunion___24a3(Vvar__0___24Anonymous__94,Vvar__1___24Anonymous__95,Vvar__2___24Anonymous__96)
=> ( ? [Vvar__0__n__98] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__98)
& Vvar__2___24Anonymous__96 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__98)
& Vvar__1___24Anonymous__95 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__98)
& Vvar__0___24Anonymous__94 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__98) )
| ? [Vvar__0__U__99] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U__99)
& ? [Vvar__1__V__100] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V__100)
& ? [Vvar__2__W__101] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W__101)
& cLambda_2eRedexes_2eunion___24a3(Vvar__0__U__99,Vvar__1__V__100,Vvar__2__W__101)
& Vvar__2___24Anonymous__96 = cLambda_2eRedexes_2eFun___24a1(Vvar__2__W__101)
& Vvar__1___24Anonymous__95 = cLambda_2eRedexes_2eFun___24a1(Vvar__1__V__100)
& Vvar__0___24Anonymous__94 = cLambda_2eRedexes_2eFun___24a1(Vvar__0__U__99) ) ) )
| ? [Vvar__0__U1__103] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__103)
& ? [Vvar__1__V1__104] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__104)
& ? [Vvar__2__W1__105] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W1__105)
& cLambda_2eRedexes_2eunion___24a3(Vvar__0__U1__103,Vvar__1__V1__104,Vvar__2__W1__105)
& ? [Vvar__4__U2__107] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__U2__107)
& ? [Vvar__5__V2__108] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__5__V2__108)
& ? [Vvar__6__W2__109] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__6__W2__109)
& cLambda_2eRedexes_2eunion___24a3(Vvar__4__U2__107,Vvar__5__V2__108,Vvar__6__W2__109)
& ? [Vvar__8__b1__111] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__8__b1__111)
& ? [Vvar__9__b2__112] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__9__b2__112)
& Vvar__2___24Anonymous__96 = cLambda_2eRedexes_2eAp___24a3(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24119___24a5(Vvar__0___24Anonymous__94,Vvar__1___24Anonymous__95,Vvar__2___24Anonymous__96,Vvar__8__b1__111,Vvar__9__b2__112),Vvar__2__W1__105,Vvar__6__W2__109)
& Vvar__1___24Anonymous__95 = cLambda_2eRedexes_2eAp___24a3(Vvar__9__b2__112,Vvar__1__V1__104,Vvar__5__V2__108)
& Vvar__0___24Anonymous__94 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b1__111,Vvar__0__U1__103,Vvar__4__U2__107) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Reduction.par_red',axiom,
! [Vvar__0___24Anonymous__24519,Vvar__1___24Anonymous__24520] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__24519)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__24520)
=> ( cLambda_2eReduction_2epar__red___24a2(Vvar__0___24Anonymous__24519,Vvar__1___24Anonymous__24520)
=> ( ? [Vvar__0__M__24522] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24522)
& ? [Vvar__1__N__24523] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__24523)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__0__M__24522,Vvar__1__N__24523)
& Vvar__1___24Anonymous__24520 = Vvar__1__N__24523
& Vvar__0___24Anonymous__24519 = Vvar__0__M__24522 ) )
| ? [Vvar__0__M__24525] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24525)
& ? [Vvar__1__N__24526] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__24526)
& ? [Vvar__2__P__24527] :
( cLambda_2eTerms_2elambda___24t(Vvar__2__P__24527)
& cLambda_2eReduction_2epar__red___24a2(Vvar__0__M__24525,Vvar__1__N__24526)
& cLambda_2eReduction_2epar__red___24a2(Vvar__1__N__24526,Vvar__2__P__24527)
& Vvar__1___24Anonymous__24520 = Vvar__2__P__24527
& Vvar__0___24Anonymous__24519 = Vvar__0__M__24525 ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Reduction.par_red1',axiom,
! [Vvar__0___24Anonymous__24180,Vvar__1___24Anonymous__24181] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__24180)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__24181)
=> ( cLambda_2eReduction_2epar__red1___24a2(Vvar__0___24Anonymous__24180,Vvar__1___24Anonymous__24181)
=> ( ? [Vvar__0__M__24183] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24183)
& ? [Vvar__1__M_27__24184] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__24184)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__0__M__24183,Vvar__1__M_27__24184)
& ? [Vvar__3__N__24186] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__N__24186)
& ? [Vvar__4__N_27__24187] :
( cLambda_2eTerms_2elambda___24t(Vvar__4__N_27__24187)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__3__N__24186,Vvar__4__N_27__24187)
& Vvar__1___24Anonymous__24181 = c_24__case__Lambda_2eTerms_2elambda_249752___24a4(Vvar__0___24Anonymous__24180,Vvar__1___24Anonymous__24181,Vvar__1__M_27__24184,Vvar__4__N_27__24187)
& Vvar__0___24Anonymous__24180 = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__24183),Vvar__3__N__24186) ) ) ) )
| ? [Vvar__0__n__24194] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__24194)
& Vvar__1___24Anonymous__24181 = cLambda_2eTerms_2eRef___24a1(Vvar__0__n__24194)
& Vvar__0___24Anonymous__24180 = cLambda_2eTerms_2eRef___24a1(Vvar__0__n__24194) )
| ? [Vvar__0__M__24195] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24195)
& ? [Vvar__1__M_27__24196] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__24196)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__0__M__24195,Vvar__1__M_27__24196)
& Vvar__1___24Anonymous__24181 = cLambda_2eTerms_2eAbs___24a1(Vvar__1__M_27__24196)
& Vvar__0___24Anonymous__24180 = cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__24195) ) )
| ? [Vvar__0__M__24198] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24198)
& ? [Vvar__1__M_27__24199] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__24199)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__0__M__24198,Vvar__1__M_27__24199)
& ? [Vvar__3__N__24201] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__N__24201)
& ? [Vvar__4__N_27__24202] :
( cLambda_2eTerms_2elambda___24t(Vvar__4__N_27__24202)
& cLambda_2eReduction_2epar__red1___24a2(Vvar__3__N__24201,Vvar__4__N_27__24202)
& Vvar__1___24Anonymous__24181 = cLambda_2eTerms_2eApp___24a2(Vvar__1__M_27__24199,Vvar__4__N_27__24202)
& Vvar__0___24Anonymous__24180 = cLambda_2eTerms_2eApp___24a2(Vvar__0__M__24198,Vvar__3__N__24201) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Reduction.red',axiom,
! [Vvar__0___24Anonymous__24168,Vvar__1___24Anonymous__24169] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__24168)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__24169)
=> ( cLambda_2eReduction_2ered___24a2(Vvar__0___24Anonymous__24168,Vvar__1___24Anonymous__24169)
=> ( ? [Vvar__0__M__24171] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24171)
& ? [Vvar__1__N__24172] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__24172)
& cLambda_2eReduction_2ered1___24a2(Vvar__0__M__24171,Vvar__1__N__24172)
& Vvar__1___24Anonymous__24169 = Vvar__1__N__24172
& Vvar__0___24Anonymous__24168 = Vvar__0__M__24171 ) )
| ? [Vvar__0__M__24174] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24174)
& Vvar__1___24Anonymous__24169 = Vvar__0__M__24174
& Vvar__0___24Anonymous__24168 = Vvar__0__M__24174 )
| ? [Vvar__0__M__24175] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__24175)
& ? [Vvar__1__N__24176] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__24176)
& ? [Vvar__2__P__24177] :
( cLambda_2eTerms_2elambda___24t(Vvar__2__P__24177)
& cLambda_2eReduction_2ered___24a2(Vvar__0__M__24175,Vvar__1__N__24176)
& cLambda_2eReduction_2ered___24a2(Vvar__1__N__24176,Vvar__2__P__24177)
& Vvar__1___24Anonymous__24169 = Vvar__2__P__24177
& Vvar__0___24Anonymous__24168 = Vvar__0__M__24175 ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Reduction.red1',axiom,
! [Vvar__0___24Anonymous__9416,Vvar__1___24Anonymous__9417] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__9416)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__9417)
=> ( cLambda_2eReduction_2ered1___24a2(Vvar__0___24Anonymous__9416,Vvar__1___24Anonymous__9417)
=> ( ? [Vvar__0__M__9419] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__9419)
& ? [Vvar__1__N__9420] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__9420)
& Vvar__1___24Anonymous__9417 = c_24__case__Lambda_2eTerms_2elambda_249752___24a4(Vvar__0___24Anonymous__9416,Vvar__1___24Anonymous__9417,Vvar__0__M__9419,Vvar__1__N__9420)
& Vvar__0___24Anonymous__9416 = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__9419),Vvar__1__N__9420) ) )
| ? [Vvar__0__M__9426] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__9426)
& ? [Vvar__1__N__9427] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__9427)
& cLambda_2eReduction_2ered1___24a2(Vvar__0__M__9426,Vvar__1__N__9427)
& Vvar__1___24Anonymous__9417 = cLambda_2eTerms_2eAbs___24a1(Vvar__1__N__9427)
& Vvar__0___24Anonymous__9416 = cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__9426) ) )
| ? [Vvar__0__M1__9429] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M1__9429)
& ? [Vvar__1__N1__9430] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N1__9430)
& cLambda_2eReduction_2ered1___24a2(Vvar__0__M1__9429,Vvar__1__N1__9430)
& ? [Vvar__3__M2__9432] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__M2__9432)
& Vvar__1___24Anonymous__9417 = cLambda_2eTerms_2eApp___24a2(Vvar__1__N1__9430,Vvar__3__M2__9432)
& Vvar__0___24Anonymous__9416 = cLambda_2eTerms_2eApp___24a2(Vvar__0__M1__9429,Vvar__3__M2__9432) ) ) )
| ? [Vvar__0__M2__9433] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M2__9433)
& ? [Vvar__1__N2__9434] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N2__9434)
& cLambda_2eReduction_2ered1___24a2(Vvar__0__M2__9433,Vvar__1__N2__9434)
& ? [Vvar__3__M1__9436] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__M1__9436)
& Vvar__1___24Anonymous__9417 = cLambda_2eTerms_2eApp___24a2(Vvar__3__M1__9436,Vvar__1__N2__9434)
& Vvar__0___24Anonymous__9416 = cLambda_2eTerms_2eApp___24a2(Vvar__3__M1__9436,Vvar__0__M2__9433) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Residuals.residuals',axiom,
! [Vvar__0___24Anonymous__306,Vvar__1___24Anonymous__307,Vvar__2___24Anonymous__308] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0___24Anonymous__306)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__1___24Anonymous__307)
=> ( cLambda_2eRedexes_2eredexes___24t(Vvar__2___24Anonymous__308)
=> ( cLambda_2eResiduals_2eresiduals___24a3(Vvar__0___24Anonymous__306,Vvar__1___24Anonymous__307,Vvar__2___24Anonymous__308)
=> ( ? [Vvar__0__n__310] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__310)
& Vvar__2___24Anonymous__308 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__310)
& Vvar__1___24Anonymous__307 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__310)
& Vvar__0___24Anonymous__306 = cLambda_2eRedexes_2eVar___24a1(Vvar__0__n__310) )
| ? [Vvar__0__U__311] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U__311)
& ? [Vvar__1__V__312] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V__312)
& ? [Vvar__2__W__313] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W__313)
& cLambda_2eResiduals_2eresiduals___24a3(Vvar__0__U__311,Vvar__1__V__312,Vvar__2__W__313)
& Vvar__2___24Anonymous__308 = cLambda_2eRedexes_2eFun___24a1(Vvar__2__W__313)
& Vvar__1___24Anonymous__307 = cLambda_2eRedexes_2eFun___24a1(Vvar__1__V__312)
& Vvar__0___24Anonymous__306 = cLambda_2eRedexes_2eFun___24a1(Vvar__0__U__311) ) ) )
| ? [Vvar__0__U1__315] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__315)
& ? [Vvar__1__V1__316] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__316)
& ? [Vvar__2__W1__317] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W1__317)
& cLambda_2eResiduals_2eresiduals___24a3(Vvar__0__U1__315,Vvar__1__V1__316,Vvar__2__W1__317)
& ? [Vvar__4__U2__319] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__U2__319)
& ? [Vvar__5__V2__320] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__5__V2__320)
& ? [Vvar__6__W2__321] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__6__W2__321)
& cLambda_2eResiduals_2eresiduals___24a3(Vvar__4__U2__319,Vvar__5__V2__320,Vvar__6__W2__321)
& ? [Vvar__8__b__323] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__8__b__323)
& Vvar__2___24Anonymous__308 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b__323,Vvar__2__W1__317,Vvar__6__W2__321)
& Vvar__1___24Anonymous__307 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,Vvar__1__V1__316,Vvar__5__V2__320)
& Vvar__0___24Anonymous__306 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b__323,Vvar__0__U1__315,Vvar__4__U2__319) ) ) ) ) ) ) )
| ? [Vvar__0__U1__324] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__0__U1__324)
& ? [Vvar__1__V1__325] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__1__V1__325)
& ? [Vvar__2__W1__326] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__2__W1__326)
& cLambda_2eResiduals_2eresiduals___24a3(Vvar__0__U1__324,Vvar__1__V1__325,Vvar__2__W1__326)
& ? [Vvar__4__U2__328] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__4__U2__328)
& ? [Vvar__5__V2__329] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__5__V2__329)
& ? [Vvar__6__W2__330] :
( cLambda_2eRedexes_2eredexes___24t(Vvar__6__W2__330)
& cLambda_2eResiduals_2eresiduals___24a3(Vvar__4__U2__328,Vvar__5__V2__329,Vvar__6__W2__330)
& ? [Vvar__8__b__332] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__8__b__332)
& Vvar__2___24Anonymous__308 = c_24__case__Lambda_2eRedexes_2eredexes_24766___24a5(Vvar__0___24Anonymous__306,Vvar__1___24Anonymous__307,Vvar__2___24Anonymous__308,Vvar__2__W1__326,Vvar__6__W2__330)
& Vvar__1___24Anonymous__307 = cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(Vvar__1__V1__325),Vvar__5__V2__329)
& Vvar__0___24Anonymous__306 = cLambda_2eRedexes_2eAp___24a3(Vvar__8__b__332,cLambda_2eRedexes_2eFun___24a1(Vvar__0__U1__324),Vvar__4__U2__328) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Lambda.Terms.lambda',axiom,
! [VX17009] :
( cLambda_2eTerms_2elambda___24t(VX17009)
=> ( ? [Vvar__0___24Anonymous__17010] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17010)
& VX17009 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__17010) )
| ? [Vvar__0___24Anonymous__17011] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__17011)
& VX17009 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__17011) )
| ? [Vvar__0___24Anonymous__17012] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__17012)
& ? [Vvar__1___24Anonymous__17013] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__17013)
& VX17009 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__17012,Vvar__1___24Anonymous__17013) ) ) ) ) ).
fof('$_lam_10218',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__10218___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_10226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__10226___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('$_lam_10234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__10234___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_10242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__10242___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('$_lam_1129',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1129___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2esumor___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1130___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_1133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__1133___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1134___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cLambda_2eTest_2ele__lt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_1137',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__1137___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2einright___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1138___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_31823',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__31823___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_31845',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__31845___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_31926',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__31926___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31927] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31927)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31927)
& c_24__lam__31926___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__31927) ) ) ) ).
fof('$_lam_31933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__31933___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31934] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31934)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31934)
& c_24__lam__31933___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__31934) ) ) ) ).
fof('$_lam_31937',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__31937___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31938] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31938)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31938)
& c_24__lam__31937___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_prop_1091',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1091___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1092',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1092___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1093',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1093___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1094',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1094___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1095',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1095___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1096',axiom,
! [V1__i,V2__k] :
( p(c_24__prop__1096___24a2(V1__i,V2__k))
<=> V2__k = V1__i ) ).
fof('$_prop_1130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1130___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_1134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1134___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_1138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1138___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_1142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1142___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_22828',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__S__22806,Vvar__1__x__22807,Vvar__2__y__22808] :
( p(c_24__prop__22828___24a4(Vvar__0___24Anonymous__22804,Vvar__0__S__22806,Vvar__1__x__22807,Vvar__2__y__22808))
<=> Vvar__1__x__22807 = Vvar__2__y__22808 ) ).
fof('$_prop_22829',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__x__22809,Vvar__1__y__22810] :
( p(c_24__prop__22829___24a3(Vvar__0___24Anonymous__22804,Vvar__0__x__22809,Vvar__1__y__22810))
<=> Vvar__0__x__22809 = Vvar__1__y__22810 ) ).
fof('$_prop_22830',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__x__22811,Vvar__1__s__22812] :
( p(c_24__prop__22830___24a3(Vvar__0___24Anonymous__22804,Vvar__0__x__22811,Vvar__1__s__22812))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__22811,Vvar__1__s__22812) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_22831',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__P__22813,Vvar__1__Q__22814] :
( p(c_24__prop__22831___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22813,Vvar__1__Q__22814))
<=> ( p(Vvar__0__P__22813)
& p(Vvar__1__Q__22814) ) ) ).
fof('$_prop_22832',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__P__22817,Vvar__1__Q__22818] :
( p(c_24__prop__22832___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22817,Vvar__1__Q__22818))
<=> ( p(Vvar__0__P__22817)
| p(Vvar__1__Q__22818) ) ) ).
fof('$_prop_22833',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__P__22821,Vvar__1__Q__22822] :
( p(c_24__prop__22833___24a3(Vvar__0___24Anonymous__22804,Vvar__0__P__22821,Vvar__1__Q__22822))
<=> ( p(Vvar__0__P__22821)
=> p(Vvar__1__Q__22822) ) ) ).
fof('$_prop_22834',axiom,
! [Vvar__0___24Anonymous__22804,Vvar__0__P__22826] :
( p(c_24__prop__22834___24a2(Vvar__0___24Anonymous__22804,Vvar__0__P__22826))
<=> ~ p(Vvar__0__P__22826) ) ).
fof('$_prop_22848',axiom,
! [Vvar__0___24Anonymous__22835,Vvar__0__s__22839] :
( p(c_24__prop__22848___24a2(Vvar__0___24Anonymous__22835,Vvar__0__s__22839))
<=> ! [Vvar__1__a__22840] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__22840)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__22840,Vvar__0__s__22839) ) ) ).
fof('$_prop_22849',axiom,
! [Vvar__0___24Anonymous__22835,Vvar__0__s1__22841,Vvar__1__s2__22842] :
( p(c_24__prop__22849___24a3(Vvar__0___24Anonymous__22835,Vvar__0__s1__22841,Vvar__1__s2__22842))
<=> ! [Vvar__2__a__22843] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__22843)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__22843,Vvar__0__s1__22841)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__22843,Vvar__1__s2__22842) ) ) ) ).
fof('$_prop_22850',axiom,
! [Vvar__0___24Anonymous__22835,Vvar__0__s1__22845,Vvar__1__s2__22846] :
( p(c_24__prop__22850___24a3(Vvar__0___24Anonymous__22835,Vvar__0__s1__22845,Vvar__1__s2__22846))
<=> ! [Vvar__2__a__22847] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__22847)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__22847,Vvar__0__s1__22845)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__22847,Vvar__1__s2__22846) ) ) ) ).
fof('$_prop_32024',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__32024___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_type_10075',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10076] :
( c_24__type__10075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10076)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10076,Vv__CANONICAL__6)) ) ) ).
fof('$_type_10104',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10105] :
( c_24__type__10104___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10105)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__10105,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_10141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10142] :
( c_24__type__10141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__10142)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> cProp___24t(happ(happ(happ(Vvar__10142,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).
