TPTP Problem File: SEV635+1.p
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%------------------------------------------------------------------------------
% File : SEV635+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - indices vec IndexSeq nats perm
% 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 : indices.vec.IndexSeq.nats.perm.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 3574 (1436 unt; 0 def)
% Number of atoms : 12441 (3484 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 8979 ( 112 ~; 742 |;1901 &)
% (1259 <=>;4965 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 661 ( 660 usr; 0 prp; 1-23 aty)
% Number of functors : 2268 (2268 usr;1326 con; 0-22 aty)
% Number of variables : 12661 (11833 !; 828 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$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] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__6)
=> ( ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__7)
=> ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& ( ( Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__19125] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__19125)
& ? [Vvar__2___24Anonymous__19126] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__19126)
& Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19125,Vvar__2___24Anonymous__19126)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vvar__1___24Anonymous__19125),c_24__fix__19265__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vvar__2___24Anonymous__19126)) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__19141] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__19141)
& ? [Vvar__2___24Anonymous__19142] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__19142)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19141,Vvar__2___24Anonymous__19142)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19141,c_24__fix__19362__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19142,c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$19226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__19230] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__19230)
& ? [Vvar__2___24Anonymous__19231] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__19231)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19230,Vvar__2___24Anonymous__19231)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__19230),c_24__fix__19265__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__19231)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$19809',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__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))) )
| ? [Vvar__1___24Anonymous__19813] :
( t(Vvar__1___24Anonymous__19813,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__19814] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__19814)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19813,Vvar__2___24Anonymous__19814)
& ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))) )
| ? [Vvar__1___24Anonymous__19825] :
( t(Vvar__1___24Anonymous__19825,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__19826] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__19826)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19825,Vvar__2___24Anonymous__19826)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__19813),cQuicksortComplexity_2elist__utils_2emerges___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19814,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19825,Vvar__2___24Anonymous__19826))),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a2(Vv__CANONICAL__0,Vvar__1___24Anonymous__19825),cQuicksortComplexity_2elist__utils_2emerges___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19813,Vvar__2___24Anonymous__19814),Vvar__2___24Anonymous__19826))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$24445',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424445___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__24449] :
( t(Vvar__1___24Anonymous__24449,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__24450] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__24450)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24449,Vvar__2___24Anonymous__24450)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424445___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24449,c_24__fix__24577__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__24450,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$24532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__24536] :
( t(Vvar__1___24Anonymous__24536,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__24537] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__24537)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24536,Vvar__2___24Anonymous__24537)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24536,c_24__fix__24577__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__24537,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$137',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24137___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__138] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__138)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__138)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24137___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__156__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__138,Vv__CANONICAL__2)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$59782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459782___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__59783] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59783)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59783)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459782___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__59783)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$59804',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__59805] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59805)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59805)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__59805)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$70592',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__70602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__6)
=> ( ( Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = c_24__lam__70695___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5) )
| ? [Vvar__0___24Anonymous__70593] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__70593)
& Vv__CANONICAL__6 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__70593)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = c_24__lam__70746___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vvar__0___24Anonymous__70593) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$74984',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__lam__75009___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) )
| ? [Vvar__0___24Anonymous__74985] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74985)
& ( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__74985)
& ( ( Vv__CANONICAL__3 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__lam__75013___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__74985) )
| ? [Vvar__1__h__74998] :
( t(Vvar__1__h__74998,Vv__CANONICAL__0)
& ? [Vvar__2__n__74999] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__74999)
& ? [Vvar__3___24Anonymous__75000] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__74999,Vvar__3___24Anonymous__75000)
& Vv__CANONICAL__3 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__74998,Vvar__2__n__74999,Vvar__3___24Anonymous__75000)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__lam__75020___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0___24Anonymous__74985,Vvar__1__h__74998,Vvar__2__n__74999,Vvar__3___24Anonymous__75000) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$34547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__34560___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__34552] :
( t(Vvar__2___24Anonymous__34552,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__34553] :
( t(Vvar__3___24Anonymous__34553,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__34552,Vvar__3___24Anonymous__34553)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2434547___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__34552)),Vvar__3___24Anonymous__34553)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$59799',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__59800] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59800)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__59800)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__59800) )
| ? [Vvar__0___24Anonymous__59801] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59801)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__59801)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__59801) ) ) ) ).