fof('$_type_10144',axiom,
! [Vv__CANONICAL__0,Vvar__10145] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vvar__10145)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10145,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1016] :
( c_24__type__1015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1016)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1016,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10285',axiom,
! [Vvar__10286] :
( c_24__type__10285___24t(Vvar__10286)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__10286,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_1029',axiom,
! [Vvar__1030] :
( c_24__type__1029___24t(Vvar__1030)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1030,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1052] :
( c_24__type__1051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1052)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1052,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10529',axiom,
! [Vvar__10530] :
( c_24__type__10529___24t(Vvar__10530)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6146___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__10530,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1067',axiom,
! [Vvar__1068] :
( c_24__type__1067___24t(Vvar__1068)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cLambda_2eRedexes_2eredexes___24t(happ(happ(happ(Vvar__1068,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1070',axiom,
! [Vvar__1071] :
( c_24__type__1070___24t(Vvar__1071)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> cLambda_2eRedexes_2eredexes___24t(happ(happ(Vvar__1071,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10778',axiom,
! [Vvar__10779] :
( c_24__type__10778___24t(Vvar__10779)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__10779,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10781',axiom,
! [Vvar__10782] :
( c_24__type__10781___24t(Vvar__10782)
<=> ! [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__10782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10786',axiom,
! [Vvar__10787] :
( c_24__type__10786___24t(Vvar__10787)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__10787,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10792',axiom,
! [Vvar__10793] :
( c_24__type__10792___24t(Vvar__10793)
<=> ! [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__10793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1112',axiom,
! [Vvar__1113] :
( c_24__type__1112___24t(Vvar__1113)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cLambda_2eRedexes_2eredexes___24t(happ(happ(happ(Vvar__1113,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1125',axiom,
! [Vvar__1126] :
( c_24__type__1125___24t(Vvar__1126)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__1126,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1140',axiom,
! [Vvar__1141] :
( c_24__type__1140___24t(Vvar__1141)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1142___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__1141,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1147',axiom,
! [Vvar__1148] :
( c_24__type__1147___24t(Vvar__1148)
<=> ! [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__1148,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1166',axiom,
! [Vv__CANONICAL__0,Vvar__1167] :
( c_24__type__1166___24t(Vv__CANONICAL__0,Vvar__1167)
<=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1167,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1209',axiom,
! [Vvar__1210] :
( c_24__type__1209___24t(Vvar__1210)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1211___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1219___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1236___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__1210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1211',axiom,
! [Vvar__1212] :
( c_24__type__1211___24t(Vvar__1212)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1212,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1214',axiom,
! [Vv__CANONICAL__0,Vvar__1215] :
( c_24__type__1214___24t(Vv__CANONICAL__0,Vvar__1215)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1215,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cLambda_2eRedexes_2eVar___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_1219',axiom,
! [Vv__CANONICAL__0,Vvar__1220] :
( c_24__type__1219___24t(Vv__CANONICAL__0,Vvar__1220)
<=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__1220,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cLambda_2eRedexes_2eFun___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_123',axiom,
! [Vvar__124] :
( c_24__type__123___24t(Vvar__124)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__124,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1236',axiom,
! [Vv__CANONICAL__0,Vvar__1237] :
( c_24__type__1236___24t(Vv__CANONICAL__0,Vvar__1237)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> ! [Vv__CANONICAL__4] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__0,Vv__CANONICAL__4))
=> t(happ(happ(happ(happ(happ(Vvar__1237,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__0,cLambda_2eRedexes_2eAp___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ) ) ) ) ) ).
fof('$_type_12392',axiom,
! [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__12393] :
( c_24__type__12392___24t(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__12393)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12393,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12456] :
( c_24__type__12455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12456)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12456,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12518',axiom,
! [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__12519] :
( c_24__type__12518___24t(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__12519)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12519,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12573] :
( c_24__type__12572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12573)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__12573,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_12635',axiom,
! [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__12636] :
( c_24__type__12635___24t(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__12636)
<=> ! [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__12636,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_12823',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12824] :
( c_24__type__12823___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12824)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12824,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12847] :
( c_24__type__12846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12847)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12847,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12870] :
( c_24__type__12869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12870)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12870,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_12892',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12893] :
( c_24__type__12892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12893)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12893,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12911] :
( c_24__type__12910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12911)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__12911,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_12936',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12937] :
( c_24__type__12936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12937)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12937,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12955] :
( c_24__type__12954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12955)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__12955,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_13064',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13065] :
( c_24__type__13064___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13065)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13065,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13094',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13095] :
( c_24__type__13094___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13095)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13095,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13118',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13119] :
( c_24__type__13118___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13119)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13119,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13149] :
( c_24__type__13148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13149)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13149,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_13178',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13179] :
( c_24__type__13178___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13179)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13179,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13203] :
( c_24__type__13202___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13203)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13203,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13235',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13236] :
( c_24__type__13235___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13236)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13236,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13260] :
( c_24__type__13259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13260)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13260,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13286',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13287] :
( c_24__type__13286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13287)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13287,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13685',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13686] :
( c_24__type__13685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__13686)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13686,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1378',axiom,
! [Vvar__1379] :
( c_24__type__1378___24t(Vvar__1379)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1379,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1380',axiom,
! [Vvar__1381] :
( c_24__type__1380___24t(Vvar__1381)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1381,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13899] :
( c_24__type__13898___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13899)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13899,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1402',axiom,
! [Vvar__1403] :
( c_24__type__1402___24t(Vvar__1403)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1403,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1407',axiom,
! [Vv__CANONICAL__0,Vvar__1408] :
( c_24__type__1407___24t(Vv__CANONICAL__0,Vvar__1408)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1408,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_14111',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14112] :
( c_24__type__14111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14112)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__14112,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1412',axiom,
! [Vv__CANONICAL__0,Vvar__1413] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vvar__1413)
<=> ! [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__1413,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_14306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14307] :
( c_24__type__14306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14307)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__14307,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_14519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14520] :
( c_24__type__14519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14520)
<=> ! [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__14520,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_14732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14733] :
( c_24__type__14732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__14733)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__14733,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_14945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14946] :
( c_24__type__14945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14946)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__14946,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_15158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__15159] :
( c_24__type__15158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__15159)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__15159,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_15353',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15354] :
( c_24__type__15353___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15354)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__15354,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_15566',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__15567] :
( c_24__type__15566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__15567)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__15567,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_15761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15762] :
( c_24__type__15761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__15762)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__15762,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_15903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15904] :
( c_24__type__15903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15904)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__15904,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_15922',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15923] :
( c_24__type__15922___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15923)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__15923,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_15936',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15937] :
( c_24__type__15936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15937)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__15937,Vv__CANONICAL__4)) ) ) ).
fof('$_type_16091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16092] :
( c_24__type__16091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16092)
<=> ! [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__16092,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_16141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16142] :
( c_24__type__16141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16142)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__16142,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_16191',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16192] :
( c_24__type__16191___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16192)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__16192,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_16233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16234] :
( c_24__type__16233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16234)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__16234,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_16283',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16284] :
( c_24__type__16283___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16284)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__16284,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_16359',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16360] :
( c_24__type__16359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16360)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__16360,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_16468',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16469] :
( c_24__type__16468___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16469)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16469,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16513] :
( c_24__type__16512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16513)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16513,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_16548',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16549] :
( c_24__type__16548___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16549)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__16549,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_16592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16593] :
( c_24__type__16592___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__16593)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__16593,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16612',axiom,
! [Vvar__16613] :
( c_24__type__16612___24t(Vvar__16613)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16613,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16698',axiom,
! [Vvar__16699] :
( c_24__type__16698___24t(Vvar__16699)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1412___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__8822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__16699,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_16777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16778] :
( c_24__type__16777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16778)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__16778,Vv__CANONICAL__2)) ) ) ).
fof('$_type_16781',axiom,
! [Vvar__16782] :
( c_24__type__16781___24t(Vvar__16782)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__16782,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16799',axiom,
! [Vvar__16800] :
( c_24__type__16799___24t(Vvar__16800)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___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__16800,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_16816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16817] :
( c_24__type__16816___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16817)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__16817,Vv__CANONICAL__2)) ) ) ).
fof('$_type_16820',axiom,
! [Vvar__16821] :
( c_24__type__16820___24t(Vvar__16821)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__16821,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16838',axiom,
! [Vvar__16839] :
( c_24__type__16838___24t(Vvar__16839)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__16839,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_16851',axiom,
! [Vvar__16852] :
( c_24__type__16851___24t(Vvar__16852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__16852,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17030',axiom,
! [Vvar__17031] :
( c_24__type__17030___24t(Vvar__17031)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> cLambda_2eTerms_2elambda___24t(happ(Vvar__17031,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17068] :
( c_24__type__17067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17068)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__17068,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_17278',axiom,
! [Vvar__17279] :
( c_24__type__17278___24t(Vvar__17279)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__17279,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17360',axiom,
! [Vvar__17361] :
( c_24__type__17360___24t(Vvar__17361)
<=> ! [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__17361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17377',axiom,
! [Vvar__17378] :
( c_24__type__17377___24t(Vvar__17378)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__17378,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17432',axiom,
! [Vvar__17433] :
( c_24__type__17432___24t(Vvar__17433)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__17433,Vv__CANONICAL__0)) ) ) ).
fof('$_type_175',axiom,
! [Vvar__176] :
( c_24__type__175___24t(Vvar__176)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> cLambda_2eRedexes_2eredexes___24t(happ(happ(Vvar__176,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17542',axiom,
! [Vvar__17543] :
( c_24__type__17542___24t(Vvar__17543)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__17377___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__17377___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__17543,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17580',axiom,
! [Vvar__17581] :
( c_24__type__17580___24t(Vvar__17581)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__17581,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17588',axiom,
! [Vvar__17589] :
( c_24__type__17588___24t(Vvar__17589)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__17589,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17812',axiom,
! [Vvar__17813] :
( c_24__type__17812___24t(Vvar__17813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__17813,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17845',axiom,
! [Vvar__17846] :
( c_24__type__17845___24t(Vvar__17846)
<=> ! [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__17846,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17873',axiom,
! [Vvar__17874] :
( c_24__type__17873___24t(Vvar__17874)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__17874,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17877',axiom,
! [Vvar__17878] :
( c_24__type__17877___24t(Vvar__17878)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__17878,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17880',axiom,
! [Vvar__17881] :
( c_24__type__17880___24t(Vvar__17881)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__17881,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17883',axiom,
! [Vvar__17884] :
( c_24__type__17883___24t(Vvar__17884)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__17884,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17887',axiom,
! [Vvar__17888] :
( c_24__type__17887___24t(Vvar__17888)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__17888,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18065',axiom,
! [Vvar__18066] :
( c_24__type__18065___24t(Vvar__18066)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__18066,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1858] :
( c_24__type__1857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1858)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1858,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18589',axiom,
! [Vvar__18590] :
( c_24__type__18589___24t(Vvar__18590)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__18590,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18656',axiom,
! [Vv__CANONICAL__0,Vvar__18657] :
( c_24__type__18656___24t(Vv__CANONICAL__0,Vvar__18657)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__18657,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_18701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18702] :
( c_24__type__18701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18702)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18702,Vv__CANONICAL__6)) ) ) ).
fof('$_type_18729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18730] :
( c_24__type__18729___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__18730)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__18730,Vv__CANONICAL__6)) ) ) ).
fof('$_type_18933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__18934] :
( c_24__type__18933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__18934)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18934,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19026',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19027] :
( c_24__type__19026___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19027)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19027,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19119',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__19120] :
( c_24__type__19119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__19120)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19120,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19202] :
( c_24__type__19201___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19202)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__19202,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_19294',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__19295] :
( c_24__type__19294___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__19295)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19295,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19377] :
( c_24__type__19376___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__19377)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__19377,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_19469',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__19470] :
( c_24__type__19469___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__19470)
<=> ! [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__19470,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1959] :
( c_24__type__1958___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1959)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1959,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19623',axiom,
! [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__19624] :
( c_24__type__19623___24t(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__19624)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19624,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19686',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__19687] :
( c_24__type__19686___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__19687)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19687,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19749',axiom,
! [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__19750] :
( c_24__type__19749___24t(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__19750)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19750,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__19804] :
( c_24__type__19803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__19804)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__19804,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_19866',axiom,
! [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__19867] :
( c_24__type__19866___24t(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__19867)
<=> ! [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__19867,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_19897',axiom,
! [Vvar__19898] :
( c_24__type__19897___24t(Vvar__19898)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__19898,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_19989',axiom,
! [Vvar__19990] :
( c_24__type__19989___24t(Vvar__19990)
<=> ! [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__19990,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2',axiom,
! [Vvar__3] :
( c_24__type__2___24t(Vvar__3)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20185',axiom,
! [Vvar__20186] :
( c_24__type__20185___24t(Vvar__20186)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2506___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__20186,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_20358',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20359] :
( c_24__type__20358___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20359)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20359,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20397',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20398] :
( c_24__type__20397___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20398)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20398,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20436',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20437] :
( c_24__type__20436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__20437)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20437,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_2059',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__2060] :
( c_24__type__2059___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__2060)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2060,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20679] :
( c_24__type__20678___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20679)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20679,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20741',axiom,
! [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__20742] :
( c_24__type__20741___24t(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__20742)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20742,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20804',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20805] :
( c_24__type__20804___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20805)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20805,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20858',axiom,
! [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__20859] :
( c_24__type__20858___24t(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__20859)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__20859,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_20921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20922] :
( c_24__type__20921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__20922)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20922,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_21194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21195] :
( c_24__type__21194___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21195)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21195,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21320] :
( c_24__type__21319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21320)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21320,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21445] :
( c_24__type__21444___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21445)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21445,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_2149',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2150] :
( c_24__type__2149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2150)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__2150,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_21569',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21570] :
( c_24__type__21569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21570)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__21570,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_21694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21695] :
( c_24__type__21694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21695)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__21695,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_21819',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21820] :
( c_24__type__21819___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21820)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21820,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_21930',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21931] :
( c_24__type__21930___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__21931)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__21931,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_22172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22173] :
( c_24__type__22172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22173)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22173,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22181] :
( c_24__type__22180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22181)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22181,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22188',axiom,
! [Vvar__22189] :
( c_24__type__22188___24t(Vvar__22189)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__22189,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22228',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22229] :
( c_24__type__22228___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22229)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22229,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22236',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22237] :
( c_24__type__22236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22237)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22237,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22244',axiom,
! [Vvar__22245] :
( c_24__type__22244___24t(Vvar__22245)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__22245,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22314',axiom,
! [Vvar__22315] :
( c_24__type__22314___24t(Vvar__22315)
<=> ! [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__22315,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2250',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2251] :
( c_24__type__2250___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2251)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2251,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_22864',axiom,
! [Vvar__22865] :
( c_24__type__22864___24t(Vvar__22865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1407___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__22865,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_22924',axiom,
! [Vvar__22925] :
( c_24__type__22924___24t(Vvar__22925)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22925,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22963',axiom,
! [Vvar__22964] :
( c_24__type__22963___24t(Vvar__22964)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__22964,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_22982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22983] :
( c_24__type__22982___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22983)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__22983,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23003',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23004] :
( c_24__type__23003___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23004)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__23004,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23008',axiom,
! [Vvar__23009] :
( c_24__type__23008___24t(Vvar__23009)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__23009,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23044] :
( c_24__type__23043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23044)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__23044,Vv__CANONICAL__5)) ) ) ).
fof('$_type_23051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23052] :
( c_24__type__23051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23052)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__23052,Vv__CANONICAL__5)) ) ) ).
fof('$_type_23056',axiom,
! [Vvar__23057] :
( c_24__type__23056___24t(Vvar__23057)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__23057,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23058',axiom,
! [Vvar__23059] :
( c_24__type__23058___24t(Vvar__23059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__23059,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23065',axiom,
! [Vv__CANONICAL__0,Vvar__23066] :
( c_24__type__23065___24t(Vv__CANONICAL__0,Vvar__23066)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__23066,Vv__CANONICAL__1)) ) ) ).
fof('$_type_23078',axiom,
! [Vvar__23079] :
( c_24__type__23078___24t(Vvar__23079)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__8417___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__23083___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__23079,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23083',axiom,
! [Vv__CANONICAL__0,Vvar__23084] :
( c_24__type__23083___24t(Vv__CANONICAL__0,Vvar__23084)
<=> ! [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__23084,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_23085',axiom,
! [Vvar__23086] :
( c_24__type__23085___24t(Vvar__23086)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23086,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23092',axiom,
! [Vvar__23093] :
( c_24__type__23092___24t(Vvar__23093)
<=> ! [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__23093,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23097',axiom,
! [Vvar__23098] :
( c_24__type__23097___24t(Vvar__23098)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__23098,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23109',axiom,
! [Vvar__23110] :
( c_24__type__23109___24t(Vvar__23110)
<=> ! [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__23110,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_23134',axiom,
! [Vvar__23135] :
( c_24__type__23134___24t(Vvar__23135)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__23135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23185',axiom,
! [Vvar__23186] :
( c_24__type__23185___24t(Vvar__23186)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__23186,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23198',axiom,
! [Vvar__23199] :
( c_24__type__23198___24t(Vvar__23199)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__23199,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23201',axiom,
! [Vvar__23202] :
( c_24__type__23201___24t(Vvar__23202)
<=> ! [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__23202,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23204',axiom,
! [Vvar__23205] :
( c_24__type__23204___24t(Vvar__23205)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__23205,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23209',axiom,
! [Vvar__23210] :
( c_24__type__23209___24t(Vvar__23210)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__23210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23217',axiom,
! [Vvar__23218] :
( c_24__type__23217___24t(Vvar__23218)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__23218,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23220',axiom,
! [Vvar__23221] :
( c_24__type__23220___24t(Vvar__23221)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__23221,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23237',axiom,
! [Vvar__23238] :
( c_24__type__23237___24t(Vvar__23238)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__23238,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_23242',axiom,
! [Vv__CANONICAL__0,Vvar__23243] :
( c_24__type__23242___24t(Vv__CANONICAL__0,Vvar__23243)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__23243,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_23253',axiom,
! [Vvar__23254] :
( c_24__type__23253___24t(Vvar__23254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__23254,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23313',axiom,
! [Vvar__23314] :
( c_24__type__23313___24t(Vvar__23314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(happ(happ(Vvar__23314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23324',axiom,
! [Vvar__23325] :
( c_24__type__23324___24t(Vvar__23325)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__23325,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_23355',axiom,
! [Vvar__23356] :
( c_24__type__23355___24t(Vvar__23356)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__23356,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_23404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23405] :
( c_24__type__23404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23405)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23405,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23428',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23429] :
( c_24__type__23428___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23429)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23429,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23475',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23476] :
( c_24__type__23475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23476)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23476,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_2351',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__2352] :
( c_24__type__2351___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__2352)
<=> ! [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__2352,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_23510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23511] :
( c_24__type__23510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23511)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23511,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23512',axiom,
! [Vvar__23513] :
( c_24__type__23512___24t(Vvar__23513)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23513,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23528',axiom,
! [Vvar__23529] :
( c_24__type__23528___24t(Vvar__23529)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__23529,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23541',axiom,
! [Vvar__23542] :
( c_24__type__23541___24t(Vvar__23542)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__23542,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23560',axiom,
! [Vvar__23561] :
( c_24__type__23560___24t(Vvar__23561)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__23561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23572',axiom,
! [Vvar__23573] :
( c_24__type__23572___24t(Vvar__23573)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23541___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23541___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23573,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_237',axiom,
! [Vvar__238] :
( c_24__type__237___24t(Vvar__238)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__238,Vv__CANONICAL__0)) ) ) ).
fof('$_type_240',axiom,
! [Vvar__241] :
( c_24__type__240___24t(Vvar__241)
<=> ! [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__241,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24162',axiom,
! [Vvar__24163] :
( c_24__type__24162___24t(Vvar__24163)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__24163,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24166',axiom,
! [Vvar__24167] :
( c_24__type__24166___24t(Vvar__24167)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24167,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_243',axiom,
! [Vvar__244] :
( c_24__type__243___24t(Vvar__244)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__244,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2452',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__2453] :
( c_24__type__2452___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__2453)
<=> ! [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__2453,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_24771',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24772] :
( c_24__type__24771___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24772)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24772,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_24796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24797] :
( c_24__type__24796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24797)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24797,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_24868',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24869] :
( c_24__type__24868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24869)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24869,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_24893',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24894] :
( c_24__type__24893___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24894)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24894,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_24935',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24936] :
( c_24__type__24935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24936)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24936,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24987] :
( c_24__type__24986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24987)
<=> ! [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__24987,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_2506',axiom,
! [Vv__CANONICAL__0,Vvar__2507] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vvar__2507)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2507,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25084',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25085] :
( c_24__type__25084___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25085)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25085,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_26040',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26041] :
( c_24__type__26040___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26041)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26041,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26386',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26387] :
( c_24__type__26386___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26387)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26387,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26733] :
( c_24__type__26732___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26733)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26733,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2682',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2683] :
( c_24__type__2682___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2683)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2683,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_27055',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27056] :
( c_24__type__27055___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27056)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__27056,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_2708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2709] :
( c_24__type__2708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2709)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__2709,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_2722',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2723] :
( c_24__type__2722___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2723)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2723,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_2729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2730] :
( c_24__type__2729___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2730)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2730,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_27401',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27402] :
( c_24__type__27401___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27402)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27402,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_27747',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27748] :
( c_24__type__27747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27748)
<=> ! [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__27748,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_28093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28094] :
( c_24__type__28093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28094)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__28094,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_2816',axiom,
! [Vvar__2817] :
( c_24__type__2816___24t(Vvar__2817)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2817,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2842',axiom,
! [Vvar__2843] :
( c_24__type__2842___24t(Vvar__2843)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__2843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_28439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__28440] :
( c_24__type__28439___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__28440)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__28440,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_2850',axiom,
! [Vvar__2851] :
( c_24__type__2850___24t(Vvar__2851)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__2851,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2855',axiom,
! [Vvar__2856] :
( c_24__type__2855___24t(Vvar__2856)
<=> ! [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__2856,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_28785',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28786] :
( c_24__type__28785___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28786)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__28786,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_29108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29109] :
( c_24__type__29108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29109)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__29109,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_29454',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29455] :
( c_24__type__29454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29455)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__29455,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_2954',axiom,
! [Vv__CANONICAL__0,Vvar__2955] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vvar__2955)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2955,Vv__CANONICAL__1)) ) ) ).