fof('$_case_Coq.Vectors.Fin.t$74541',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( ? [Vvar__0__n__74543] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74543)
& Vv__CANONICAL__2 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74543)
& c_24__case__Coq_2eVectors_2eFin_2et_2474541___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a4(Vv__CANONICAL__0,c_24__lam__74573___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__lam__74583___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vvar__0__n__74543) )
| ? [Vvar__0__n__74549] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74549)
& ? [Vvar__1___24Anonymous__74550] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__74549,Vvar__1___24Anonymous__74550)
& Vv__CANONICAL__2 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74549,Vvar__1___24Anonymous__74550)
& c_24__case__Coq_2eVectors_2eFin_2et_2474541___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__lam__74632___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0__n__74549,Vvar__1___24Anonymous__74550) ) ) ) ) ) ).
fof('$_case_Coq.Vectors.Fin.t$74763',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( ? [Vvar__0__n__74765] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74765)
& Vv__CANONICAL__2 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__74765)
& c_24__case__Coq_2eVectors_2eFin_2et_2474763___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__lam__74801___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__0__n__74765) )
| ? [Vvar__0__n__74770] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__74770)
& ? [Vvar__1___24Anonymous__74771] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__74770,Vvar__1___24Anonymous__74771)
& Vv__CANONICAL__2 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__74770,Vvar__1___24Anonymous__74771)
& c_24__case__Coq_2eVectors_2eFin_2et_2474763___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__lam__74837___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__0__n__74770,Vvar__1___24Anonymous__74771) ) ) ) ) ) ) ).
fof('$_case_QuicksortComplexity.nat_below.natBelow$931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__type__962___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> ? [Vvar__0__v__933] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__933)
& ? [Vvar__1__p__934] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__934)
& ( c_24__type__962___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__933)
=> ( Vv__CANONICAL__4 = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__933,Vvar__1__p__934)
& ( ( Vvar__0__v__933 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__lam__978___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__1__p__934) )
| ? [Vvar__0___24Anonymous__954] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__954)
& Vvar__0__v__933 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__954)
& c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__lam__992___24a5(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1__p__934,Vvar__0___24Anonymous__954) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_8800',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__8800___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_16_mkpow_55942',axiom,
! [V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p] :
( cType___24t(V0__R)
=> ( cType___24t(V12__Cpow)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V17__p)
=> ( ? [Vvar__0___24Anonymous__55945] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55945)
& V17__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__55945)
& c_24__let__16__mkpow__55942___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ? [Vvar__0___24Anonymous__55946] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__55946)
& V17__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__55946)
& c_24__let__16__mkpow__55942___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = happ(happ(V14__rpow,V16__x),happ(V13__Cp__phi,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V17__p))) )
| ( V17__p = cCoq_2eNumbers_2eBinNums_2exH
& c_24__let__16__mkpow__55942___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V16__x,V17__p) = V16__x ) ) ) ) ) ).
fof('$_def_$_let_17_mkopp_pow_55943',axiom,
! [V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p] : c_24__let__17__mkopp__pow__55943___24a8(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p) = happ(V6__ropp,c_24__let__16__mkpow__55942___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V17__x,V18__p)) ).
fof('$_def_$_let_18_mkmult_pow_55944',axiom,
! [V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p] : c_24__let__18__mkmult__pow__55944___24a9(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V18__r,V19__x,V20__p) = happ(happ(V4__rmul,V18__r),c_24__let__16__mkpow__55942___24a7(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow,V19__x,V20__p)) ).
fof('$_def_$_let_4_n_8244',axiom,
! [V0__A,V1__l] : c_24__let__4__n__8244___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ).
fof('$_def_$_let_var_6_p_30386_30389',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30385] : c_24__let__var__6__p__30386__30389___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30385) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30385) ).
fof('$_def_$_let_var_6_p_30388_30390',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30387] : c_24__let__var__6__p__30388__30390___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30387) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30387) ).
fof('$_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('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__59724] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59724)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59724)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__59725] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59725)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59725)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__59728] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59728)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59728)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__59725,Vvar__0___24Anonymous__59728) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.Factorial.fact',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__7699] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7699)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7699)
& cCoq_2eArith_2eFactorial_2efact___24a1(V1__n) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7699),cCoq_2eArith_2eFactorial_2efact___24a1(Vvar__0___24Anonymous__7699)) ) ) ) ).
fof('$_def_Coq.Arith.Mult.mult_acc',axiom,
! [V1__s,V2__m,V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2eMult_2emult__acc___24a3(V1__s,V2__m,V3__n) = V1__s )
| ? [Vvar__0___24Anonymous__77137] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77137)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77137)
& cCoq_2eArith_2eMult_2emult__acc___24a3(V1__s,V2__m,V3__n) = cCoq_2eArith_2eMult_2emult__acc___24a3(cCoq_2eArith_2ePlus_2etail__plus___24a2(V2__m,V1__s),V2__m,Vvar__0___24Anonymous__77137) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
! [V0__n,V1__m] :
( cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V0__n,V1__m)
<=> ? [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
& cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n) = V1__m ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__60122___24a1(V0__A)) ).
fof('$_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__59751] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59751)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59751)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__59751,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.gtof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2egtof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> cCoq_2eInit_2ePeano_2egt___24a2(happ(V1__f,V3__b),happ(V1__f,V2__a)) ) ).
fof('$_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('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bvector.BVand',axiom,
cCoq_2eBool_2eBvector_2eBVand = cCoq_2eVectors_2eVectorDef_2emap2___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_def_Coq.Bool.Bvector.BVeq',axiom,
! [V0__m,V1__n] : cCoq_2eBool_2eBvector_2eBVeq___24a2(V0__m,V1__n) = cCoq_2eVectors_2eVectorEq_2eeqb___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eBool_2eBool_2eeqb,V0__m,V1__n) ).
fof('$_def_Coq.Bool.Bvector.BVor',axiom,
cCoq_2eBool_2eBvector_2eBVor = cCoq_2eVectors_2eVectorDef_2emap2___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_def_Coq.Bool.Bvector.BVxor',axiom,
cCoq_2eBool_2eBvector_2eBVxor = cCoq_2eVectors_2eVectorDef_2emap2___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_def_Coq.Bool.Bvector.Bcons',axiom,
cCoq_2eBool_2eBvector_2eBcons = cCoq_2eVectors_2eVectorDef_2econs___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Bhigh',axiom,
cCoq_2eBool_2eBvector_2eBhigh = cCoq_2eVectors_2eVectorDef_2etl___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Blow',axiom,
cCoq_2eBool_2eBvector_2eBlow = cCoq_2eVectors_2eVectorDef_2ehd___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Bneg',axiom,
cCoq_2eBool_2eBvector_2eBneg = cCoq_2eVectors_2eVectorDef_2emap___24a3(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_def_Coq.Bool.Bvector.Bnil',axiom,
cCoq_2eBool_2eBvector_2eBnil = cCoq_2eVectors_2eVectorDef_2enil___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Bsign',axiom,
cCoq_2eBool_2eBvector_2eBsign = cCoq_2eVectors_2eVectorDef_2elast___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Bvector.Bvect_false',axiom,
cCoq_2eBool_2eBvector_2eBvect__false = cCoq_2eVectors_2eVectorDef_2econst___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_def_Coq.Bool.Bvector.Bvect_true',axiom,
cCoq_2eBool_2eBvector_2eBvect__true = cCoq_2eVectors_2eVectorDef_2econst___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__60031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__60031)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__60031)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
! [V1__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__20391] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__20391)
& ? [Vvar__1___24Anonymous__20392] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__20392)
& ? [Vvar__2___24Anonymous__20393] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__20393)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__20392)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20391,Vvar__1___24Anonymous__20392,Vvar__2___24Anonymous__20393)
& ( ( Vvar__1___24Anonymous__20392 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__20391),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__20393))) )
| ( Vvar__1___24Anonymous__20392 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__0___24Anonymous__20391),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(Vvar__2___24Anonymous__20393)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
! [V0__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V0__m,cCoq_2eNumbers_2eBinNums_2exH,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt)) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__20275] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__20275)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__20275) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__39588] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__39588)
& ? [Vvar__1___24Anonymous__39589] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__39589)
& ? [Vvar__2___24Anonymous__39590] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__39590)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__39588,Vvar__1___24Anonymous__39589,Vvar__2___24Anonymous__39590)
& ( ? [Vvar__0___24Anonymous__39603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__39603)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__39603)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__39603,Vvar__2___24Anonymous__39590) )
| ? [Vvar__0___24Anonymous__39604] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__39604)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__39604)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__39604,Vvar__0___24Anonymous__39588) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__39589 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
! [V0__x] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V0__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__20301] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__20301)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__20301) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.xelements',axiom,
! [V1__m,V2__i,V3__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = V3__a )
| ? [Vvar__0___24Anonymous__20374] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__20374)
& ? [Vvar__1___24Anonymous__20375] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__20375)
& ? [Vvar__2___24Anonymous__20376] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__20376)
& ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__20375)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20374,Vvar__1___24Anonymous__20375,Vvar__2___24Anonymous__20376)
& ( ( Vvar__1___24Anonymous__20375 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__0___24Anonymous__20374,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__i),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V2__i),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__2___24Anonymous__20376,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__i),V3__a))) )
| ( Vvar__1___24Anonymous__20375 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V1__m,V2__i,V3__a) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__0___24Anonymous__20374,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__i),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(Vvar__2___24Anonymous__20376,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__i),V3__a)) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__1349] :
( t(Vvar__1___24Anonymous__1349,V0__A)
& ? [Vvar__2___24Anonymous__1350] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1350)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1349,Vvar__2___24Anonymous__1350)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1349,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__1350,V3__m)) ) ) ) ) ) ).