fof('$_type_29800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29801] :
( c_24__type__29800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29801)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__29801,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_30123',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30124] :
( c_24__type__30123___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30124)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__30124,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_30446',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30447] :
( c_24__type__30446___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30447)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__30447,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_30792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30793] :
( c_24__type__30792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30793)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__30793,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30809',axiom,
! [Vvar__30810] :
( c_24__type__30809___24t(Vvar__30810)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__30810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30822',axiom,
! [Vvar__30823] :
( c_24__type__30822___24t(Vvar__30823)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__30823,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30827',axiom,
! [Vvar__30828] :
( c_24__type__30827___24t(Vvar__30828)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__30828,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30835',axiom,
! [Vvar__30836] :
( c_24__type__30835___24t(Vvar__30836)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__30836,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30838',axiom,
! [Vvar__30839] :
( c_24__type__30838___24t(Vvar__30839)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__30839,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30841',axiom,
! [Vvar__30842] :
( c_24__type__30841___24t(Vvar__30842)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__30842,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30862',axiom,
! [Vvar__30863] :
( c_24__type__30862___24t(Vvar__30863)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__30863,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_30969',axiom,
! [Vvar__30970] :
( c_24__type__30969___24t(Vvar__30970)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__30970,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30975',axiom,
! [Vvar__30976] :
( c_24__type__30975___24t(Vvar__30976)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30976,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31017',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31018] :
( c_24__type__31017___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31018)
<=> ! [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__31018,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_31052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31053] :
( c_24__type__31052___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31053)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31053,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_31092',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31093] :
( c_24__type__31092___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31093)
<=> ! [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__31093,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_31125',axiom,
! [Vvar__31126] :
( c_24__type__31125___24t(Vvar__31126)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1412___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__31135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__8822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__31126,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_31135',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31136] :
( c_24__type__31135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31136)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31136,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_3119',axiom,
! [Vvar__3120] :
( c_24__type__3119___24t(Vvar__3120)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31232',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31233] :
( c_24__type__31232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31233)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31233,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_31271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31272] :
( c_24__type__31271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31272)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31272,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_31306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31307] :
( c_24__type__31306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31307)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31307,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_31341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31342] :
( c_24__type__31341___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31342)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31342,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_31357',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31358] :
( c_24__type__31357___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31358)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31358,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31363',axiom,
! [Vvar__31364] :
( c_24__type__31363___24t(Vvar__31364)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__31364,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_31380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31381] :
( c_24__type__31380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31381)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__31381,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31386',axiom,
! [Vvar__31387] :
( c_24__type__31386___24t(Vvar__31387)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__31387,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_31392',axiom,
! [Vvar__31393] :
( c_24__type__31392___24t(Vvar__31393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__31393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31397',axiom,
! [Vvar__31398] :
( c_24__type__31397___24t(Vvar__31398)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__31398,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_31400',axiom,
! [Vvar__31401] :
( c_24__type__31400___24t(Vvar__31401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__31401,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31409',axiom,
! [Vvar__31410] :
( c_24__type__31409___24t(Vvar__31410)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__31410,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31427',axiom,
! [Vvar__31428] :
( c_24__type__31427___24t(Vvar__31428)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__31428,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_31444',axiom,
! [Vvar__31445] :
( c_24__type__31444___24t(Vvar__31445)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__31445,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_31453',axiom,
! [Vvar__31454] :
( c_24__type__31453___24t(Vvar__31454)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cLambda_2eTerms_2elambda___24t(happ(Vvar__31454,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31456',axiom,
! [Vvar__31457] :
( c_24__type__31456___24t(Vvar__31457)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> cLambda_2eTerms_2elambda___24t(happ(happ(Vvar__31457,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31458',axiom,
! [Vvar__31459] :
( c_24__type__31458___24t(Vvar__31459)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__31459,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31489] :
( c_24__type__31488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31489)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31489,Vv__CANONICAL__4)) ) ) ).
fof('$_type_31554',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31555] :
( c_24__type__31554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31555)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31555,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_3161',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3162] :
( c_24__type__3161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__3162)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3162,Vv__CANONICAL__4)) ) ) ).
fof('$_type_31610',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31611] :
( c_24__type__31610___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31611)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31611,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_31616',axiom,
! [Vvar__31617] :
( c_24__type__31616___24t(Vvar__31617)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31617,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31628',axiom,
! [Vvar__31629] :
( c_24__type__31628___24t(Vvar__31629)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__31631___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__31629,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31631',axiom,
! [Vv__CANONICAL__0,Vvar__31632] :
( c_24__type__31631___24t(Vv__CANONICAL__0,Vvar__31632)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__31632,Vv__CANONICAL__1)) ) ) ).
fof('$_type_31756',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31757] :
( c_24__type__31756___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31757)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31757,Vv__CANONICAL__4)) ) ) ).
fof('$_type_31765',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31766] :
( c_24__type__31765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31766)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31766,Vv__CANONICAL__4)) ) ) ).
fof('$_type_31797',axiom,
! [Vvar__31798] :
( c_24__type__31797___24t(Vvar__31798)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__31798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31818',axiom,
! [Vvar__31819] :
( c_24__type__31818___24t(Vvar__31819)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__31819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31835',axiom,
! [Vvar__31836] :
( c_24__type__31835___24t(Vvar__31836)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__31840___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__31836,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_31840',axiom,
! [Vv__CANONICAL__0,Vvar__31841] :
( c_24__type__31840___24t(Vv__CANONICAL__0,Vvar__31841)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31841,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31857',axiom,
! [Vvar__31858] :
( c_24__type__31857___24t(Vvar__31858)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__31862___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__31858,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_31862',axiom,
! [Vv__CANONICAL__0,Vvar__31863] :
( c_24__type__31862___24t(Vv__CANONICAL__0,Vvar__31863)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31863,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31868',axiom,
! [Vvar__31869] :
( c_24__type__31868___24t(Vvar__31869)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__31869,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31884',axiom,
! [Vvar__31885] :
( c_24__type__31884___24t(Vvar__31885)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__31885,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31890',axiom,
! [Vvar__31891] :
( c_24__type__31890___24t(Vvar__31891)
<=> ! [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__31891,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31910',axiom,
! [Vvar__31911] :
( c_24__type__31910___24t(Vvar__31911)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31911,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31940',axiom,
! [Vvar__31941] :
( c_24__type__31940___24t(Vvar__31941)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31941,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31954',axiom,
! [Vvar__31955] :
( c_24__type__31954___24t(Vvar__31955)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__31955,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_31964',axiom,
! [Vvar__31965] :
( c_24__type__31964___24t(Vvar__31965)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__31965,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31986',axiom,
! [Vvar__31987] :
( c_24__type__31986___24t(Vvar__31987)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__31987,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32017',axiom,
! [Vvar__32018] :
( c_24__type__32017___24t(Vvar__32018)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__32018,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32034',axiom,
! [Vvar__32035] :
( c_24__type__32034___24t(Vvar__32035)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__18065___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__18065___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__32035,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35',axiom,
! [Vvar__36] :
( c_24__type__35___24t(Vvar__36)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cLambda_2eRedexes_2eredexes___24t(happ(Vvar__36,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37',axiom,
! [Vvar__38] :
( c_24__type__37___24t(Vvar__38)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> cLambda_2eRedexes_2eredexes___24t(happ(Vvar__38,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3856',axiom,
! [Vvar__3857] :
( c_24__type__3856___24t(Vvar__3857)
<=> ! [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__3857,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3863',axiom,
! [Vvar__3864] :
( c_24__type__3863___24t(Vvar__3864)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__3864,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3872',axiom,
! [Vvar__3873] :
( c_24__type__3872___24t(Vvar__3873)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3876',axiom,
! [Vvar__3877] :
( c_24__type__3876___24t(Vvar__3877)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3877,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3898',axiom,
! [Vvar__3899] :
( c_24__type__3898___24t(Vvar__3899)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__3899,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3920',axiom,
! [Vvar__3921] :
( c_24__type__3920___24t(Vvar__3921)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3921,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3951',axiom,
! [Vvar__3952] :
( c_24__type__3951___24t(Vvar__3952)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3952,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3955',axiom,
! [Vvar__3956] :
( c_24__type__3955___24t(Vvar__3956)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3956,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3996',axiom,
! [Vvar__3997] :
( c_24__type__3996___24t(Vvar__3997)
<=> ! [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__3997,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3999',axiom,
! [Vvar__4000] :
( c_24__type__3999___24t(Vvar__4000)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4000,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4029',axiom,
! [Vvar__4030] :
( c_24__type__4029___24t(Vvar__4030)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__4030,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42',axiom,
! [Vvar__43] :
( c_24__type__42___24t(Vvar__43)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__2)
=> cLambda_2eRedexes_2eredexes___24t(happ(happ(happ(Vvar__43,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4682',axiom,
! [Vvar__4683] :
( c_24__type__4682___24t(Vvar__4683)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4683,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4701',axiom,
! [Vvar__4702] :
( c_24__type__4701___24t(Vvar__4702)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__4702,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4703',axiom,
! [Vvar__4704] :
( c_24__type__4703___24t(Vvar__4704)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__4704,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4715',axiom,
! [Vvar__4716] :
( c_24__type__4715___24t(Vvar__4716)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4716,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4757',axiom,
! [Vvar__4758] :
( c_24__type__4757___24t(Vvar__4758)
<=> ! [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__4758,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4775',axiom,
! [Vvar__4776] :
( c_24__type__4775___24t(Vvar__4776)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__4776,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_4795',axiom,
! [Vvar__4796] :
( c_24__type__4795___24t(Vvar__4796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__4796,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4800',axiom,
! [Vvar__4801] :
( c_24__type__4800___24t(Vvar__4801)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4801,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4868',axiom,
! [Vvar__4869] :
( c_24__type__4868___24t(Vvar__4869)
<=> ! [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__4869,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4880',axiom,
! [Vvar__4881] :
( c_24__type__4880___24t(Vvar__4881)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4881,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4882',axiom,
! [Vvar__4883] :
( c_24__type__4882___24t(Vvar__4883)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__4883,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4901',axiom,
! [Vvar__4902] :
( c_24__type__4901___24t(Vvar__4902)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4902,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5035',axiom,
! [Vvar__5036] :
( c_24__type__5035___24t(Vvar__5036)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__5036,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5254',axiom,
! [Vvar__5255] :
( c_24__type__5254___24t(Vvar__5255)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__5255,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5467] :
( c_24__type__5466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5467)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5467,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5560] :
( c_24__type__5559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5560)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5560,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5653] :
( c_24__type__5652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5653)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5653,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5734',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5735] :
( c_24__type__5734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5735)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5735,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_5827',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5828] :
( c_24__type__5827___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5828)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5828,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5910] :
( c_24__type__5909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5910)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5910,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6002',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6003] :
( c_24__type__6002___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6003)
<=> ! [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__6003,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_6146',axiom,
! [Vv__CANONICAL__0,Vvar__6147] :
( c_24__type__6146___24t(Vv__CANONICAL__0,Vvar__6147)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6147,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_66',axiom,
! [Vvar__67] :
( c_24__type__66___24t(Vvar__67)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eRedexes_2eredexes___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__67,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7124',axiom,
! [Vvar__7125] :
( c_24__type__7124___24t(Vvar__7125)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__7125,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7127',axiom,
! [Vvar__7128] :
( c_24__type__7127___24t(Vvar__7128)
<=> ! [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__7128,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7132',axiom,
! [Vvar__7133] :
( c_24__type__7132___24t(Vvar__7133)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7133,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7135',axiom,
! [Vvar__7136] :
( c_24__type__7135___24t(Vvar__7136)
<=> ! [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__7136,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8417',axiom,
! [Vvar__8418] :
( c_24__type__8417___24t(Vvar__8418)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8418,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8673',axiom,
! [Vvar__8674] :
( c_24__type__8673___24t(Vvar__8674)
<=> ! [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__8674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8698',axiom,
! [Vvar__8699] :
( c_24__type__8698___24t(Vvar__8699)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__8699,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_8730',axiom,
! [Vvar__8731] :
( c_24__type__8730___24t(Vvar__8731)
<=> ! [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__8731,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8777',axiom,
! [Vvar__8778] :
( c_24__type__8777___24t(Vvar__8778)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8784___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__8778,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8785] :
( c_24__type__8784___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8785)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__8785,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8808',axiom,
! [Vvar__8809] :
( c_24__type__8808___24t(Vvar__8809)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__8809,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8816] :
( c_24__type__8815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8816)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8816,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8822',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8823] :
( c_24__type__8822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8823)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__8823,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_8868',axiom,
! [Vvar__8869] :
( c_24__type__8868___24t(Vvar__8869)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8869,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8876',axiom,
! [Vvar__8877] :
( c_24__type__8876___24t(Vvar__8877)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8877,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8952] :
( c_24__type__8951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8952)
<=> ! [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__8952,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_8970',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8971] :
( c_24__type__8970___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8971)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8971,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_8990',axiom,
! [Vvar__8991] :
( c_24__type__8990___24t(Vvar__8991)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1412___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__8991,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_9112',axiom,
! [Vvar__9113] :
( c_24__type__9112___24t(Vvar__9113)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__9113,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9117',axiom,
! [Vvar__9118] :
( c_24__type__9117___24t(Vvar__9118)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__9118,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9122',axiom,
! [Vvar__9123] :
( c_24__type__9122___24t(Vvar__9123)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__9123,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9167',axiom,
! [Vvar__9168] :
( c_24__type__9167___24t(Vvar__9168)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__9168,Vv__CANONICAL__0)) ) ) ).
fof('$_type_92',axiom,
! [Vvar__93] :
( c_24__type__92___24t(Vvar__93)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__93,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9326',axiom,
! [Vvar__9327] :
( c_24__type__9326___24t(Vvar__9327)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__9327,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9328',axiom,
! [Vvar__9329] :
( c_24__type__9328___24t(Vvar__9329)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__9329,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9331',axiom,
! [Vvar__9332] :
( c_24__type__9331___24t(Vvar__9332)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__9332,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9338',axiom,
! [Vvar__9339] :
( c_24__type__9338___24t(Vvar__9339)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__9339,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9386',axiom,
! [Vvar__9387] :
( c_24__type__9386___24t(Vvar__9387)
<=> ! [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__9387,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9399',axiom,
! [Vvar__9400] :
( c_24__type__9399___24t(Vvar__9400)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__9400,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9407',axiom,
! [Vvar__9408] :
( c_24__type__9407___24t(Vvar__9408)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__9408,Vv__CANONICAL__0)) ) ) ).
fof('$_type_993',axiom,
! [Vvar__994] :
( c_24__type__993___24t(Vvar__994)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__994,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9930',axiom,
! [Vvar__9931] :
( c_24__type__9930___24t(Vvar__9931)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___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__9931,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_9960',axiom,
! [Vvar__9961] :
( c_24__type__9960___24t(Vvar__9961)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__9961,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__23008___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__240___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__31868___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__240___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__240___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__23572___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__240___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__240___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__31857___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__1147___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__31628___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__2___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__92___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__23056___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__18589___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__8417___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__23541___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__17812___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__3951___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__3898___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__17812___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__17812___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__3920___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
c_24__type__23058___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.x1a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).
fof('$_typeof_Coq.Init.Byte.x1b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).
fof('$_typeof_Coq.Init.Byte.x1c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).
fof('$_typeof_Coq.Init.Byte.x1d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).
fof('$_typeof_Coq.Init.Byte.x1e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).
fof('$_typeof_Coq.Init.Byte.x1f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).
fof('$_typeof_Coq.Init.Byte.x20',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).
fof('$_typeof_Coq.Init.Byte.x21',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).
fof('$_typeof_Coq.Init.Byte.x22',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).
fof('$_typeof_Coq.Init.Byte.x23',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).
fof('$_typeof_Coq.Init.Byte.x24',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).
fof('$_typeof_Coq.Init.Byte.x25',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).
fof('$_typeof_Coq.Init.Byte.x26',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).
fof('$_typeof_Coq.Init.Byte.x27',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).
fof('$_typeof_Coq.Init.Byte.x28',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).
fof('$_typeof_Coq.Init.Byte.x29',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).
fof('$_typeof_Coq.Init.Byte.x2a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).
fof('$_typeof_Coq.Init.Byte.x2b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).
fof('$_typeof_Coq.Init.Byte.x2c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).
fof('$_typeof_Coq.Init.Byte.x2d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).
fof('$_typeof_Coq.Init.Byte.x2e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).
fof('$_typeof_Coq.Init.Byte.x2f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).
fof('$_typeof_Coq.Init.Byte.x30',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).
fof('$_typeof_Coq.Init.Byte.x31',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).
fof('$_typeof_Coq.Init.Byte.x32',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).
fof('$_typeof_Coq.Init.Byte.x33',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).
fof('$_typeof_Coq.Init.Byte.x34',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).
fof('$_typeof_Coq.Init.Byte.x35',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).
fof('$_typeof_Coq.Init.Byte.x36',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).
fof('$_typeof_Coq.Init.Byte.x37',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).
fof('$_typeof_Coq.Init.Byte.x38',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).
fof('$_typeof_Coq.Init.Byte.x39',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).
fof('$_typeof_Coq.Init.Byte.x3a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).
fof('$_typeof_Coq.Init.Byte.x3b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).
fof('$_typeof_Coq.Init.Byte.x3c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).
fof('$_typeof_Coq.Init.Byte.x3d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).
fof('$_typeof_Coq.Init.Byte.x3e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).
fof('$_typeof_Coq.Init.Byte.x3f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).
fof('$_typeof_Coq.Init.Byte.x40',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).
fof('$_typeof_Coq.Init.Byte.x41',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).
fof('$_typeof_Coq.Init.Byte.x42',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).
fof('$_typeof_Coq.Init.Byte.x43',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).
fof('$_typeof_Coq.Init.Byte.x44',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).
fof('$_typeof_Coq.Init.Byte.x45',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).
fof('$_typeof_Coq.Init.Byte.x46',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).
fof('$_typeof_Coq.Init.Byte.x47',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).
fof('$_typeof_Coq.Init.Byte.x48',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).
fof('$_typeof_Coq.Init.Byte.x49',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).
fof('$_typeof_Coq.Init.Byte.x4a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).
fof('$_typeof_Coq.Init.Byte.x4b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).
fof('$_typeof_Coq.Init.Byte.x4c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).
fof('$_typeof_Coq.Init.Byte.x4d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).
fof('$_typeof_Coq.Init.Byte.x4e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).
fof('$_typeof_Coq.Init.Byte.x4f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).
fof('$_typeof_Coq.Init.Byte.x50',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).
fof('$_typeof_Coq.Init.Byte.x51',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).
fof('$_typeof_Coq.Init.Byte.x52',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).
fof('$_typeof_Coq.Init.Byte.x53',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).
fof('$_typeof_Coq.Init.Byte.x54',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).
fof('$_typeof_Coq.Init.Byte.x55',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).
fof('$_typeof_Coq.Init.Byte.x56',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).
fof('$_typeof_Coq.Init.Byte.x57',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).
fof('$_typeof_Coq.Init.Byte.x58',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).
fof('$_typeof_Coq.Init.Byte.x59',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).
fof('$_typeof_Coq.Init.Byte.x5a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).
fof('$_typeof_Coq.Init.Byte.x5b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).
fof('$_typeof_Coq.Init.Byte.x5c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).
fof('$_typeof_Coq.Init.Byte.x5d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).
fof('$_typeof_Coq.Init.Byte.x5e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).
fof('$_typeof_Coq.Init.Byte.x5f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).
fof('$_typeof_Coq.Init.Byte.x60',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).
fof('$_typeof_Coq.Init.Byte.x61',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).
fof('$_typeof_Coq.Init.Byte.x62',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).
fof('$_typeof_Coq.Init.Byte.x63',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).
fof('$_typeof_Coq.Init.Byte.x64',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).
fof('$_typeof_Coq.Init.Byte.x65',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).
fof('$_typeof_Coq.Init.Byte.x66',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).
fof('$_typeof_Coq.Init.Byte.x67',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).
fof('$_typeof_Coq.Init.Byte.x68',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).
fof('$_typeof_Coq.Init.Byte.x69',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).
fof('$_typeof_Coq.Init.Byte.x6a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).
fof('$_typeof_Coq.Init.Byte.x6b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).
fof('$_typeof_Coq.Init.Byte.x6c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).
fof('$_typeof_Coq.Init.Byte.x6d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).
fof('$_typeof_Coq.Init.Byte.x6e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).
fof('$_typeof_Coq.Init.Byte.x6f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).
fof('$_typeof_Coq.Init.Byte.x70',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).
fof('$_typeof_Coq.Init.Byte.x71',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).
fof('$_typeof_Coq.Init.Byte.x72',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).
fof('$_typeof_Coq.Init.Byte.x73',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).
fof('$_typeof_Coq.Init.Byte.x74',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).
fof('$_typeof_Coq.Init.Byte.x75',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).
fof('$_typeof_Coq.Init.Byte.x76',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).
fof('$_typeof_Coq.Init.Byte.x77',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).
fof('$_typeof_Coq.Init.Byte.x78',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).
fof('$_typeof_Coq.Init.Byte.x79',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).
fof('$_typeof_Coq.Init.Byte.x7a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).
fof('$_typeof_Coq.Init.Byte.x7b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).
fof('$_typeof_Coq.Init.Byte.x7c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).
fof('$_typeof_Coq.Init.Byte.x7d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).
fof('$_typeof_Coq.Init.Byte.x7e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).