fof('$_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__7318] :
( t(Vvar__2___24Anonymous__7318,V0__A)
& ? [Vvar__3___24Anonymous__7319] :
( t(Vvar__3___24Anonymous__7319,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__7318,Vvar__3___24Anonymous__7319)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__7318 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__38] :
( t(Vvar__1___24Anonymous__38,V0__A)
& ? [Vvar__2___24Anonymous__39] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__39)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38,Vvar__2___24Anonymous__39)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__39)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__37432___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__37430] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__37430)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__37430)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__37430),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__37430)) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__7330] :
( t(Vvar__2___24Anonymous__7330,V0__A)
& ? [Vvar__3___24Anonymous__7331] :
( t(Vvar__3___24Anonymous__7331,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__7330,Vvar__3___24Anonymous__7331)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__7331 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__81] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__81)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__81)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__81,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.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__1837] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1837)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1837)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__1838] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1838)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1838)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__1841] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1841)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1841)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__1838,Vvar__0___24Anonymous__1841) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8205] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8205)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8205)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8205)
& ( ( Vvar__0___24Anonymous__8205 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8208] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8208)
& Vvar__0___24Anonymous__8205 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8208)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__8208)) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__22806] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22806)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22806)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__22807] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22807)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22807)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__22810] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22810)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22810)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__22807,Vvar__0___24Anonymous__22810) ) ) ) ) ) ) ) ).
fof('$_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__38526] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38526)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38526)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38526)
& ( ( Vvar__0___24Anonymous__38526 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__38529] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38529)
& Vvar__0___24Anonymous__38526 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38529)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__38529) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__38531] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38531)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38531)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38531)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38531)) ) ) ) ).
fof('$_def_Coq.Init.Nat.iter',axiom,
! [V0__n,V1__A,V2__f,V3__x] : cCoq_2eInit_2eNat_2eiter___24a4(V0__n,V1__A,V2__f,V3__x) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(c_24__lam__60122___24a1(V1__A),V3__x,c_24__lam__77148___24a2(V1__A,V2__f),V0__n) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__8156] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8156)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8156)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8159] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8159)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8159)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__8156,Vvar__0___24Anonymous__8159) ) ) ) ) ) ) ) ).
fof('$_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__8194] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8194)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8194)
& ( ( 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__8194,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__8197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8197)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8197)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__8194,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__8197) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__8164] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8164)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8164)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8167] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8167)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8167)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__8164,Vvar__0___24Anonymous__8167)) ) ) ) ) ) ) ) ).
fof('$_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__8170] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8170)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8170)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8173] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8173)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8173)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__8170,Vvar__0___24Anonymous__8173)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8147] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8147)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8147)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__8147,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.odd',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__8176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8176)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8176)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__8176)) ) ) ) ).
fof('$_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__8145] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8145)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8145)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__8145 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__22813,V0__a,c_24__lam__38533) ).
fof('$_def_Coq.Init.Nat.shiftr',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftr___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__22813,V0__a,c_24__lam__22814) ).
fof('$_def_Coq.Init.Nat.sqrt',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.sqrt_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_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__8181] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8181)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8181)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__8181,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q))) )
| ? [Vvar__0___24Anonymous__8184] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8184)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8184)
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__8181,V2__p,V3__q,Vvar__0___24Anonymous__8184) ) ) ) ) ) ) ) ).