fof('$_typeof_Coq.Init.Byte.x7f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).
fof('$_typeof_Coq.Init.Byte.x80',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).
fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.x82',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).
fof('$_typeof_Coq.Init.Byte.x83',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).
fof('$_typeof_Coq.Init.Byte.x84',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).
fof('$_typeof_Coq.Init.Byte.x85',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).
fof('$_typeof_Coq.Init.Byte.x86',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).
fof('$_typeof_Coq.Init.Byte.x87',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).
fof('$_typeof_Coq.Init.Byte.x88',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).
fof('$_typeof_Coq.Init.Byte.x89',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).
fof('$_typeof_Coq.Init.Byte.x8a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).
fof('$_typeof_Coq.Init.Byte.x8b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).
fof('$_typeof_Coq.Init.Byte.x8c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).
fof('$_typeof_Coq.Init.Byte.x8d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).
fof('$_typeof_Coq.Init.Byte.x8e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).
fof('$_typeof_Coq.Init.Byte.x8f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).
fof('$_typeof_Coq.Init.Byte.x90',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).
fof('$_typeof_Coq.Init.Byte.x91',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).
fof('$_typeof_Coq.Init.Byte.x92',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).
fof('$_typeof_Coq.Init.Byte.x93',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).
fof('$_typeof_Coq.Init.Byte.x94',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).
fof('$_typeof_Coq.Init.Byte.x95',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).
fof('$_typeof_Coq.Init.Byte.x96',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).
fof('$_typeof_Coq.Init.Byte.x97',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).
fof('$_typeof_Coq.Init.Byte.x98',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).
fof('$_typeof_Coq.Init.Byte.x99',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).
fof('$_typeof_Coq.Init.Byte.x9a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).
fof('$_typeof_Coq.Init.Byte.x9b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).
fof('$_typeof_Coq.Init.Byte.x9c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).
fof('$_typeof_Coq.Init.Byte.x9d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).
fof('$_typeof_Coq.Init.Byte.x9e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).
fof('$_typeof_Coq.Init.Byte.x9f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).
fof('$_typeof_Coq.Init.Byte.xa0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).
fof('$_typeof_Coq.Init.Byte.xa1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).
fof('$_typeof_Coq.Init.Byte.xa2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).
fof('$_typeof_Coq.Init.Byte.xa3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).
fof('$_typeof_Coq.Init.Byte.xa4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).
fof('$_typeof_Coq.Init.Byte.xa5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).
fof('$_typeof_Coq.Init.Byte.xa6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).
fof('$_typeof_Coq.Init.Byte.xa7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).
fof('$_typeof_Coq.Init.Byte.xa8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).
fof('$_typeof_Coq.Init.Byte.xa9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).
fof('$_typeof_Coq.Init.Byte.xaa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).
fof('$_typeof_Coq.Init.Byte.xab',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).
fof('$_typeof_Coq.Init.Byte.xac',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).
fof('$_typeof_Coq.Init.Byte.xad',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).
fof('$_typeof_Coq.Init.Byte.xae',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).
fof('$_typeof_Coq.Init.Byte.xaf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).
fof('$_typeof_Coq.Init.Byte.xb0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).
fof('$_typeof_Coq.Init.Byte.xb1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).
fof('$_typeof_Coq.Init.Byte.xb2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).
fof('$_typeof_Coq.Init.Byte.xb3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).
fof('$_typeof_Coq.Init.Byte.xb4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).
fof('$_typeof_Coq.Init.Byte.xb5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).
fof('$_typeof_Coq.Init.Byte.xb6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).
fof('$_typeof_Coq.Init.Byte.xb7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).
fof('$_typeof_Coq.Init.Byte.xb8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).
fof('$_typeof_Coq.Init.Byte.xb9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).
fof('$_typeof_Coq.Init.Byte.xba',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).
fof('$_typeof_Coq.Init.Byte.xbb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).
fof('$_typeof_Coq.Init.Byte.xbc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).
fof('$_typeof_Coq.Init.Byte.xbd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).
fof('$_typeof_Coq.Init.Byte.xbe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).
fof('$_typeof_Coq.Init.Byte.xbf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).
fof('$_typeof_Coq.Init.Byte.xc0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).
fof('$_typeof_Coq.Init.Byte.xc1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).
fof('$_typeof_Coq.Init.Byte.xc2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Byte.xc6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).
fof('$_typeof_Coq.Init.Byte.xc7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).
fof('$_typeof_Coq.Init.Byte.xc8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).
fof('$_typeof_Coq.Init.Byte.xc9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).
fof('$_typeof_Coq.Init.Byte.xca',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).
fof('$_typeof_Coq.Init.Byte.xcb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).
fof('$_typeof_Coq.Init.Byte.xcc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__4882___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__23134___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.ID',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__4703___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__237___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__4701___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__4880___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__4800___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__4775___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__23092___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__23097___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__4868___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__2816___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__23078___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__4682___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__4795___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__2816___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__4757___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__4715___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__23109___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__4715___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__92___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
c_24__type__23185___24t(cCoq_2eInit_2eDecimal_2ePos) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.int_of_int',axiom,
c_24__type__23198___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).
fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
c_24__type__5035___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__23512___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__23528___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__237___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__237___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__8868___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__23541___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__8868___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__23560___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.one',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2eone) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__237___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.square',axiom,
c_24__type__237___24t(cCoq_2eInit_2eNat_2esquare) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__237___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__1147___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__8868___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__23085___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__240___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__240___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__240___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.Exc',axiom,
c_24__type__2816___24t(cCoq_2eInit_2eSpecif_2eExc) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__31400___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__16799___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__16838___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__31392___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__31397___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__2850___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__31363___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__31386___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__2855___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__16781___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__22188___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__16820___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__22244___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__993___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__1029___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__31616___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__8673___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__8777___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__8808___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__23324___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__23355___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__8698___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__8730___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__16698___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__16698___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__31125___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__31125___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__4901___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__23237___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__3872___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__3872___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__17542___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__3872___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__3872___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__31835___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__3863___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__3876___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__3876___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__17377___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__3863___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__3863___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__3863___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__3863___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__3876___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__3876___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__17360___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__17432___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__23572___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__4029___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__1402___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1402___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__1378___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__1378___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__22924___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__17278___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__17278___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__31986___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__17588___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__31890___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__1378___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__31910___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__22864___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__31954___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__17580___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__17580___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__17580___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__31964___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__31964___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
c_24__type__1378___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__31884___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__17580___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__1378___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__31940___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__9122___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__9112___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__9117___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__9167___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__9407___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__9399___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__9399___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__9167___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__9399___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__9399___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__9386___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__9167___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__9386___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__24162___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__19989___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__2816___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__30975___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__2816___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__22963___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__16851___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
c_24__type__23253___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__23253___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__8990___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__3872___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__3872___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__240___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__240___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__17278___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__17278___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__17278___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__17278___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__17278___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__32017___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__3999___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__3999___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__8417___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__31458___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__3119___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__32034___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__3999___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__3955___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__17877___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__17873___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__3996___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__18065___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__3856___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__18065___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__17883___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__3955___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__3955___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__17845___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__3955___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__17877___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__17873___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__17887___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__3856___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__8876___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__8876___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__1380___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
c_24__type__1402___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__19989___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__31797___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__23204___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__23201___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__23217___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__5254___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__23209___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__23220___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__23220___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).
fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__9338___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
c_24__type__9331___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__9331___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
c_24__type__9338___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__9331___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
c_24__type__9326___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__9328___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__9960___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__9930___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__30809___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__10285___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__8868___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__31444___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__31409___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__22314___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__22314___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__31409___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__31427___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__4715___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__2816___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__31818___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_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.micromega.ZMicromega.coneMember',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
c_24__type__17883___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__17880___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__1402___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__1402___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
c_24__type__17432___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__7127___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__7124___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__7135___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__7132___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__2816___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__2816___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__2816___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__3876___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__19897___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__19897___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
c_24__type__23313___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__30841___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__30841___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__10781___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__10786___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__10778___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__10786___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__10792___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__10786___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__2816___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__30835___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__30822___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__10529___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__30827___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__2816___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__30862___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__30838___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__30838___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__16612___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__16612___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__30969___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__3876___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__2842___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__20185___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).
fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__24166___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__24166___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_Lambda.Redexes.Ap',axiom,
c_24__type__42___24t(cLambda_2eRedexes_2eAp) ).
fof('$_typeof_Lambda.Redexes.Fun',axiom,
c_24__type__37___24t(cLambda_2eRedexes_2eFun) ).
fof('$_typeof_Lambda.Redexes.Var',axiom,
c_24__type__35___24t(cLambda_2eRedexes_2eVar) ).
fof('$_typeof_Lambda.Redexes.bool_max',axiom,
c_24__type__92___24t(cLambda_2eRedexes_2ebool__max) ).
fof('$_typeof_Lambda.Redexes.redexes',axiom,
cType___24t(cLambda_2eRedexes_2eredexes) ).
fof('$_typeof_Lambda.Redexes.redexes_rec',axiom,
c_24__type__1209___24t(cLambda_2eRedexes_2eredexes__rec) ).
fof('$_typeof_Lambda.Redexes.redexes_rect',axiom,
c_24__type__1209___24t(cLambda_2eRedexes_2eredexes__rect) ).
fof('$_typeof_Lambda.Redexes.regular',axiom,
c_24__type__243___24t(cLambda_2eRedexes_2eregular) ).
fof('$_typeof_Lambda.Substitution.insert_Var',axiom,
c_24__type__1067___24t(cLambda_2eSubstitution_2einsert__Var) ).
fof('$_typeof_Lambda.Substitution.lift_r',axiom,
c_24__type__1070___24t(cLambda_2eSubstitution_2elift__r) ).
fof('$_typeof_Lambda.Substitution.lift_rec_r',axiom,
c_24__type__1067___24t(cLambda_2eSubstitution_2elift__rec__r) ).
fof('$_typeof_Lambda.Substitution.subst_r',axiom,
c_24__type__175___24t(cLambda_2eSubstitution_2esubst__r) ).
fof('$_typeof_Lambda.Substitution.subst_rec_r',axiom,
c_24__type__1112___24t(cLambda_2eSubstitution_2esubst__rec__r) ).
fof('$_typeof_Lambda.Terms.Abs',axiom,
c_24__type__17030___24t(cLambda_2eTerms_2eAbs) ).
fof('$_typeof_Lambda.Terms.App',axiom,
c_24__type__31456___24t(cLambda_2eTerms_2eApp) ).
fof('$_typeof_Lambda.Terms.Ref',axiom,
c_24__type__31453___24t(cLambda_2eTerms_2eRef) ).
fof('$_typeof_Lambda.Terms.lambda',axiom,
cType___24t(cLambda_2eTerms_2elambda) ).
fof('$_typeof_Lambda.Terms.relocate',axiom,
c_24__type__1125___24t(cLambda_2eTerms_2erelocate) ).
fof('$_typeof_Lambda.Test.compare',axiom,
c_24__type__1140___24t(cLambda_2eTest_2ecompare) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Gt.gt_Sn_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n)) ) ).
fof('Coq.Arith.Gt.gt_asym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(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)
=> ( p(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.Gt.gt_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_2egt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__p,V1__m))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.Gt.gt_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_2egt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eNat_2epred___24a1(V1__m),V0__n)) ) ) ) ).
fof('Coq.Arith.Gt.gt_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_2egt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.Gt.le_gt_S',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_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),V0__n)) ) ) ) ).
fof('Coq.Arith.Gt.le_gt_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(V1__m,V0__n))
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.Gt.le_not_gt',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_2egt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.plus_gt_compat_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.Arith.Gt.plus_gt_reg_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',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_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.S_pred',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(V1__m,V0__n))
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
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_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_2ele___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_pred',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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eNat_2epred___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_shuffle3',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.divide_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( 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_1',axiom,
p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_asymm',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_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ 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.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2elt___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.lt_trichotomy',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))
| V0__n = V1__m
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.Plus.le_plus_l',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,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Plus.le_plus_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(V1__m,cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m))) ) ) ).
fof('Coq.Arith.Plus.plus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) ) ) ) ).
fof('Coq.Arith.Plus.plus_le_compat_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.Arith.Plus.plus_le_reg_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ) ).
fof('Coq.Arith.Plus.plus_reg_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
! [V0__P] :
( c_24__type__240___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ! [V3__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
=> ! [V4__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__q)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__p,V1__n))
=> p(happ(happ(V0__P,V3__p),V4__q)) ) ) )
=> ( ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__p)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__p,V2__m))
=> p(happ(happ(V0__P,V1__n),V4__p)) ) )
=> p(happ(happ(V0__P,V1__n),V2__m)) ) ) ) )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> p(happ(happ(V0__P,V2__n),V3__m)) ) ) ) ) ).
fof('Coq.Arith.Wf_nat.lt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__23085___24t(V1__P)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n))
=> p(happ(V1__P,V3__m)) ) )
=> p(happ(V1__P,V2__n)) ) )
=> p(happ(V1__P,V0__n)) ) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( p(c_24False)
=> V0__b = V1__b_27 ) ) ) ).
fof('Coq.Init.Datatypes.bool_ind',axiom,
! [V0__P] :
( c_24__type__2___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2etrue))
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2efalse))
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
=> p(happ(V0__P,V3__b)) ) ) ) ) ).
fof('Coq.Init.Datatypes.idProp',axiom,
p(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__23085___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.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.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__240___24t(V0__R)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).
fof('Coq.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__1015___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Init.Specif.sumor_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__1051___24t(V0__A,V1__B,V2__P)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einleft___24a3(V0__A,V1__B,V3__a))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2einright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_false_iff',axiom,
( ( p(c_24False)
=> p(c_24False) )
<=> p(c_24True) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_true_iff',axiom,
( ( p(c_24True)
=> p(c_24False) )
<=> p(c_24False) ) ).
fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__10144___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.le_refl',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V0__p) ) ).
fof('Coq.Structures.OrderedTypeEx.Z_as_OT.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.A\'A_left',axiom,
! [V0__A] :
( c_24__type__8876___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [Vvar__4__m__32025] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__32025)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__32025,V1__z))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__32025))
=> p(happ(V0__A,Vvar__4__m__32025)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.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_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__32024___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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_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_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_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.micromega.OrderedRing.Rle_antisymm',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V11__n))
=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_gt_cases',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_lt_trans',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_refl',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_trans',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_0_1',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> p(happ(happ(V9__rlt,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_trans',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_lt_succ',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_succ_r',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trans',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_l',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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(V7__req,happ(happ(V3__rplus,V1__rO),V11__n)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_r',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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(V7__req,happ(happ(V3__rplus,V11__n),V1__rO)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_comm',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V12__m)),happ(happ(V3__rplus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_lt_mono',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_mono',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_le_mono',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_mono',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_pos',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_pos',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_l',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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(V7__req,happ(happ(V4__rtimes,V1__rO),V11__n)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_r',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_nonneg_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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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.ZCoeff.req_refl',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,V11__x),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_sym',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ( p(happ(happ(V7__req,V11__x),V12__y))
=> p(happ(happ(V7__req,V12__y),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_trans',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__2506___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__2506___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__2506___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1412___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1412___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__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> ( p(happ(happ(V7__req,V11__x),V12__y))
=> ( p(happ(happ(V7__req,V12__y),V13__z))
=> p(happ(happ(V7__req,V11__x),V13__z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_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__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_art',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__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___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)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V12__x)),V1__rO)) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),V14__y)),happ(happ(V4__rmul,V14__y),V13__x))) ) )
=> ( ! [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,V14__x),happ(happ(V4__rmul,V15__y),V16__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V14__x),V15__y)),V16__z))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> ! [V17__z] :
( t(V17__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V15__x),V16__y)),V17__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V15__x),V17__z)),happ(happ(V4__rmul,V16__y),V17__z)))) ) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> ! [V17__y] :
( t(V17__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V16__x),V17__y))),happ(happ(V4__rmul,happ(V6__ropp,V16__x)),V17__y))) ) )
=> ( ! [V17__x] :
( t(V17__x,V0__R)
=> ! [V18__y] :
( t(V18__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V17__x),V18__y))),happ(happ(V3__radd,happ(V6__ropp,V17__x)),happ(V6__ropp,V18__y)))) ) )
=> ( ! [V18__x] :
( t(V18__x,V0__R)
=> ! [V19__y] :
( t(V19__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V18__x),V19__y)),happ(happ(V3__radd,V18__x),happ(V6__ropp,V19__y)))) ) )
=> 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_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__2506___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__2506___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__2506___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1407___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1412___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('Cube.Compat_Ap1',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__W1] :
( cLambda_2eRedexes_2eredexes___24t(V2__W1)
=> ( cCube_2ecompat___24a3(V0__U1,V1__V1,V2__W1)
=> ! [V4__U2] :
( cLambda_2eRedexes_2eredexes___24t(V4__U2)
=> ! [V5__V2] :
( cLambda_2eRedexes_2eredexes___24t(V5__V2)
=> ! [V6__W2] :
( cLambda_2eRedexes_2eredexes___24t(V6__W2)
=> ( cCube_2ecompat___24a3(V4__U2,V5__V2,V6__W2)
=> ! [V8__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V8__b)
=> cCube_2ecompat___24a3(cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V0__U1,V4__U2),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V1__V1,V5__V2),cLambda_2eRedexes_2eAp___24a3(V8__b,V2__W1,V6__W2)) ) ) ) ) ) ) ) ) ) ).
fof('Cube.Compat_Ap2',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__W1] :
( cLambda_2eRedexes_2eredexes___24t(V2__W1)
=> ( cCube_2ecompat___24a3(V0__U1,V1__V1,V2__W1)
=> ! [V4__U2] :
( cLambda_2eRedexes_2eredexes___24t(V4__U2)
=> ! [V5__V2] :
( cLambda_2eRedexes_2eredexes___24t(V5__V2)
=> ! [V6__W2] :
( cLambda_2eRedexes_2eredexes___24t(V6__W2)
=> ( cCube_2ecompat___24a3(V4__U2,V5__V2,V6__W2)
=> ! [V8__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V8__b)
=> ! [V9__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V9__b_27)
=> cCube_2ecompat___24a3(cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(V0__U1),V4__U2),cLambda_2eRedexes_2eAp___24a3(V8__b,cLambda_2eRedexes_2eFun___24a1(V1__V1),V5__V2),cLambda_2eRedexes_2eAp___24a3(V9__b_27,cLambda_2eRedexes_2eFun___24a1(V2__W1),V6__W2)) ) ) ) ) ) ) ) ) ) ) ).
fof('Cube.Compat_Fun',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cCube_2ecompat___24a3(V0__U,V1__V,V2__W)
=> cCube_2ecompat___24a3(cLambda_2eRedexes_2eFun___24a1(V0__U),cLambda_2eRedexes_2eFun___24a1(V1__V),cLambda_2eRedexes_2eFun___24a1(V2__W)) ) ) ) ) ).
fof('Cube.Compat_Var',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCube_2ecompat___24a3(cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n)) ) ).
fof('Cube.compat_ind',axiom,
! [V0__P] :
( c_24__type__123___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__U] :
( cLambda_2eRedexes_2eredexes___24t(V2__U)
=> ! [V3__V] :
( cLambda_2eRedexes_2eredexes___24t(V3__V)
=> ! [V4__W] :
( cLambda_2eRedexes_2eredexes___24t(V4__W)
=> ( cCube_2ecompat___24a3(V2__U,V3__V,V4__W)
=> ( p(happ(happ(happ(V0__P,V2__U),V3__V),V4__W))
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__U)),cLambda_2eRedexes_2eFun___24a1(V3__V)),cLambda_2eRedexes_2eFun___24a1(V4__W))) ) ) ) ) )
=> ( ! [V3__U1] :
( cLambda_2eRedexes_2eredexes___24t(V3__U1)
=> ! [V4__V1] :
( cLambda_2eRedexes_2eredexes___24t(V4__V1)
=> ! [V5__W1] :
( cLambda_2eRedexes_2eredexes___24t(V5__W1)
=> ( cCube_2ecompat___24a3(V3__U1,V4__V1,V5__W1)
=> ( p(happ(happ(happ(V0__P,V3__U1),V4__V1),V5__W1))
=> ! [V8__U2] :
( cLambda_2eRedexes_2eredexes___24t(V8__U2)
=> ! [V9__V2] :
( cLambda_2eRedexes_2eredexes___24t(V9__V2)
=> ! [V10__W2] :
( cLambda_2eRedexes_2eredexes___24t(V10__W2)
=> ( cCube_2ecompat___24a3(V8__U2,V9__V2,V10__W2)
=> ( p(happ(happ(happ(V0__P,V8__U2),V9__V2),V10__W2))
=> ! [V13__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V13__b)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V3__U1,V8__U2)),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V4__V1,V9__V2)),cLambda_2eRedexes_2eAp___24a3(V13__b,V5__W1,V10__W2))) ) ) ) ) ) ) ) ) ) ) )
=> ( ! [V4__U1] :
( cLambda_2eRedexes_2eredexes___24t(V4__U1)
=> ! [V5__V1] :
( cLambda_2eRedexes_2eredexes___24t(V5__V1)
=> ! [V6__W1] :
( cLambda_2eRedexes_2eredexes___24t(V6__W1)
=> ( cCube_2ecompat___24a3(V4__U1,V5__V1,V6__W1)
=> ( p(happ(happ(happ(V0__P,V4__U1),V5__V1),V6__W1))
=> ! [V9__U2] :
( cLambda_2eRedexes_2eredexes___24t(V9__U2)
=> ! [V10__V2] :
( cLambda_2eRedexes_2eredexes___24t(V10__V2)
=> ! [V11__W2] :
( cLambda_2eRedexes_2eredexes___24t(V11__W2)
=> ( cCube_2ecompat___24a3(V9__U2,V10__V2,V11__W2)
=> ( p(happ(happ(happ(V0__P,V9__U2),V10__V2),V11__W2))
=> ! [V14__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V14__b)
=> ! [V15__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V15__b_27)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(V4__U1),V9__U2)),cLambda_2eRedexes_2eAp___24a3(V14__b,cLambda_2eRedexes_2eFun___24a1(V5__V1),V10__V2)),cLambda_2eRedexes_2eAp___24a3(V15__b_27,cLambda_2eRedexes_2eFun___24a1(V6__W1),V11__W2))) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V5__r] :
( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ! [V6__r] :
( cLambda_2eRedexes_2eredexes___24t(V6__r)
=> ! [V7__r] :
( cLambda_2eRedexes_2eredexes___24t(V7__r)
=> ( cCube_2ecompat___24a3(V5__r,V6__r,V7__r)
=> p(happ(happ(happ(V0__P,V5__r),V6__r),V7__r)) ) ) ) ) ) ) ) ) ) ).
fof('Cube.compat_intro',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__W] :
( cLambda_2eRedexes_2eredexes___24t(V1__W)
=> ! [V2__WU] :
( cLambda_2eRedexes_2eredexes___24t(V2__WU)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V1__W,V0__U,V2__WU)
=> ! [V4__V] :
( cLambda_2eRedexes_2eredexes___24t(V4__V)
=> ! [V5__WV] :
( cLambda_2eRedexes_2eredexes___24t(V5__WV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V1__W,V4__V,V5__WV)
=> ( cLambda_2eRedexes_2esub___24a2(V4__V,V0__U)
=> cCube_2ecompat___24a3(V0__U,V4__V,V1__W) ) ) ) ) ) ) ) ) ).
fof('Cube.prism0',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cCube_2ecompat___24a3(V0__U,V1__V,V2__W)
=> ! [V4__UV] :
( cLambda_2eRedexes_2eredexes___24t(V4__UV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V4__UV)
=> ! [V6__WU] :
( cLambda_2eRedexes_2eredexes___24t(V6__WU)
=> ! [V7__WV] :
( cLambda_2eRedexes_2eredexes___24t(V7__WV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__W,V0__U,V6__WU)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__W,V1__V,V7__WV)
=> cLambda_2eResiduals_2eresiduals___24a3(V7__WV,V4__UV,V6__WU) ) ) ) ) ) ) ) ) ) ) ).
fof('Cube.prism1',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2esub___24a2(V1__V,V0__U)
=> ! [V4__UV] :
( cLambda_2eRedexes_2eredexes___24t(V4__UV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V4__UV)
=> ! [V6__WV] :
( cLambda_2eRedexes_2eredexes___24t(V6__WV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__W,V1__V,V6__WV)
=> ! [V8__WU] :
( cLambda_2eRedexes_2eredexes___24t(V8__WU)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__W,V0__U,V8__WU)
=> cLambda_2eResiduals_2eresiduals___24a3(V6__WV,V4__UV,V8__WU) ) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.Comp_Ap',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U1,V1__V1)
=> ! [V3__U2] :
( cLambda_2eRedexes_2eredexes___24t(V3__U2)
=> ! [V4__V2] :
( cLambda_2eRedexes_2eredexes___24t(V4__V2)
=> ( cLambda_2eRedexes_2ecomp___24a2(V3__U2,V4__V2)
=> ! [V6__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V6__b1)
=> ! [V7__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V7__b2)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eRedexes_2eAp___24a3(V6__b1,V0__U1,V3__U2),cLambda_2eRedexes_2eAp___24a3(V7__b2,V1__V1,V4__V2)) ) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.Comp_Fun',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eRedexes_2eFun___24a1(V0__U),cLambda_2eRedexes_2eFun___24a1(V1__V)) ) ) ) ).
fof('Lambda.Redexes.Comp_Var',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n)) ) ).
fof('Lambda.Redexes.Sub_Ap1',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ( cLambda_2eRedexes_2esub___24a2(V0__U1,V1__V1)
=> ! [V3__U2] :
( cLambda_2eRedexes_2eredexes___24t(V3__U2)
=> ! [V4__V2] :
( cLambda_2eRedexes_2eredexes___24t(V4__V2)
=> ( cLambda_2eRedexes_2esub___24a2(V3__U2,V4__V2)
=> ! [V6__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V6__b)
=> cLambda_2eRedexes_2esub___24a2(cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V0__U1,V3__U2),cLambda_2eRedexes_2eAp___24a3(V6__b,V1__V1,V4__V2)) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.Sub_Ap2',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ( cLambda_2eRedexes_2esub___24a2(V0__U1,V1__V1)
=> ! [V3__U2] :
( cLambda_2eRedexes_2eredexes___24t(V3__U2)
=> ! [V4__V2] :
( cLambda_2eRedexes_2eredexes___24t(V4__V2)
=> ( cLambda_2eRedexes_2esub___24a2(V3__U2,V4__V2)
=> ! [V6__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V6__b)
=> cLambda_2eRedexes_2esub___24a2(cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,V0__U1,V3__U2),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,V1__V1,V4__V2)) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.Sub_Fun',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2esub___24a2(V0__U,V1__V)
=> cLambda_2eRedexes_2esub___24a2(cLambda_2eRedexes_2eFun___24a1(V0__U),cLambda_2eRedexes_2eFun___24a1(V1__V)) ) ) ) ).
fof('Lambda.Redexes.Sub_Var',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cLambda_2eRedexes_2esub___24a2(cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n)) ) ).
fof('Lambda.Redexes.Union_Ap',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__W1] :
( cLambda_2eRedexes_2eredexes___24t(V2__W1)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U1,V1__V1,V2__W1)
=> ! [V4__U2] :
( cLambda_2eRedexes_2eredexes___24t(V4__U2)
=> ! [V5__V2] :
( cLambda_2eRedexes_2eredexes___24t(V5__V2)
=> ! [V6__W2] :
( cLambda_2eRedexes_2eredexes___24t(V6__W2)
=> ( cLambda_2eRedexes_2eunion___24a3(V4__U2,V5__V2,V6__W2)
=> ! [V8__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V8__b1)
=> ! [V9__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V9__b2)
=> cLambda_2eRedexes_2eunion___24a3(cLambda_2eRedexes_2eAp___24a3(V8__b1,V0__U1,V4__U2),cLambda_2eRedexes_2eAp___24a3(V9__b2,V1__V1,V5__V2),cLambda_2eRedexes_2eAp___24a3(cLambda_2eRedexes_2ebool__max___24a2(V8__b1,V9__b2),V2__W1,V6__W2)) ) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.Union_Fun',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2eunion___24a3(cLambda_2eRedexes_2eFun___24a1(V0__U),cLambda_2eRedexes_2eFun___24a1(V1__V),cLambda_2eRedexes_2eFun___24a1(V2__W)) ) ) ) ) ).
fof('Lambda.Redexes.Union_Var',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cLambda_2eRedexes_2eunion___24a3(cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n)) ) ).
fof('Lambda.Redexes.bool_max_Sym',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> cLambda_2eRedexes_2ebool__max___24a2(V0__b,V1__b_27) = cLambda_2eRedexes_2ebool__max___24a2(V1__b_27,V0__b) ) ) ).
fof('Lambda.Redexes.comp_ind',axiom,
! [V0__P] :
( c_24__type__66___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__U] :
( cLambda_2eRedexes_2eredexes___24t(V2__U)
=> ! [V3__V] :
( cLambda_2eRedexes_2eredexes___24t(V3__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V2__U,V3__V)
=> ( p(happ(happ(V0__P,V2__U),V3__V))
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__U)),cLambda_2eRedexes_2eFun___24a1(V3__V))) ) ) ) )
=> ( ! [V3__U1] :
( cLambda_2eRedexes_2eredexes___24t(V3__U1)
=> ! [V4__V1] :
( cLambda_2eRedexes_2eredexes___24t(V4__V1)
=> ( cLambda_2eRedexes_2ecomp___24a2(V3__U1,V4__V1)
=> ( p(happ(happ(V0__P,V3__U1),V4__V1))
=> ! [V7__U2] :
( cLambda_2eRedexes_2eredexes___24t(V7__U2)
=> ! [V8__V2] :
( cLambda_2eRedexes_2eredexes___24t(V8__V2)
=> ( cLambda_2eRedexes_2ecomp___24a2(V7__U2,V8__V2)
=> ( p(happ(happ(V0__P,V7__U2),V8__V2))
=> ! [V11__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V11__b1)
=> ! [V12__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V12__b2)
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(V11__b1,V3__U1,V7__U2)),cLambda_2eRedexes_2eAp___24a3(V12__b2,V4__V1,V8__V2))) ) ) ) ) ) ) ) ) ) )
=> ! [V4__r] :
( cLambda_2eRedexes_2eredexes___24t(V4__r)
=> ! [V5__r] :
( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ( cLambda_2eRedexes_2ecomp___24a2(V4__r,V5__r)
=> p(happ(happ(V0__P,V4__r),V5__r)) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.comp_refl',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> cLambda_2eRedexes_2ecomp___24a2(V0__U,V0__U) ) ).
fof('Lambda.Redexes.comp_sym',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V)
=> cLambda_2eRedexes_2ecomp___24a2(V1__V,V0__U) ) ) ) ).
fof('Lambda.Redexes.comp_trans',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V)
=> ! [V3__W] :
( cLambda_2eRedexes_2eredexes___24t(V3__W)
=> ( cLambda_2eRedexes_2ecomp___24a2(V1__V,V3__W)
=> cLambda_2eRedexes_2ecomp___24a2(V0__U,V3__W) ) ) ) ) ) ).
fof('Lambda.Redexes.max_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cLambda_2eRedexes_2ebool__max___24a2(V0__b,cCoq_2eInit_2eDatatypes_2efalse) = V0__b ) ).
fof('Lambda.Redexes.redexes_ind',axiom,
! [V0__P] :
( c_24__type__243___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__r] :
( cLambda_2eRedexes_2eredexes___24t(V2__r)
=> ( p(happ(V0__P,V2__r))
=> p(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__r))) ) )
=> ( ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V3__b)
=> ! [V4__r] :
( cLambda_2eRedexes_2eredexes___24t(V4__r)
=> ( p(happ(V0__P,V4__r))
=> ! [V6__r] :
( cLambda_2eRedexes_2eredexes___24t(V6__r)
=> ( p(happ(V0__P,V6__r))
=> p(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(V3__b,V4__r,V6__r))) ) ) ) ) )
=> ! [V4__r] :
( cLambda_2eRedexes_2eredexes___24t(V4__r)
=> p(happ(V0__P,V4__r)) ) ) ) ) ) ).
fof('Lambda.Redexes.sub_ind',axiom,
! [V0__P] :
( c_24__type__66___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__U] :
( cLambda_2eRedexes_2eredexes___24t(V2__U)
=> ! [V3__V] :
( cLambda_2eRedexes_2eredexes___24t(V3__V)
=> ( cLambda_2eRedexes_2esub___24a2(V2__U,V3__V)
=> ( p(happ(happ(V0__P,V2__U),V3__V))
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__U)),cLambda_2eRedexes_2eFun___24a1(V3__V))) ) ) ) )
=> ( ! [V3__U1] :
( cLambda_2eRedexes_2eredexes___24t(V3__U1)
=> ! [V4__V1] :
( cLambda_2eRedexes_2eredexes___24t(V4__V1)
=> ( cLambda_2eRedexes_2esub___24a2(V3__U1,V4__V1)
=> ( p(happ(happ(V0__P,V3__U1),V4__V1))
=> ! [V7__U2] :
( cLambda_2eRedexes_2eredexes___24t(V7__U2)
=> ! [V8__V2] :
( cLambda_2eRedexes_2eredexes___24t(V8__V2)
=> ( cLambda_2eRedexes_2esub___24a2(V7__U2,V8__V2)
=> ( p(happ(happ(V0__P,V7__U2),V8__V2))
=> ! [V11__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V11__b)
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V3__U1,V7__U2)),cLambda_2eRedexes_2eAp___24a3(V11__b,V4__V1,V8__V2))) ) ) ) ) ) ) ) ) )
=> ( ! [V4__U1] :
( cLambda_2eRedexes_2eredexes___24t(V4__U1)
=> ! [V5__V1] :
( cLambda_2eRedexes_2eredexes___24t(V5__V1)
=> ( cLambda_2eRedexes_2esub___24a2(V4__U1,V5__V1)
=> ( p(happ(happ(V0__P,V4__U1),V5__V1))
=> ! [V8__U2] :
( cLambda_2eRedexes_2eredexes___24t(V8__U2)
=> ! [V9__V2] :
( cLambda_2eRedexes_2eredexes___24t(V9__V2)
=> ( cLambda_2eRedexes_2esub___24a2(V8__U2,V9__V2)
=> ( p(happ(happ(V0__P,V8__U2),V9__V2))
=> ! [V12__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V12__b)
=> p(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,V4__U1,V8__U2)),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,V5__V1,V9__V2))) ) ) ) ) ) ) ) ) )
=> ! [V5__r] :
( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ! [V6__r] :
( cLambda_2eRedexes_2eredexes___24t(V6__r)
=> ( cLambda_2eRedexes_2esub___24a2(V5__r,V6__r)
=> p(happ(happ(V0__P,V5__r),V6__r)) ) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.union_defined',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V)
=> ? [V3__W] :
( cLambda_2eRedexes_2eredexes___24t(V3__W)
& cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V3__W) ) ) ) ) ).
fof('Lambda.Redexes.union_ind',axiom,
! [V0__P] :
( c_24__type__123___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__U] :
( cLambda_2eRedexes_2eredexes___24t(V2__U)
=> ! [V3__V] :
( cLambda_2eRedexes_2eredexes___24t(V3__V)
=> ! [V4__W] :
( cLambda_2eRedexes_2eredexes___24t(V4__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V2__U,V3__V,V4__W)
=> ( p(happ(happ(happ(V0__P,V2__U),V3__V),V4__W))
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__U)),cLambda_2eRedexes_2eFun___24a1(V3__V)),cLambda_2eRedexes_2eFun___24a1(V4__W))) ) ) ) ) )
=> ( ! [V3__U1] :
( cLambda_2eRedexes_2eredexes___24t(V3__U1)
=> ! [V4__V1] :
( cLambda_2eRedexes_2eredexes___24t(V4__V1)
=> ! [V5__W1] :
( cLambda_2eRedexes_2eredexes___24t(V5__W1)
=> ( cLambda_2eRedexes_2eunion___24a3(V3__U1,V4__V1,V5__W1)
=> ( p(happ(happ(happ(V0__P,V3__U1),V4__V1),V5__W1))
=> ! [V8__U2] :
( cLambda_2eRedexes_2eredexes___24t(V8__U2)
=> ! [V9__V2] :
( cLambda_2eRedexes_2eredexes___24t(V9__V2)
=> ! [V10__W2] :
( cLambda_2eRedexes_2eredexes___24t(V10__W2)
=> ( cLambda_2eRedexes_2eunion___24a3(V8__U2,V9__V2,V10__W2)
=> ( p(happ(happ(happ(V0__P,V8__U2),V9__V2),V10__W2))
=> ! [V13__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V13__b1)
=> ! [V14__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V14__b2)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(V13__b1,V3__U1,V8__U2)),cLambda_2eRedexes_2eAp___24a3(V14__b2,V4__V1,V9__V2)),cLambda_2eRedexes_2eAp___24a3(cLambda_2eRedexes_2ebool__max___24a2(V13__b1,V14__b2),V5__W1,V10__W2))) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V4__r] :
( cLambda_2eRedexes_2eredexes___24t(V4__r)
=> ! [V5__r] :
( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ! [V6__r] :
( cLambda_2eRedexes_2eredexes___24t(V6__r)
=> ( cLambda_2eRedexes_2eunion___24a3(V4__r,V5__r,V6__r)
=> p(happ(happ(happ(V0__P,V4__r),V5__r),V6__r)) ) ) ) ) ) ) ) ) ).
fof('Lambda.Redexes.union_l',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2esub___24a2(V0__U,V2__W) ) ) ) ) ).
fof('Lambda.Redexes.union_preserve_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> ( cLambda_2eRedexes_2eregular___24a1(V1__V)
=> cLambda_2eRedexes_2eregular___24a1(V2__W) ) ) ) ) ) ) ).
fof('Lambda.Redexes.union_r',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2esub___24a2(V1__V,V2__W) ) ) ) ) ).
fof('Lambda.Redexes.union_sym',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2eunion___24a3(V1__V,V0__U,V2__W) ) ) ) ) ).
fof('Lambda.Residuals.Res_Ap',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__W1] :
( cLambda_2eRedexes_2eredexes___24t(V2__W1)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__V1,V2__W1)
=> ! [V4__U2] :
( cLambda_2eRedexes_2eredexes___24t(V4__U2)
=> ! [V5__V2] :
( cLambda_2eRedexes_2eredexes___24t(V5__V2)
=> ! [V6__W2] :
( cLambda_2eRedexes_2eredexes___24t(V6__W2)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V4__U2,V5__V2,V6__W2)
=> ! [V8__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V8__b)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eRedexes_2eAp___24a3(V8__b,V0__U1,V4__U2),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V1__V1,V5__V2),cLambda_2eRedexes_2eAp___24a3(V8__b,V2__W1,V6__W2)) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Residuals.Res_Fun',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eRedexes_2eFun___24a1(V0__U),cLambda_2eRedexes_2eFun___24a1(V1__V),cLambda_2eRedexes_2eFun___24a1(V2__W)) ) ) ) ) ).
fof('Lambda.Residuals.Res_Var',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n),cLambda_2eRedexes_2eVar___24a1(V0__n)) ) ).
fof('Lambda.Residuals.Res_redex',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__W1] :
( cLambda_2eRedexes_2eredexes___24t(V2__W1)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__V1,V2__W1)
=> ! [V4__U2] :
( cLambda_2eRedexes_2eredexes___24t(V4__U2)
=> ! [V5__V2] :
( cLambda_2eRedexes_2eredexes___24t(V5__V2)
=> ! [V6__W2] :
( cLambda_2eRedexes_2eredexes___24t(V6__W2)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V4__U2,V5__V2,V6__W2)
=> ! [V8__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V8__b)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eRedexes_2eAp___24a3(V8__b,cLambda_2eRedexes_2eFun___24a1(V0__U1),V4__U2),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(V1__V1),V5__V2),cLambda_2eSubstitution_2esubst__r___24a2(V6__W2,V2__W1)) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Residuals.commutation',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__U2] :
( cLambda_2eRedexes_2eredexes___24t(V1__U2)
=> ! [V2__U3] :
( cLambda_2eRedexes_2eredexes___24t(V2__U3)
=> ! [V3__V1] :
( cLambda_2eRedexes_2eredexes___24t(V3__V1)
=> ! [V4__V2] :
( cLambda_2eRedexes_2eredexes___24t(V4__V2)
=> ! [V5__V3] :
( cLambda_2eRedexes_2eredexes___24t(V5__V3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__U2,V2__U3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V3__V1,V4__V2,V5__V3)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eSubstitution_2esubst__r___24a2(V3__V1,V0__U1),cLambda_2eSubstitution_2esubst__r___24a2(V4__V2,V1__U2),cLambda_2eSubstitution_2esubst__r___24a2(V5__V3,V2__U3)) ) ) ) ) ) ) ) ) ).
fof('Lambda.Residuals.mutual_residuals_comp',axiom,
! [V0__W] :
( cLambda_2eRedexes_2eredexes___24t(V0__W)
=> ! [V1__U] :
( cLambda_2eRedexes_2eredexes___24t(V1__U)
=> ! [V2__UW] :
( cLambda_2eRedexes_2eredexes___24t(V2__UW)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V1__U,V0__W,V2__UW)
=> ! [V4__V] :
( cLambda_2eRedexes_2eredexes___24t(V4__V)
=> ! [V5__VW] :
( cLambda_2eRedexes_2eredexes___24t(V5__VW)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V4__V,V0__W,V5__VW)
=> cLambda_2eRedexes_2ecomp___24a2(V2__UW,V5__VW) ) ) ) ) ) ) ) ).
fof('Lambda.Residuals.preservation',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ! [V3__UV] :
( cLambda_2eRedexes_2eredexes___24t(V3__UV)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V3__UV)
=> cLambda_2eResiduals_2eresiduals___24a3(V2__W,V1__V,V3__UV) ) ) ) ) ) ) ).