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__8150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8150)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8150)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8153] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8153)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8153)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__8150,Vvar__0___24Anonymous__8153) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__77143] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__77143)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__77143) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__59744] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59744)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59744)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__59744,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_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__8210] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8210)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8210)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__8210) ) ) ) ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__59748] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59748)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__59748)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_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('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__2215___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__2209] :
( t(Vvar__2__x__2209,V0__A)
& p(happ(V1__P,Vvar__2__x__2209))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__2209)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__2209 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__73738___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__73732] :
( t(Vvar__2__x__73732,V0__A)
& ? [Vvar__3___24Anonymous__73733] :
( t(Vvar__3___24Anonymous__73733,happ(V1__P,Vvar__2__x__73732))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__73732,Vvar__3___24Anonymous__73733)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__73732 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__73761___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__73755] :
( t(Vvar__2__x__73755,V0__A)
& ? [Vvar__3___24Anonymous__73756] :
( t(Vvar__3___24Anonymous__73756,happ(V1__P,Vvar__2__x__73755))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__73755,Vvar__3___24Anonymous__73756)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__73756 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Wf.well_founded_induction_type',axiom,
! [V0__A,V1__R,V3__P,V4__X,V5__a] : cCoq_2eInit_2eWf_2ewell__founded__induction__type___24a5(V0__A,V1__R,V3__P,V4__X,V5__a) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V0__A,V1__R,V3__P,c_24__lam__9527___24a4(V0__A,V1__R,V3__P,V4__X),V5__a) ).
fof('$_def_Coq.Lists.List.ForallPairs',axiom,
! [V0__A,V1__R,V2__l] :
( cCoq_2eLists_2eList_2eForallPairs___24a3(V0__A,V1__R,V2__l)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__b,V2__l)
=> p(happ(happ(V1__R,V3__a),V4__b)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__51] :
( t(Vvar__1___24Anonymous__51,V0__A)
& ? [Vvar__2___24Anonymous__52] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__52)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__51,Vvar__2___24Anonymous__52)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__51 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__52) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.combine',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__8013] :
( t(Vvar__1___24Anonymous__8013,V0__A)
& ? [Vvar__2___24Anonymous__8014] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8014)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8013,Vvar__2___24Anonymous__8014)
& ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__8025] :
( t(Vvar__1___24Anonymous__8025,V1__B)
& ? [Vvar__2___24Anonymous__8026] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8026)
& V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8025,Vvar__2___24Anonymous__8026)
& cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__8013,Vvar__1___24Anonymous__8025),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__8014,Vvar__2___24Anonymous__8026)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.existsb',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__7900] :
( t(Vvar__1___24Anonymous__7900,V0__A)
& ? [Vvar__2___24Anonymous__7901] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7901)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7900,Vvar__2___24Anonymous__7901)
& cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(happ(V1__f,Vvar__1___24Anonymous__7900),cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,Vvar__2___24Anonymous__7901)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7917] :
( t(Vvar__1___24Anonymous__7917,V0__A)
& ? [Vvar__2___24Anonymous__7918] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7918)
& ( cType___24t(V0__A)
=> ( c_24__type__7910___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__7917,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7917,Vvar__2___24Anonymous__7918)
& ( ( happ(V1__f,Vvar__1___24Anonymous__7917) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7917,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__7918)) )
| ( happ(V1__f,Vvar__1___24Anonymous__7917) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__7918) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.firstn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__8064] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8064)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8064)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__8071] :
( t(Vvar__1___24Anonymous__8071,V0__A)
& ? [Vvar__2___24Anonymous__8072] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8072)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8071,Vvar__2___24Anonymous__8072)
& cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8071,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,Vvar__0___24Anonymous__8064,Vvar__2___24Anonymous__8072)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__7865] :
( t(Vvar__1___24Anonymous__7865,V1__B)
& ? [Vvar__2___24Anonymous__7866] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__7866)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__7865,Vvar__2___24Anonymous__7866)
& 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__7866,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__7865)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__22632] :
( t(Vvar__1___24Anonymous__22632,V1__B)
& ? [Vvar__2___24Anonymous__22633] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__22633)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__22632,Vvar__2___24Anonymous__22633)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__22632),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__22633)) ) ) ) ) ) ) ).