fof('Lambda.Residuals.preservation1',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__UV] :
( cLambda_2eRedexes_2eredexes___24t(V2__UV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__UV)
=> ! [V4__T] :
( cLambda_2eRedexes_2eredexes___24t(V4__T)
=> ( cLambda_2eRedexes_2eunion___24a3(V0__U,V1__V,V4__T)
=> cLambda_2eResiduals_2eresiduals___24a3(V4__T,V1__V,V2__UV) ) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_comp',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V) ) ) ) ) ).
fof('Lambda.Residuals.residuals_function',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__W)
=> ! [V4__W_27] :
( cLambda_2eRedexes_2eredexes___24t(V4__W_27)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V4__W_27)
=> V4__W_27 = V2__W ) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_ind',axiom,
! [V0__P] :
( c_24__type__123___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n)),cLambda_2eRedexes_2eVar___24a1(V1__n))) )
=> ( ! [V2__U] :
( cLambda_2eRedexes_2eredexes___24t(V2__U)
=> ! [V3__V] :
( cLambda_2eRedexes_2eredexes___24t(V3__V)
=> ! [V4__W] :
( cLambda_2eRedexes_2eredexes___24t(V4__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__U,V3__V,V4__W)
=> ( p(happ(happ(happ(V0__P,V2__U),V3__V),V4__W))
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eFun___24a1(V2__U)),cLambda_2eRedexes_2eFun___24a1(V3__V)),cLambda_2eRedexes_2eFun___24a1(V4__W))) ) ) ) ) )
=> ( ! [V3__U1] :
( cLambda_2eRedexes_2eredexes___24t(V3__U1)
=> ! [V4__V1] :
( cLambda_2eRedexes_2eredexes___24t(V4__V1)
=> ! [V5__W1] :
( cLambda_2eRedexes_2eredexes___24t(V5__W1)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V3__U1,V4__V1,V5__W1)
=> ( p(happ(happ(happ(V0__P,V3__U1),V4__V1),V5__W1))
=> ! [V8__U2] :
( cLambda_2eRedexes_2eredexes___24t(V8__U2)
=> ! [V9__V2] :
( cLambda_2eRedexes_2eredexes___24t(V9__V2)
=> ! [V10__W2] :
( cLambda_2eRedexes_2eredexes___24t(V10__W2)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V8__U2,V9__V2,V10__W2)
=> ( p(happ(happ(happ(V0__P,V8__U2),V9__V2),V10__W2))
=> ! [V13__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V13__b)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(V13__b,V3__U1,V8__U2)),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2efalse,V4__V1,V9__V2)),cLambda_2eRedexes_2eAp___24a3(V13__b,V5__W1,V10__W2))) ) ) ) ) ) ) ) ) ) ) )
=> ( ! [V4__U1] :
( cLambda_2eRedexes_2eredexes___24t(V4__U1)
=> ! [V5__V1] :
( cLambda_2eRedexes_2eredexes___24t(V5__V1)
=> ! [V6__W1] :
( cLambda_2eRedexes_2eredexes___24t(V6__W1)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V4__U1,V5__V1,V6__W1)
=> ( p(happ(happ(happ(V0__P,V4__U1),V5__V1),V6__W1))
=> ! [V9__U2] :
( cLambda_2eRedexes_2eredexes___24t(V9__U2)
=> ! [V10__V2] :
( cLambda_2eRedexes_2eredexes___24t(V10__V2)
=> ! [V11__W2] :
( cLambda_2eRedexes_2eredexes___24t(V11__W2)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V9__U2,V10__V2,V11__W2)
=> ( p(happ(happ(happ(V0__P,V9__U2),V10__V2),V11__W2))
=> ! [V14__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V14__b)
=> p(happ(happ(happ(V0__P,cLambda_2eRedexes_2eAp___24a3(V14__b,cLambda_2eRedexes_2eFun___24a1(V4__U1),V9__U2)),cLambda_2eRedexes_2eAp___24a3(cCoq_2eInit_2eDatatypes_2etrue,cLambda_2eRedexes_2eFun___24a1(V5__V1),V10__V2)),cLambda_2eSubstitution_2esubst__r___24a2(V11__W2,V6__W1))) ) ) ) ) ) ) ) ) ) ) )
=> ! [V5__r] :
( cLambda_2eRedexes_2eredexes___24t(V5__r)
=> ! [V6__r] :
( cLambda_2eRedexes_2eredexes___24t(V6__r)
=> ! [V7__r] :
( cLambda_2eRedexes_2eredexes___24t(V7__r)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V5__r,V6__r,V7__r)
=> p(happ(happ(happ(V0__P,V5__r),V6__r),V7__r)) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_intro',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U,V1__V)
=> ( cLambda_2eRedexes_2eregular___24a1(V1__V)
=> ? [V4__W] :
( cLambda_2eRedexes_2eredexes___24t(V4__W)
& cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V4__W) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_lift',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__U2] :
( cLambda_2eRedexes_2eredexes___24t(V1__U2)
=> ! [V2__U3] :
( cLambda_2eRedexes_2eredexes___24t(V2__U3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__U2,V2__U3)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eSubstitution_2elift__r___24a2(V4__k,V0__U1),cLambda_2eSubstitution_2elift__r___24a2(V4__k,V1__U2),cLambda_2eSubstitution_2elift__r___24a2(V4__k,V2__U3)) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_lift_rec',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__U2] :
( cLambda_2eRedexes_2eredexes___24t(V1__U2)
=> ! [V2__U3] :
( cLambda_2eRedexes_2eredexes___24t(V2__U3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__U2,V2__U3)
=> ! [V4__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__k)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U1,V5__n,V4__k),cLambda_2eSubstitution_2elift__rec__r___24a3(V1__U2,V5__n,V4__k),cLambda_2eSubstitution_2elift__rec__r___24a3(V2__U3,V5__n,V4__k)) ) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_preserve_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__W)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> cLambda_2eRedexes_2eregular___24a1(V2__W) ) ) ) ) ) ).
fof('Lambda.Residuals.residuals_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V2__W)
=> cLambda_2eRedexes_2eregular___24a1(V1__V) ) ) ) ) ).
fof('Lambda.Residuals.residuals_subst_rec',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__U2] :
( cLambda_2eRedexes_2eredexes___24t(V1__U2)
=> ! [V2__U3] :
( cLambda_2eRedexes_2eredexes___24t(V2__U3)
=> ! [V3__V1] :
( cLambda_2eRedexes_2eredexes___24t(V3__V1)
=> ! [V4__V2] :
( cLambda_2eRedexes_2eredexes___24t(V4__V2)
=> ! [V5__V3] :
( cLambda_2eRedexes_2eredexes___24t(V5__V3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U1,V1__U2,V2__U3)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V3__V1,V4__V2,V5__V3)
=> ! [V8__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V8__k)
=> cLambda_2eResiduals_2eresiduals___24a3(cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U1,V3__V1,V8__k),cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__U2,V4__V2,V8__k),cLambda_2eSubstitution_2esubst__rec__r___24a3(V2__U3,V5__V3,V8__k)) ) ) ) ) ) ) ) ) ) ).
fof('Lambda.Substitution.lift1',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__j)
=> ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V2__i,V1__j),cCoq_2eInit_2eNat_2eadd___24a2(V1__j,V2__i),V3__k) = cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V2__i,cCoq_2eInit_2eNat_2eadd___24a2(V1__j,V3__k)) ) ) ) ) ).
fof('Lambda.Substitution.liftO',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> cLambda_2eSubstitution_2elift__r___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__U) = V0__U ) ).
fof('Lambda.Substitution.lift_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V2__k,V1__i))
=> cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eRedexes_2eVar___24a1(V1__i),V2__k,V0__n) = cLambda_2eRedexes_2eVar___24a1(V1__i) ) ) ) ) ).
fof('Lambda.Substitution.lift_lift_rec',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__i)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V4__i,V3__n))
=> cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V4__i,V2__p),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V3__n),V1__k) = cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V3__n,V1__k),V4__i,V2__p) ) ) ) ) ) ) ).
fof('Lambda.Substitution.lift_rec_lift_rec',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> ! [V4__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__i)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__k,cCoq_2eInit_2eNat_2eadd___24a2(V4__i,V1__n)))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V4__i,V3__k))
=> cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V4__i,V1__n),V3__k,V2__p) = cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V4__i,cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__n)) ) ) ) ) ) ) ) ).
fof('Lambda.Substitution.lift_rec_preserve_comp',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U1,V1__V1)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U1,V4__m,V3__n),cLambda_2eSubstitution_2elift__rec__r___24a3(V1__V1,V4__m,V3__n)) ) ) ) ) ) ).
fof('Lambda.Substitution.lift_rec_preserve_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> cLambda_2eRedexes_2eregular___24a1(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V3__m,V2__n)) ) ) ) ) ).
fof('Lambda.Substitution.lift_subst',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> cLambda_2eSubstitution_2elift__rec__r___24a3(cLambda_2eSubstitution_2esubst__r___24a2(V0__U,V1__V),V3__n,V2__k) = cLambda_2eSubstitution_2esubst__r___24a2(cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V3__n,V2__k),cLambda_2eSubstitution_2elift__rec__r___24a3(V1__V,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V2__k)) ) ) ) ) ).
fof('Lambda.Substitution.liftrecO',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cLambda_2eSubstitution_2elift__rec__r___24a3(V0__U,V1__n,cCoq_2eInit_2eDatatypes_2eO) = V0__U ) ) ).
fof('Lambda.Substitution.subst_eq',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eRedexes_2eVar___24a1(V1__n),V0__U,V1__n) = cLambda_2eSubstitution_2elift__r___24a2(V1__n,V0__U) ) ) ).
fof('Lambda.Substitution.subst_lt',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V2__p,V1__n))
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eRedexes_2eVar___24a1(V1__n),V0__U,V2__p) = cLambda_2eRedexes_2eVar___24a1(V1__n) ) ) ) ) ).
fof('Lambda.Substitution.subst_preserve_comp',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__U2] :
( cLambda_2eRedexes_2eredexes___24t(V2__U2)
=> ! [V3__V2] :
( cLambda_2eRedexes_2eredexes___24t(V3__V2)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U1,V1__V1)
=> ( cLambda_2eRedexes_2ecomp___24a2(V2__U2,V3__V2)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eSubstitution_2esubst__r___24a2(V2__U2,V0__U1),cLambda_2eSubstitution_2esubst__r___24a2(V3__V2,V1__V1)) ) ) ) ) ) ) ).
fof('Lambda.Substitution.subst_preserve_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> ( cLambda_2eRedexes_2eregular___24a1(V1__V)
=> cLambda_2eRedexes_2eregular___24a1(cLambda_2eSubstitution_2esubst__r___24a2(V0__U,V1__V)) ) ) ) ) ).
fof('Lambda.Substitution.subst_rec_lift',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__q)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__q,V2__p))
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2elift__r___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),V0__U),V1__V,V3__q) = cLambda_2eSubstitution_2elift__r___24a2(V2__p,V0__U) ) ) ) ) ) ).
fof('Lambda.Substitution.subst_rec_preserve_comp',axiom,
! [V0__U1] :
( cLambda_2eRedexes_2eredexes___24t(V0__U1)
=> ! [V1__V1] :
( cLambda_2eRedexes_2eredexes___24t(V1__V1)
=> ! [V2__U2] :
( cLambda_2eRedexes_2eredexes___24t(V2__U2)
=> ! [V3__V2] :
( cLambda_2eRedexes_2eredexes___24t(V3__V2)
=> ( cLambda_2eRedexes_2ecomp___24a2(V0__U1,V1__V1)
=> ( cLambda_2eRedexes_2ecomp___24a2(V2__U2,V3__V2)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> cLambda_2eRedexes_2ecomp___24a2(cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U1,V2__U2,V6__n),cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V1,V3__V2,V6__n)) ) ) ) ) ) ) ) ).
fof('Lambda.Substitution.subst_rec_preserve_regular',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> ( cLambda_2eRedexes_2eregular___24a1(V1__V)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> cLambda_2eRedexes_2eregular___24a1(cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U,V1__V,V4__n)) ) ) ) ) ) ).
fof('Lambda.Substitution.subst_rec_subst_0',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V,V0__U,cCoq_2eInit_2eDatatypes_2eO),V2__W,V3__n) = cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V,V2__W,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U,V2__W,V3__n),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ) ).
fof('Lambda.Substitution.subst_rec_subst_rec',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__p)
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V,V0__U,V4__p),V2__W,cCoq_2eInit_2eNat_2eadd___24a2(V4__p,V3__n)) = cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V,V2__W,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V4__p,V3__n))),cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U,V2__W,V3__n),V4__p) ) ) ) ) ) ).
fof('Lambda.Substitution.substitution',axiom,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> cLambda_2eSubstitution_2esubst__rec__r___24a3(cLambda_2eSubstitution_2esubst__r___24a2(V0__U,V1__V),V2__W,V3__n) = cLambda_2eSubstitution_2esubst__r___24a2(cLambda_2eSubstitution_2esubst__rec__r___24a3(V0__U,V2__W,V3__n),cLambda_2eSubstitution_2esubst__rec__r___24a3(V1__V,V2__W,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) ) ) ) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_lam_10226_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10226,V_24X1),V_24X2),V_24X3) = c_24__lam__10226___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Structures.GenericMinMax.gmin_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Cube.compat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCube_2ecompat,V_24X1),V_24X2),V_24X3))
<=> cCube_2ecompat___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.le_AsB_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2ele__AsB,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_$_prop_1142_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1142,V_24X1),V_24X2) = c_24__prop__1142___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Substitution.lift_r_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eSubstitution_2elift__r,V_24X1),V_24X2) = cLambda_2eSubstitution_2elift__r___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_1134_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1134,V_24X1),V_24X2) = c_24__prop__1134___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).
fof('$adef_Lambda.Reduction.par_red1_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eReduction_2epar__red1,V_24X1),V_24X2))
<=> cLambda_2eReduction_2epar__red1___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$25369_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2425369___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_22850_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22850,V_24X1),V_24X2),V_24X3) = c_24__prop__22850___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_Lambda.Reduction.red1_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eReduction_2ered1,V_24X1),V_24X2))
<=> cLambda_2eReduction_2ered1___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_var_6_p_20171_20174_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__20171__20174,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__20171__20174___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.Exists_$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('$adef_$_lam_10218_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__10218,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__10218___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_22829_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22829,V_24X1),V_24X2),V_24X3) = c_24__prop__22829___24a3(V_24X1,V_24X2,V_24X3) ).
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_10226_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__10226,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__10226___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_25414_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__25414__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__25414__v__CANONICAL__1___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('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.Forall_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$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_1095_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1095,V_24X1),V_24X2) = c_24__prop__1095___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$119_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24119,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24119___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.DeclConstant.GT_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Lambda.Redexes.union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cLambda_2eRedexes_2eunion,V_24X1),V_24X2),V_24X3))
<=> cLambda_2eRedexes_2eunion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.PArith.BinPosDef.Pos.succ_$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('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Lambda.Terms.Abs_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2eAbs,V_24X1) = cLambda_2eTerms_2eAbs___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.D_$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('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Datatypes.prod_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_$_fix_9848_v_CANONICAL_0_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__9848__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__9848__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1129_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1129,V_24X1),V_24X2) = c_24__lam__1129___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.Exc_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Vectors.VectorDef.Forall2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$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('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_$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('$adef_$_fix_22921_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__22921__v__CANONICAL__0,V_24X1) = c_24__fix__22921__v__CANONICAL__0___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$22905_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2422905___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$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('$adef_Coq.Relations.Relation_Operators.lexprod_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2elexprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_$_lam_10218_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10218,V_24X1),V_24X2),V_24X3) = c_24__lam__10218___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.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_Lambda.Redexes.Var_$a1',axiom,
! [V_24X1] : happ(cLambda_2eRedexes_2eVar,V_24X1) = cLambda_2eRedexes_2eVar___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_22849_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22849,V_24X1),V_24X2),V_24X3) = c_24__prop__22849___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_10242_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__10242,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__10242___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_let_var_6_p_20173_20175_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__20173__20175,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__20173__20175___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Lambda.Test.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTest_2ecompare,V_24X1),V_24X2) = cLambda_2eTest_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_$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('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_1091_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1091,V_24X1),V_24X2) = c_24__prop__1091___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$19982_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2419982___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___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('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Lambda.Residuals.residuals_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cLambda_2eResiduals_2eresiduals,V_24X1),V_24X2),V_24X3))
<=> cLambda_2eResiduals_2eresiduals___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.Exists_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eExists___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31845_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31845,V_24X1),V_24X2) = c_24__lam__31845___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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_$_lam_31933_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31933,V_24X1),V_24X2) = c_24__lam__31933___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_Lambda.Substitution.subst_r_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eSubstitution_2esubst__r,V_24X1),V_24X2) = cLambda_2eSubstitution_2esubst__r___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.option_$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('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_1130_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1130,V_24X1),V_24X2) = c_24__prop__1130___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Redexes.comp_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eRedexes_2ecomp,V_24X1),V_24X2))
<=> cLambda_2eRedexes_2ecomp___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Lambda.Terms.App_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTerms_2eApp,V_24X1),V_24X2) = cLambda_2eTerms_2eApp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$16346_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416346,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2416346___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
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('$adef_Lambda.Test.test_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTest_2etest,V_24X1),V_24X2) = cLambda_2eTest_2etest___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$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('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Redexes.Fun_$a1',axiom,
! [V_24X1] : happ(cLambda_2eRedexes_2eFun,V_24X1) = cLambda_2eRedexes_2eFun___24a1(V_24X1) ).
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('$adef_$_lam_31926_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31926,V_24X1) = c_24__lam__31926___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_22848_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__22848,V_24X1),V_24X2) = c_24__prop__22848___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esquare,V_24X1) = cCoq_2eInit_2eNat_2esquare___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_$_prop_22830_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22830,V_24X1),V_24X2),V_24X3) = c_24__prop__22830___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Lambda.Substitution.insert_Var_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eSubstitution_2einsert__Var,V_24X1),V_24X2),V_24X3) = cLambda_2eSubstitution_2einsert__Var___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$19960_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2419960,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2419960___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1129_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1129,V_24X1),V_24X2),V_24X3) = c_24__lam__1129___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Lambda.Test.le_lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTest_2ele__lt,V_24X1),V_24X2) = cLambda_2eTest_2ele__lt___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_1093_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1093,V_24X1),V_24X2) = c_24__prop__1093___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$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('$adef_Coq.Init.Peano.ge_$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('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_rec_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2esumbool__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2esumbool__rec___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.In_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eIn,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eIn___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_$_lam_31823_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31823,V_24X1),V_24X2) = c_24__lam__31823___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_case_Coq.Init.Datatypes.list$25282_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2425282,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2425282___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.Tauto.A_$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('$adef_$_lam_31937_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31937,V_24X1) = c_24__lam__31937___24a1(V_24X1) ).
fof('$adef_Lambda.Reduction.par_red_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eReduction_2epar__red,V_24X1),V_24X2))
<=> cLambda_2eReduction_2epar__red___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_10234_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__10234,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__10234___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.Zdivide_pol_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eZdivide__pol,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$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('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Substitution.lift_rec_r_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eSubstitution_2elift__rec__r,V_24X1),V_24X2),V_24X3) = cLambda_2eSubstitution_2elift__rec__r___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$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('$adef_Lambda.Redexes.redexes_rect_$a1',axiom,
! [V_24X1] : happ(cLambda_2eRedexes_2eredexes__rect,V_24X1) = cLambda_2eRedexes_2eredexes__rect___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$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] :
( p(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('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31823_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31823,V_24X1) = c_24__lam__31823___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_22833_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22833,V_24X1),V_24X2),V_24X3) = c_24__prop__22833___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Lambda.Redexes.bool_max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eRedexes_2ebool__max,V_24X1),V_24X2) = cLambda_2eRedexes_2ebool__max___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Redexes.Ap_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eRedexes_2eAp,V_24X1),V_24X2),V_24X3) = cLambda_2eRedexes_2eAp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$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('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist_$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('$adef_Lambda.Redexes.regular_$a1',axiom,
! [V_24X1] :
( p(happ(cLambda_2eRedexes_2eregular,V_24X1))
<=> cLambda_2eRedexes_2eregular___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_22834_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__22834,V_24X1),V_24X2) = c_24__prop__22834___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Terms.Ref_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2eRef,V_24X1) = cLambda_2eTerms_2eRef___24a1(V_24X1) ).
fof('$adef_$_lam_10234_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10234,V_24X1),V_24X2),V_24X3) = c_24__lam__10234___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Lambda.Terms.lambda$9752_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Lambda_2eTerms_2elambda_249752,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Lambda_2eTerms_2elambda_249752___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$19977_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2419977___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___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('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.micromega.RMicromega.CPlus_$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('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_$_case_Lambda.Redexes.redexes$766_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Lambda_2eRedexes_2eredexes_24766,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Lambda_2eRedexes_2eredexes_24766___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_prop_22832_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22832,V_24X1),V_24X2),V_24X3) = c_24__prop__22832___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.int_of_int_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eint__of__int,V_24X1) = cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.Exists2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_31933_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31933,V_24X1) = c_24__lam__31933___24a1(V_24X1) ).
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('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_1094_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1094,V_24X1),V_24X2) = c_24__prop__1094___24a2(V_24X1,V_24X2) ).
fof('$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.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_lam_31845_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31845,V_24X1) = c_24__lam__31845___24a1(V_24X1) ).
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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_22831_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22831,V_24X1),V_24X2),V_24X3) = c_24__prop__22831___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_Lambda.Reduction.red_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eReduction_2ered,V_24X1),V_24X2))
<=> cLambda_2eReduction_2ered___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Lambda.Redexes.redexes_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cLambda_2eRedexes_2eredexes__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cLambda_2eRedexes_2eredexes__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.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.ZArith.Zlogarithm.log_inf_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Init.Decimal.uint_of_uint_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_lam_10242_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__10242,V_24X1),V_24X2),V_24X3) = c_24__lam__10242___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$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('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$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('$adef_$_prop_1092_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1092,V_24X1),V_24X2) = c_24__prop__1092___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_31926_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31926,V_24X1),V_24X2) = c_24__lam__31926___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Substitution.subst_rec_r_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eSubstitution_2esubst__rec__r,V_24X1),V_24X2),V_24X3) = cLambda_2eSubstitution_2esubst__rec__r___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Terms.insert_Ref_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2einsert__Ref,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2einsert__Ref___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$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('$adef_Coq.ZArith.BinIntDef.Z.div_$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('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1137_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1137,V_24X1),V_24X2) = c_24__lam__1137___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_22828_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__22828,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__22828___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$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('$adef_Coq.Lists.List.fold_right_$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('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_1096_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1096,V_24X1),V_24X2) = c_24__prop__1096___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.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.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_$_prop_32024_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__32024,V_24X1),V_24X2) = c_24__prop__32024___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sigT_$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('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Lambda.Redexes.redexes_rec_$a1',axiom,
! [V_24X1] : happ(cLambda_2eRedexes_2eredexes__rec,V_24X1) = cLambda_2eRedexes_2eredexes__rec___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('$adef_Coq.QArith.QArith_base.Qmake_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Redexes.sub_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cLambda_2eRedexes_2esub,V_24X1),V_24X2))
<=> cLambda_2eRedexes_2esub___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_902_v_CANONICAL_0_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__902__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__902__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_1138_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1138,V_24X1),V_24X2) = c_24__prop__1138___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1133_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1133,V_24X1),V_24X2) = c_24__lam__1133___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Terms.relocate_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2erelocate,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2erelocate___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$tdef_$_type_9112',axiom,
! [V_24Y] :
( c_24__type__9112___24t(V_24Y)
<=> t(V_24Y,c_24__type__9112) ) ).
fof('$tdef_$_type_17887',axiom,
! [V_24Y] :
( c_24__type__17887___24t(V_24Y)
<=> t(V_24Y,c_24__type__17887) ) ).
fof('$tdef_$_type_1147',axiom,
! [V_24Y] :
( c_24__type__1147___24t(V_24Y)
<=> t(V_24Y,c_24__type__1147) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23237',axiom,
! [V_24Y] :
( c_24__type__23237___24t(V_24Y)
<=> t(V_24Y,c_24__type__23237) ) ).
fof('$tdef_$_type_23220',axiom,
! [V_24Y] :
( c_24__type__23220___24t(V_24Y)
<=> t(V_24Y,c_24__type__23220) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_2682',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2682___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2682___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23475',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23475___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23475___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Lambda.Terms.lambda',axiom,
! [V_24Y] :
( cLambda_2eTerms_2elambda___24t(V_24Y)
<=> t(V_24Y,cLambda_2eTerms_2elambda) ) ).
fof('$tdef_$_type_23085',axiom,
! [V_24Y] :
( c_24__type__23085___24t(V_24Y)
<=> t(V_24Y,c_24__type__23085) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_4795',axiom,
! [V_24Y] :
( c_24__type__4795___24t(V_24Y)
<=> t(V_24Y,c_24__type__4795) ) ).
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_$_type_10075',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__10075___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__10075___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_4882',axiom,
! [V_24Y] :
( c_24__type__4882___24t(V_24Y)
<=> t(V_24Y,c_24__type__4882) ) ).
fof('$tdef_$_type_31910',axiom,
! [V_24Y] :
( c_24__type__31910___24t(V_24Y)
<=> t(V_24Y,c_24__type__31910) ) ).
fof('$tdef_$_type_23078',axiom,
! [V_24Y] :
( c_24__type__23078___24t(V_24Y)
<=> t(V_24Y,c_24__type__23078) ) ).
fof('$tdef_$_type_10141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__10141___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__10141___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21444',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21444___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21444___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_9122',axiom,
! [V_24Y] :
( c_24__type__9122___24t(V_24Y)
<=> t(V_24Y,c_24__type__9122) ) ).
fof('$tdef_$_type_1140',axiom,
! [V_24Y] :
( c_24__type__1140___24t(V_24Y)
<=> t(V_24Y,c_24__type__1140) ) ).
fof('$tdef_$_type_2855',axiom,
! [V_24Y] :
( c_24__type__2855___24t(V_24Y)
<=> t(V_24Y,c_24__type__2855) ) ).
fof('$tdef_$_type_18701',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18701___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_13685',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__13685___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__13685___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_31135',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31135___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31135___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10104',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__10104___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__10104___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_10781',axiom,
! [V_24Y] :
( c_24__type__10781___24t(V_24Y)
<=> t(V_24Y,c_24__type__10781) ) ).
fof('$tdef_$_type_23051',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23051___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_31610',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__31610___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__31610___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_23083',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23083___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23083___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28439',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__28439___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__28439___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_25084',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25084___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25084___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30123',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__30123___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__30123___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_Lambda.Redexes.redexes',axiom,
! [V_24Y] :
( cLambda_2eRedexes_2eredexes___24t(V_24Y)
<=> t(V_24Y,cLambda_2eRedexes_2eredexes) ) ).
fof('$tdef_$_type_37',axiom,
! [V_24Y] :
( c_24__type__37___24t(V_24Y)
<=> t(V_24Y,c_24__type__37) ) ).
fof('$tdef_$_type_16283',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16283___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16283___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_24986',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24986___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24986___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).
fof('$tdef_$_type_8808',axiom,
! [V_24Y] :
( c_24__type__8808___24t(V_24Y)
<=> t(V_24Y,c_24__type__8808) ) ).
fof('$tdef_$_type_16233',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16233___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16233___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_4901',axiom,
! [V_24Y] :
( c_24__type__4901___24t(V_24Y)
<=> t(V_24Y,c_24__type__4901) ) ).
fof('$tdef_$_type_16851',axiom,
! [V_24Y] :
( c_24__type__16851___24t(V_24Y)
<=> t(V_24Y,c_24__type__16851) ) ).
fof('$tdef_$_type_2954',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2954___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2954___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5466',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5466___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5466___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1067',axiom,
! [V_24Y] :
( c_24__type__1067___24t(V_24Y)
<=> t(V_24Y,c_24__type__1067) ) ).
fof('$tdef_$_type_27747',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__27747___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__27747___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_13202',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13202___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13202___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_12455',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12455___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12455___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_16781',axiom,
! [V_24Y] :
( c_24__type__16781___24t(V_24Y)
<=> t(V_24Y,c_24__type__16781) ) ).
fof('$tdef_$_type_12936',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12936___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12936___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_23510',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23510___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23510___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13094',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13094___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13094___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_30827',axiom,
! [V_24Y] :
( c_24__type__30827___24t(V_24Y)
<=> t(V_24Y,c_24__type__30827) ) ).
fof('$tdef_$_type_1380',axiom,
! [V_24Y] :
( c_24__type__1380___24t(V_24Y)
<=> t(V_24Y,c_24__type__1380) ) ).
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_8784',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8784___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8784___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31890',axiom,
! [V_24Y] :
( c_24__type__31890___24t(V_24Y)
<=> t(V_24Y,c_24__type__31890) ) ).
fof('$tdef_$_type_15936',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15936___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15936___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30838',axiom,
! [V_24Y] :
( c_24__type__30838___24t(V_24Y)
<=> t(V_24Y,c_24__type__30838) ) ).
fof('$tdef_$_type_2722',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2722___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2722___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19294',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__19294___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__19294___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5559',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__5559___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__5559___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31840',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31840___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31840___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5035',axiom,
! [V_24Y] :
( c_24__type__5035___24t(V_24Y)
<=> t(V_24Y,c_24__type__5035) ) ).
fof('$tdef_$_type_10529',axiom,
! [V_24Y] :
( c_24__type__10529___24t(V_24Y)
<=> t(V_24Y,c_24__type__10529) ) ).
fof('$tdef_$_type_20858',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20858___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__20858___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_31092',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31092___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31092___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_4880',axiom,
! [V_24Y] :
( c_24__type__4880___24t(V_24Y)
<=> t(V_24Y,c_24__type__4880) ) ).
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_23560',axiom,
! [V_24Y] :
( c_24__type__23560___24t(V_24Y)
<=> t(V_24Y,c_24__type__23560) ) ).
fof('$tdef_$_type_16191',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16191___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16191___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12892',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12892___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12892___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_9930',axiom,
! [V_24Y] :
( c_24__type__9930___24t(V_24Y)
<=> t(V_24Y,c_24__type__9930) ) ).
fof('$tdef_$_type_23572',axiom,
! [V_24Y] :
( c_24__type__23572___24t(V_24Y)
<=> t(V_24Y,c_24__type__23572) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_$_type_19866',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__19866___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__19866___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23058',axiom,
! [V_24Y] :
( c_24__type__23058___24t(V_24Y)
<=> t(V_24Y,c_24__type__23058) ) ).
fof('$tdef_$_type_4775',axiom,
! [V_24Y] :
( c_24__type__4775___24t(V_24Y)
<=> t(V_24Y,c_24__type__4775) ) ).
fof('$tdef_$_type_16799',axiom,
! [V_24Y] :
( c_24__type__16799___24t(V_24Y)
<=> t(V_24Y,c_24__type__16799) ) ).
fof('$tdef_$_type_12954',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12954___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12954___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_22172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22172___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22172___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31862',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31862___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31862___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13148___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13148___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23134',axiom,
! [V_24Y] :
( c_24__type__23134___24t(V_24Y)
<=> t(V_24Y,c_24__type__23134) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_1112',axiom,
! [V_24Y] :
( c_24__type__1112___24t(V_24Y)
<=> t(V_24Y,c_24__type__1112) ) ).
fof('$tdef_$_type_31453',axiom,
! [V_24Y] :
( c_24__type__31453___24t(V_24Y)
<=> t(V_24Y,c_24__type__31453) ) ).
fof('$tdef_$_type_17588',axiom,
! [V_24Y] :
( c_24__type__17588___24t(V_24Y)
<=> t(V_24Y,c_24__type__17588) ) ).
fof('$tdef_$_type_20436',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__20436___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__20436___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_31554',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__31554___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__31554___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
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_$_type_243',axiom,
! [V_24Y] :
( c_24__type__243___24t(V_24Y)
<=> t(V_24Y,c_24__type__243) ) ).
fof('$tdef_$_type_31616',axiom,
! [V_24Y] :
( c_24__type__31616___24t(V_24Y)
<=> t(V_24Y,c_24__type__31616) ) ).
fof('$tdef_$_type_16820',axiom,
! [V_24Y] :
( c_24__type__16820___24t(V_24Y)
<=> t(V_24Y,c_24__type__16820) ) ).
fof('$tdef_$_type_1166',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1166___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1166___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2816',axiom,
! [V_24Y] :
( c_24__type__2816___24t(V_24Y)
<=> t(V_24Y,c_24__type__2816) ) ).
fof('$tdef_$_type_31986',axiom,
! [V_24Y] :
( c_24__type__31986___24t(V_24Y)
<=> t(V_24Y,c_24__type__31986) ) ).
fof('$tdef_$_type_28785',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__28785___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__28785___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23428',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23428___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23428___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_23092',axiom,
! [V_24Y] :
( c_24__type__23092___24t(V_24Y)
<=> t(V_24Y,c_24__type__23092) ) ).
fof('$tdef_$_type_31400',axiom,
! [V_24Y] :
( c_24__type__31400___24t(V_24Y)
<=> t(V_24Y,c_24__type__31400) ) ).
fof('$tdef_$_type_23056',axiom,
! [V_24Y] :
( c_24__type__23056___24t(V_24Y)
<=> t(V_24Y,c_24__type__23056) ) ).
fof('$tdef_$_type_5909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5909___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20741',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20741___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20741___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_17360',axiom,
! [V_24Y] :
( c_24__type__17360___24t(V_24Y)
<=> t(V_24Y,c_24__type__17360) ) ).
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('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_9386',axiom,
! [V_24Y] :
( c_24__type__9386___24t(V_24Y)
<=> t(V_24Y,c_24__type__9386) ) ).
fof('$tdef_$_type_17542',axiom,
! [V_24Y] :
( c_24__type__17542___24t(V_24Y)
<=> t(V_24Y,c_24__type__17542) ) ).
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_$_type_175',axiom,
! [V_24Y] :
( c_24__type__175___24t(V_24Y)
<=> t(V_24Y,c_24__type__175) ) ).
fof('$tdef_$_type_20921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20921___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2506',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2506___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2506___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1070',axiom,
! [V_24Y] :
( c_24__type__1070___24t(V_24Y)
<=> t(V_24Y,c_24__type__1070) ) ).
fof('$tdef_$_type_31341',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31341___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31341___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_237',axiom,
! [V_24Y] :
( c_24__type__237___24t(V_24Y)
<=> t(V_24Y,c_24__type__237) ) ).
fof('$tdef_$_type_20397',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__20397___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__20397___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_2452',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__2452___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__2452___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29108',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__29108___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__29108___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('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4701',axiom,
! [V_24Y] :
( c_24__type__4701___24t(V_24Y)
<=> t(V_24Y,c_24__type__4701) ) ).
fof('$tdef_$_type_8822',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8822___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8822___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16141___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16141___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_19469',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19469___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19469___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16816',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16816___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16816___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31868',axiom,
! [V_24Y] :
( c_24__type__31868___24t(V_24Y)
<=> t(V_24Y,c_24__type__31868) ) ).
fof('$tdef_$_type_10786',axiom,
! [V_24Y] :
( c_24__type__10786___24t(V_24Y)
<=> t(V_24Y,c_24__type__10786) ) ).
fof('$tdef_$_type_42',axiom,
! [V_24Y] :
( c_24__type__42___24t(V_24Y)
<=> t(V_24Y,c_24__type__42) ) ).
fof('$tdef_$_type_12910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12910___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12910___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10144',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10144___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10144___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31427',axiom,
! [V_24Y] :
( c_24__type__31427___24t(V_24Y)
<=> t(V_24Y,c_24__type__31427) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_9399',axiom,
! [V_24Y] :
( c_24__type__9399___24t(V_24Y)
<=> t(V_24Y,c_24__type__9399) ) ).
fof('$tdef_$_type_4757',axiom,
! [V_24Y] :
( c_24__type__4757___24t(V_24Y)
<=> t(V_24Y,c_24__type__4757) ) ).
fof('$tdef_$_type_23512',axiom,
! [V_24Y] :
( c_24__type__23512___24t(V_24Y)
<=> t(V_24Y,c_24__type__23512) ) ).
fof('$tdef_$_type_21569',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21569___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21569___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_16592',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16592___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16592___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_31857',axiom,
! [V_24Y] :
( c_24__type__31857___24t(V_24Y)
<=> t(V_24Y,c_24__type__31857) ) ).
fof('$tdef_$_type_15566',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__15566___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__15566___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_6146',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6146___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6146___24a1(V_24X1)) ) ).
fof('$tdef_$_type_993',axiom,
! [V_24Y] :
( c_24__type__993___24t(V_24Y)
<=> t(V_24Y,c_24__type__993) ) ).
fof('$tdef_$_type_1125',axiom,
! [V_24Y] :
( c_24__type__1125___24t(V_24Y)
<=> t(V_24Y,c_24__type__1125) ) ).
fof('$tdef_$_type_30975',axiom,
! [V_24Y] :
( c_24__type__30975___24t(V_24Y)
<=> t(V_24Y,c_24__type__30975) ) ).
fof('$tdef_$_type_21819',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21819___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21819___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_13286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13286___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_16468',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16468___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16468___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_8698',axiom,
! [V_24Y] :
( c_24__type__8698___24t(V_24Y)
<=> t(V_24Y,c_24__type__8698) ) ).
fof('$tdef_$_type_23541',axiom,
! [V_24Y] :
( c_24__type__23541___24t(V_24Y)
<=> t(V_24Y,c_24__type__23541) ) ).
fof('$tdef_$_type_1015',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1015___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1015___24a2(V_24X1,V_24X2)) ) ).
fof('$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_31271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31271___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_12635',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12635___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__12635___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_3161',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__3161___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__3161___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22188',axiom,
! [V_24Y] :
( c_24__type__22188___24t(V_24Y)
<=> t(V_24Y,c_24__type__22188) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_31964',axiom,
! [V_24Y] :
( c_24__type__31964___24t(V_24Y)
<=> t(V_24Y,c_24__type__31964) ) ).
fof('$tdef_$_type_123',axiom,
! [V_24Y] :
( c_24__type__123___24t(V_24Y)
<=> t(V_24Y,c_24__type__123) ) ).
fof('$tdef_$_type_17883',axiom,
! [V_24Y] :
( c_24__type__17883___24t(V_24Y)
<=> t(V_24Y,c_24__type__17883) ) ).
fof('$tdef_$_type_30792',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__30792___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__30792___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_24868',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24868___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24868___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_23355',axiom,
! [V_24Y] :
( c_24__type__23355___24t(V_24Y)
<=> t(V_24Y,c_24__type__23355) ) ).
fof('$tdef_$_type_21694',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21694___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21694___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_32034',axiom,
! [V_24Y] :
( c_24__type__32034___24t(V_24Y)
<=> t(V_24Y,c_24__type__32034) ) ).
fof('$tdef_$_type_1219',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1219___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1219___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15761',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__15761___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__15761___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_20358',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__20358___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__20358___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_5254',axiom,
! [V_24Y] :
( c_24__type__5254___24t(V_24Y)
<=> t(V_24Y,c_24__type__5254) ) ).
fof('$tdef_$_type_23209',axiom,
! [V_24Y] :
( c_24__type__23209___24t(V_24Y)
<=> t(V_24Y,c_24__type__23209) ) ).
fof('$tdef_$_type_16838',axiom,
! [V_24Y] :
( c_24__type__16838___24t(V_24Y)
<=> t(V_24Y,c_24__type__16838) ) ).
fof('$tdef_$_type_23313',axiom,
! [V_24Y] :
( c_24__type__23313___24t(V_24Y)
<=> t(V_24Y,c_24__type__23313) ) ).
fof('$tdef_$_type_22924',axiom,
! [V_24Y] :
( c_24__type__22924___24t(V_24Y)
<=> t(V_24Y,c_24__type__22924) ) ).
fof('$tdef_$_type_19803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__19803___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__19803___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6002',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__6002___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__6002___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23003',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23003___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23003___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8777',axiom,
! [V_24Y] :
( c_24__type__8777___24t(V_24Y)
<=> t(V_24Y,c_24__type__8777) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_3119',axiom,
! [V_24Y] :
( c_24__type__3119___24t(V_24Y)
<=> t(V_24Y,c_24__type__3119) ) ).
fof('$tdef_$_type_15922',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15922___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15922___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1412',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1412___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1412___24a1(V_24X1)) ) ).
fof('$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_19686',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__19686___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__19686___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_19119',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__19119___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__19119___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_3951',axiom,
! [V_24Y] :
( c_24__type__3951___24t(V_24Y)
<=> t(V_24Y,c_24__type__3951) ) ).
fof('$tdef_$_type_4682',axiom,
! [V_24Y] :
( c_24__type__4682___24t(V_24Y)
<=> t(V_24Y,c_24__type__4682) ) ).
fof('$tdef_$_type_3872',axiom,
! [V_24Y] :
( c_24__type__3872___24t(V_24Y)
<=> t(V_24Y,c_24__type__3872) ) ).
fof('$tdef_$_type_17812',axiom,
! [V_24Y] :
( c_24__type__17812___24t(V_24Y)
<=> t(V_24Y,c_24__type__17812) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_17845',axiom,
! [V_24Y] :
( c_24__type__17845___24t(V_24Y)
<=> t(V_24Y,c_24__type__17845) ) ).
fof('$tdef_$_type_3955',axiom,
! [V_24Y] :
( c_24__type__3955___24t(V_24Y)
<=> t(V_24Y,c_24__type__3955) ) ).
fof('$tdef_$_type_13898',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__13898___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__13898___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_9167',axiom,
! [V_24Y] :
( c_24__type__9167___24t(V_24Y)
<=> t(V_24Y,c_24__type__9167) ) ).
fof('$tdef_$_type_9331',axiom,
! [V_24Y] :
( c_24__type__9331___24t(V_24Y)
<=> t(V_24Y,c_24__type__9331) ) ).
fof('$tdef_$_type_15158',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__15158___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__15158___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_3863',axiom,
! [V_24Y] :
( c_24__type__3863___24t(V_24Y)
<=> t(V_24Y,c_24__type__3863) ) ).
fof('$tdef_$_type_17377',axiom,
! [V_24Y] :
( c_24__type__17377___24t(V_24Y)
<=> t(V_24Y,c_24__type__17377) ) ).
fof('$tdef_$_type_1029',axiom,
! [V_24Y] :
( c_24__type__1029___24t(V_24Y)
<=> t(V_24Y,c_24__type__1029) ) ).
fof('$tdef_$_type_19623',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__19623___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__19623___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_19026',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19026___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19026___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_17278',axiom,
! [V_24Y] :
( c_24__type__17278___24t(V_24Y)
<=> t(V_24Y,c_24__type__17278) ) ).
fof('$tdef_$_type_21194',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21194___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21194___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_19376',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19376___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19376___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_19201',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__19201___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__19201___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1958',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1958___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1958___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9326',axiom,
! [V_24Y] :
( c_24__type__9326___24t(V_24Y)
<=> t(V_24Y,c_24__type__9326) ) ).
fof('$tdef_$_type_14306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14306___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14306___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_16091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16091___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16091___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_28093',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__28093___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__28093___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31125',axiom,
! [V_24Y] :
( c_24__type__31125___24t(V_24Y)
<=> t(V_24Y,c_24__type__31125) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_7132',axiom,
! [V_24Y] :
( c_24__type__7132___24t(V_24Y)
<=> t(V_24Y,c_24__type__7132) ) ).
fof('$tdef_$_type_23043',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23043___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23043___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).
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_$_type_24893',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24893___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24893___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_2059',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2059___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2059___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20804',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20804___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__20804___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21930',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21930___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21930___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_22228',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22228___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22228___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31954',axiom,
! [V_24Y] :
( c_24__type__31954___24t(V_24Y)
<=> t(V_24Y,c_24__type__31954) ) ).
fof('$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_23185',axiom,
! [V_24Y] :
( c_24__type__23185___24t(V_24Y)
<=> t(V_24Y,c_24__type__23185) ) ).
fof('$tdef_$_type_19749',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__19749___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__19749___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_31940',axiom,
! [V_24Y] :
( c_24__type__31940___24t(V_24Y)
<=> t(V_24Y,c_24__type__31940) ) ).
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_$_type_31357',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31357___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31357___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3999',axiom,
! [V_24Y] :
( c_24__type__3999___24t(V_24Y)
<=> t(V_24Y,c_24__type__3999) ) ).
fof('$tdef_$_type_19989',axiom,
! [V_24Y] :
( c_24__type__19989___24t(V_24Y)
<=> t(V_24Y,c_24__type__19989) ) ).
fof('$tdef_$_type_1051',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1051___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1051___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2842',axiom,
! [V_24Y] :
( c_24__type__2842___24t(V_24Y)
<=> t(V_24Y,c_24__type__2842) ) ).
fof('$tdef_$_type_8990',axiom,
! [V_24Y] :
( c_24__type__8990___24t(V_24Y)
<=> t(V_24Y,c_24__type__8990) ) ).
fof('$tdef_$_type_31363',axiom,
! [V_24Y] :
( c_24__type__31363___24t(V_24Y)
<=> t(V_24Y,c_24__type__31363) ) ).
fof('$tdef_$_type_4029',axiom,
! [V_24Y] :
( c_24__type__4029___24t(V_24Y)
<=> t(V_24Y,c_24__type__4029) ) ).
fof('$tdef_$_type_4715',axiom,
! [V_24Y] :
( c_24__type__4715___24t(V_24Y)
<=> t(V_24Y,c_24__type__4715) ) ).
fof('$tdef_$_type_30969',axiom,
! [V_24Y] :
( c_24__type__30969___24t(V_24Y)
<=> t(V_24Y,c_24__type__30969) ) ).
fof('$tdef_$_type_16612',axiom,
! [V_24Y] :
( c_24__type__16612___24t(V_24Y)
<=> t(V_24Y,c_24__type__16612) ) ).
fof('$tdef_$_type_13235',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13235___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13235___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9328',axiom,
! [V_24Y] :
( c_24__type__9328___24t(V_24Y)
<=> t(V_24Y,c_24__type__9328) ) ).
fof('$tdef_$_type_17880',axiom,
! [V_24Y] :
( c_24__type__17880___24t(V_24Y)
<=> t(V_24Y,c_24__type__17880) ) ).
fof('$tdef_$_type_31386',axiom,
! [V_24Y] :
( c_24__type__31386___24t(V_24Y)
<=> t(V_24Y,c_24__type__31386) ) ).
fof('$tdef_$_type_1402',axiom,
! [V_24Y] :
( c_24__type__1402___24t(V_24Y)
<=> t(V_24Y,c_24__type__1402) ) ).
fof('$tdef_$_type_31444',axiom,
! [V_24Y] :
( c_24__type__31444___24t(V_24Y)
<=> t(V_24Y,c_24__type__31444) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31397',axiom,
! [V_24Y] :
( c_24__type__31397___24t(V_24Y)
<=> t(V_24Y,c_24__type__31397) ) ).
fof('$tdef_$_type_12823',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12823___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12823___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15353',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__15353___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__15353___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_4868',axiom,
! [V_24Y] :
( c_24__type__4868___24t(V_24Y)
<=> t(V_24Y,c_24__type__4868) ) ).
fof('$tdef_$_type_12869',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12869___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12869___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_7135',axiom,
! [V_24Y] :
( c_24__type__7135___24t(V_24Y)
<=> t(V_24Y,c_24__type__7135) ) ).
fof('$tdef_$_type_18065',axiom,
! [V_24Y] :
( c_24__type__18065___24t(V_24Y)
<=> t(V_24Y,c_24__type__18065) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_8673',axiom,
! [V_24Y] :
( c_24__type__8673___24t(V_24Y)
<=> t(V_24Y,c_24__type__8673) ) ).
fof('$tdef_$_type_30841',axiom,
! [V_24Y] :
( c_24__type__30841___24t(V_24Y)
<=> t(V_24Y,c_24__type__30841) ) ).
fof('$tdef_$_type_24166',axiom,
! [V_24Y] :
( c_24__type__24166___24t(V_24Y)
<=> t(V_24Y,c_24__type__24166) ) ).
fof('$tdef_$_type_1857',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__1857___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__1857___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_10285',axiom,
! [V_24Y] :
( c_24__type__10285___24t(V_24Y)
<=> t(V_24Y,c_24__type__10285) ) ).
fof('$tdef_$_type_7127',axiom,
! [V_24Y] :
( c_24__type__7127___24t(V_24Y)
<=> t(V_24Y,c_24__type__7127) ) ).
fof('$tdef_$_type_31456',axiom,
! [V_24Y] :
( c_24__type__31456___24t(V_24Y)
<=> t(V_24Y,c_24__type__31456) ) ).
fof('$tdef_$_type_12572',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12572___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__12572___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30446',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__30446___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__30446___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_29454',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__29454___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__29454___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_17873',axiom,
! [V_24Y] :
( c_24__type__17873___24t(V_24Y)
<=> t(V_24Y,c_24__type__17873) ) ).
fof('$tdef_$_type_27055',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__27055___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__27055___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_3856',axiom,
! [V_24Y] :
( c_24__type__3856___24t(V_24Y)
<=> t(V_24Y,c_24__type__3856) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9338',axiom,
! [V_24Y] :
( c_24__type__9338___24t(V_24Y)
<=> t(V_24Y,c_24__type__9338) ) ).
fof('$tdef_$_type_3996',axiom,
! [V_24Y] :
( c_24__type__3996___24t(V_24Y)
<=> t(V_24Y,c_24__type__3996) ) ).
fof('$tdef_$_type_31884',axiom,
! [V_24Y] :
( c_24__type__31884___24t(V_24Y)
<=> t(V_24Y,c_24__type__31884) ) ).
fof('$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_31818',axiom,
! [V_24Y] :
( c_24__type__31818___24t(V_24Y)
<=> t(V_24Y,c_24__type__31818) ) ).
fof('$tdef_$_type_8951',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8951___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8951___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8868',axiom,
! [V_24Y] :
( c_24__type__8868___24t(V_24Y)
<=> t(V_24Y,c_24__type__8868) ) ).
fof('$tdef_$_type_20678',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__20678___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__20678___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_24771',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24771___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24771___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_30809',axiom,
! [V_24Y] :
( c_24__type__30809___24t(V_24Y)
<=> t(V_24Y,c_24__type__30809) ) ).
fof('$tdef_$_type_22314',axiom,
! [V_24Y] :
( c_24__type__22314___24t(V_24Y)
<=> t(V_24Y,c_24__type__22314) ) ).
fof('$tdef_$_type_22236',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22236___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22236___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_9117',axiom,
! [V_24Y] :
( c_24__type__9117___24t(V_24Y)
<=> t(V_24Y,c_24__type__9117) ) ).
fof('$tdef_$_type_2708',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2708___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2708___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8730',axiom,
! [V_24Y] :
( c_24__type__8730___24t(V_24Y)
<=> t(V_24Y,c_24__type__8730) ) ).
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_$_type_23324',axiom,
! [V_24Y] :
( c_24__type__23324___24t(V_24Y)
<=> t(V_24Y,c_24__type__23324) ) ).
fof('$tdef_$_type_31488',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31488___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31488___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_20185',axiom,
! [V_24Y] :
( c_24__type__20185___24t(V_24Y)
<=> t(V_24Y,c_24__type__20185) ) ).
fof('$tdef_$_type_1209',axiom,
! [V_24Y] :
( c_24__type__1209___24t(V_24Y)
<=> t(V_24Y,c_24__type__1209) ) ).
fof('$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_31797',axiom,
! [V_24Y] :
( c_24__type__31797___24t(V_24Y)
<=> t(V_24Y,c_24__type__31797) ) ).
fof('$tdef_$_type_31631',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31631___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31631___24a1(V_24X1)) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_23109',axiom,
! [V_24Y] :
( c_24__type__23109___24t(V_24Y)
<=> t(V_24Y,c_24__type__23109) ) ).
fof('$tdef_$_type_16698',axiom,
! [V_24Y] :
( c_24__type__16698___24t(V_24Y)
<=> t(V_24Y,c_24__type__16698) ) ).
fof('$tdef_$_type_31765',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31765___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31765___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22982',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22982___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22982___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_23008',axiom,
! [V_24Y] :
( c_24__type__23008___24t(V_24Y)
<=> t(V_24Y,c_24__type__23008) ) ).
fof('$tdef_$_type_18933',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18933___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18933___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32017',axiom,
! [V_24Y] :
( c_24__type__32017___24t(V_24Y)
<=> t(V_24Y,c_24__type__32017) ) ).
fof('$tdef_$_type_23528',axiom,
! [V_24Y] :
( c_24__type__23528___24t(V_24Y)
<=> t(V_24Y,c_24__type__23528) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_22244',axiom,
! [V_24Y] :
( c_24__type__22244___24t(V_24Y)
<=> t(V_24Y,c_24__type__22244) ) ).
fof('$tdef_$_type_31392',axiom,
! [V_24Y] :
( c_24__type__31392___24t(V_24Y)
<=> t(V_24Y,c_24__type__31392) ) ).
fof('$tdef_$_type_18656',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18656___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18656___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10778',axiom,
! [V_24Y] :
( c_24__type__10778___24t(V_24Y)
<=> t(V_24Y,c_24__type__10778) ) ).
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_$_type_23204',axiom,
! [V_24Y] :
( c_24__type__23204___24t(V_24Y)
<=> t(V_24Y,c_24__type__23204) ) ).
fof('$tdef_$_type_8417',axiom,
! [V_24Y] :
( c_24__type__8417___24t(V_24Y)
<=> t(V_24Y,c_24__type__8417) ) ).
fof('$tdef_$_type_23097',axiom,
! [V_24Y] :
( c_24__type__23097___24t(V_24Y)
<=> t(V_24Y,c_24__type__23097) ) ).
fof('$tdef_$_type_35',axiom,
! [V_24Y] :
( c_24__type__35___24t(V_24Y)
<=> t(V_24Y,c_24__type__35) ) ).
fof('$tdef_$_type_18589',axiom,
! [V_24Y] :
( c_24__type__18589___24t(V_24Y)
<=> t(V_24Y,c_24__type__18589) ) ).
fof('$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_27401',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__27401___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__27401___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_31306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31306___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31306___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14519',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__14519___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__14519___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_8815',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8815___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8815___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26040',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26040___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26040___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.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_24796',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24796___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24796___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_3898',axiom,
! [V_24Y] :
( c_24__type__3898___24t(V_24Y)
<=> t(V_24Y,c_24__type__3898) ) ).
fof('$tdef_$_type_29800',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__29800___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__29800___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_1378',axiom,
! [V_24Y] :
( c_24__type__1378___24t(V_24Y)
<=> t(V_24Y,c_24__type__1378) ) ).
fof('$tdef_$_type_5734',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__5734___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__5734___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_$_type_31409',axiom,
! [V_24Y] :
( c_24__type__31409___24t(V_24Y)
<=> t(V_24Y,c_24__type__31409) ) ).
fof('$tdef_$_type_13259',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13259___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13259___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_13064',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13064___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13064___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_4800',axiom,
! [V_24Y] :
( c_24__type__4800___24t(V_24Y)
<=> t(V_24Y,c_24__type__4800) ) ).
fof('$tdef_$_type_23201',axiom,
! [V_24Y] :
( c_24__type__23201___24t(V_24Y)
<=> t(V_24Y,c_24__type__23201) ) ).
fof('$tdef_$_type_26732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26732___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31232',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31232___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31232___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7124',axiom,
! [V_24Y] :
( c_24__type__7124___24t(V_24Y)
<=> t(V_24Y,c_24__type__7124) ) ).
fof('$tdef_$_type_15903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__15903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__15903___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31628',axiom,
! [V_24Y] :
( c_24__type__31628___24t(V_24Y)
<=> t(V_24Y,c_24__type__31628) ) ).
fof('$tdef_$_type_10792',axiom,
! [V_24Y] :
( c_24__type__10792___24t(V_24Y)
<=> t(V_24Y,c_24__type__10792) ) ).
fof('$tdef_$_type_2729',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2729___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2729___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12518',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12518___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12518___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2850',axiom,
! [V_24Y] :
( c_24__type__2850___24t(V_24Y)
<=> t(V_24Y,c_24__type__2850) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_$_type_240',axiom,
! [V_24Y] :
( c_24__type__240___24t(V_24Y)
<=> t(V_24Y,c_24__type__240) ) ).
fof('$tdef_$_type_16548',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16548___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16548___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31017',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31017___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31017___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22180',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22180___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22180___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_66',axiom,
! [V_24Y] :
( c_24__type__66___24t(V_24Y)
<=> t(V_24Y,c_24__type__66) ) ).
fof('$tdef_$_type_1236',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1236___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1236___24a1(V_24X1)) ) ).
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_$_type_30862',axiom,
! [V_24Y] :
( c_24__type__30862___24t(V_24Y)
<=> t(V_24Y,c_24__type__30862) ) ).
fof('$tdef_$_type_17432',axiom,
! [V_24Y] :
( c_24__type__17432___24t(V_24Y)
<=> t(V_24Y,c_24__type__17432) ) ).
fof('$tdef_$_type_14111',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14111___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14111___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_13118',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13118___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13118___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_18729',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__18729___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__18729___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_16512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__16512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__16512___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_24935',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24935___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24935___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21319',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__21319___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__21319___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_1407',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1407___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1407___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2149',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2149___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31835',axiom,
! [V_24Y] :
( c_24__type__31835___24t(V_24Y)
<=> t(V_24Y,c_24__type__31835) ) ).
fof('$tdef_$_type_16777',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16777___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16777___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22864',axiom,
! [V_24Y] :
( c_24__type__22864___24t(V_24Y)
<=> t(V_24Y,c_24__type__22864) ) ).
fof('$tdef_$_type_31380',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31380___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31380___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1211',axiom,
! [V_24Y] :
( c_24__type__1211___24t(V_24Y)
<=> t(V_24Y,c_24__type__1211) ) ).
fof('$tdef_$_type_12392',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12392___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12392___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30835',axiom,
! [V_24Y] :
( c_24__type__30835___24t(V_24Y)
<=> t(V_24Y,c_24__type__30835) ) ).
fof('$tdef_$_type_23217',axiom,
! [V_24Y] :
( c_24__type__23217___24t(V_24Y)
<=> t(V_24Y,c_24__type__23217) ) ).
fof('$tdef_$_type_1214',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1214___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1214___24a1(V_24X1)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24Y] :
( c_24__type__92___24t(V_24Y)
<=> t(V_24Y,c_24__type__92) ) ).
fof('$tdef_$_type_17580',axiom,
! [V_24Y] :
( c_24__type__17580___24t(V_24Y)
<=> t(V_24Y,c_24__type__17580) ) ).
fof('$tdef_$_type_5827',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5827___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5827___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2250',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2250___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2250___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8970___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8970___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_31052',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31052___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31052___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_17067',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17067___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17067___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13178',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13178___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13178___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3920',axiom,
! [V_24Y] :
( c_24__type__3920___24t(V_24Y)
<=> t(V_24Y,c_24__type__3920) ) ).
fof('$tdef_$_type_23253',axiom,
! [V_24Y] :
( c_24__type__23253___24t(V_24Y)
<=> t(V_24Y,c_24__type__23253) ) ).
fof('$tdef_$_type_14732',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__14732___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__14732___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_9960',axiom,
! [V_24Y] :
( c_24__type__9960___24t(V_24Y)
<=> t(V_24Y,c_24__type__9960) ) ).
fof('$tdef_$_type_30822',axiom,
! [V_24Y] :
( c_24__type__30822___24t(V_24Y)
<=> t(V_24Y,c_24__type__30822) ) ).
fof('$tdef_$_type_17877',axiom,
! [V_24Y] :
( c_24__type__17877___24t(V_24Y)
<=> t(V_24Y,c_24__type__17877) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_23242',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23242___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23242___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9407',axiom,
! [V_24Y] :
( c_24__type__9407___24t(V_24Y)
<=> t(V_24Y,c_24__type__9407) ) ).
fof('$tdef_$_type_23404',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23404___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23404___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4703',axiom,
! [V_24Y] :
( c_24__type__4703___24t(V_24Y)
<=> t(V_24Y,c_24__type__4703) ) ).
fof('$tdef_$_type_26386',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26386___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26386___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31458',axiom,
! [V_24Y] :
( c_24__type__31458___24t(V_24Y)
<=> t(V_24Y,c_24__type__31458) ) ).
fof('$tdef_$_type_24162',axiom,
! [V_24Y] :
( c_24__type__24162___24t(V_24Y)
<=> t(V_24Y,c_24__type__24162) ) ).
fof('$tdef_$_type_2',axiom,
! [V_24Y] :
( c_24__type__2___24t(V_24Y)
<=> t(V_24Y,c_24__type__2) ) ).
fof('$tdef_$_type_17030',axiom,
! [V_24Y] :
( c_24__type__17030___24t(V_24Y)
<=> t(V_24Y,c_24__type__17030) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
fof('$tdef_$_type_23065',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23065___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23065___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16359',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16359___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16359___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3876',axiom,
! [V_24Y] :
( c_24__type__3876___24t(V_24Y)
<=> t(V_24Y,c_24__type__3876) ) ).
fof('$tdef_$_type_14945',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__14945___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__14945___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_2351',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__2351___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__2351___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_23198',axiom,
! [V_24Y] :
( c_24__type__23198___24t(V_24Y)
<=> t(V_24Y,c_24__type__23198) ) ).
fof('$tdef_$_type_12846',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12846___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12846___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_8876',axiom,
! [V_24Y] :
( c_24__type__8876___24t(V_24Y)
<=> t(V_24Y,c_24__type__8876) ) ).
fof('$tdef_$_type_5652',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5652___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5652___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22963',axiom,
! [V_24Y] :
( c_24__type__22963___24t(V_24Y)
<=> t(V_24Y,c_24__type__22963) ) ).
fof('$tdef_$_type_19897',axiom,
! [V_24Y] :
( c_24__type__19897___24t(V_24Y)
<=> t(V_24Y,c_24__type__19897) ) ).
fof('$tdef_$_type_31756',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31756___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31756___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__U] :
( cLambda_2eRedexes_2eredexes___24t(V0__U)
=> ! [V1__V] :
( cLambda_2eRedexes_2eredexes___24t(V1__V)
=> ! [V2__W] :
( cLambda_2eRedexes_2eredexes___24t(V2__W)
=> ( cLambda_2eRedexes_2esub___24a2(V1__V,V0__U)
=> ( cLambda_2eRedexes_2eregular___24a1(V0__U)
=> ! [V5__UV] :
( cLambda_2eRedexes_2eredexes___24t(V5__UV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V0__U,V1__V,V5__UV)
=> ! [V7__WV] :
( cLambda_2eRedexes_2eredexes___24t(V7__WV)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V2__W,V1__V,V7__WV)
=> ! [V9__WU] :
( cLambda_2eRedexes_2eredexes___24t(V9__WU)
=> ( cLambda_2eResiduals_2eresiduals___24a3(V7__WV,V5__UV,V9__WU)
=> cLambda_2eResiduals_2eresiduals___24a3(V2__W,V0__U,V9__WU) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------