fof('$_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__22584] :
( t(Vvar__1___24Anonymous__22584,V0__A)
& ? [Vvar__2___24Anonymous__22585] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__22585)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__22584,Vvar__2___24Anonymous__22585)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__22584 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.incl',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ).
fof('$_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__22603] :
( t(Vvar__1___24Anonymous__22603,V0__A)
& ? [Vvar__2___24Anonymous__22604] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__22604)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__22604)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__22603,Vvar__2___24Anonymous__22604)
& ( ( Vvar__2___24Anonymous__22604 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__22603 )
| ? [Vvar__1___24Anonymous__22615] :
( t(Vvar__1___24Anonymous__22615,V0__A)
& ? [Vvar__2___24Anonymous__22616] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__22616)
& Vvar__2___24Anonymous__22604 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__22615,Vvar__2___24Anonymous__22616)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__22604,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.lel',axiom,
! [V0__A,V1__l,V2__m] :
( cCoq_2eLists_2eList_2elel___24a3(V0__A,V1__l,V2__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__m))) ) ).
fof('$_def_Coq.Lists.List.list_prod',axiom,
! [V0__A,V1__B,V3__l,V4__l_27] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
| ? [Vvar__1___24Anonymous__8040] :
( t(Vvar__1___24Anonymous__8040,V0__A)
& ? [Vvar__2___24Anonymous__8041] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8041)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8040,Vvar__2___24Anonymous__8041)
& cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2eapp___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2emap___24a4(V1__B,cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),c_24__lam__8048___24a3(V0__A,V1__B,Vvar__1___24Anonymous__8040),V4__l_27),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,Vvar__2___24Anonymous__8041,V4__l_27)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__63] :
( t(Vvar__1___24Anonymous__63,V0__A)
& ? [Vvar__2___24Anonymous__64] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__64)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__63,Vvar__2___24Anonymous__64)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__63),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__64)) ) ) ) ) ) ) ).
fof('$_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__7750] :
( t(Vvar__1___24Anonymous__7750,V0__A)
& ? [Vvar__2___24Anonymous__7751] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7751)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7750,Vvar__2___24Anonymous__7751)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__7750 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__7753] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7753)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7753)
& ( ( 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__7760] :
( t(Vvar__1___24Anonymous__7760,V0__A)
& ? [Vvar__2___24Anonymous__7761] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7761)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7760,Vvar__2___24Anonymous__7761)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__7753,Vvar__2___24Anonymous__7761,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_default',axiom,
! [V0__A,V1__default,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ? [Vvar__1___24Anonymous__7795] :
( t(Vvar__1___24Anonymous__7795,V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__7795)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = Vvar__1___24Anonymous__7795 )
| ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V1__default,V2__l,V3__n) = V1__default ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_error',axiom,
! [V0__A,V2__l,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7775] :
( t(Vvar__1___24Anonymous__7775,V0__A)
& ? [Vvar__2___24Anonymous__7776] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7776)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7775,Vvar__2___24Anonymous__7776)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__7775) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__7778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7778)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7778)
& ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7785] :
( t(Vvar__1___24Anonymous__7785,V0__A)
& ? [Vvar__2___24Anonymous__7786] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7786)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7785,Vvar__2___24Anonymous__7786)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l,V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,Vvar__2___24Anonymous__7786,Vvar__0___24Anonymous__7778) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth_ok',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__38442] :
( t(Vvar__1___24Anonymous__38442,V0__A)
& ? [Vvar__2___24Anonymous__38443] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38443)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38442,Vvar__2___24Anonymous__38443)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__38445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__38445)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__38445)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__38452] :
( t(Vvar__1___24Anonymous__38452,V0__A)
& ? [Vvar__2___24Anonymous__38453] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38453)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38452,Vvar__2___24Anonymous__38453)
& cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth__ok___24a4(V0__A,Vvar__0___24Anonymous__38445,Vvar__2___24Anonymous__38453,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.partition',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
| ? [Vvar__1___24Anonymous__7935] :
( t(Vvar__1___24Anonymous__7935,V0__A)
& ? [Vvar__2___24Anonymous__7936] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7936)
& ( cType___24t(V0__A)
=> ( c_24__type__7910___24t(V0__A,V1__f)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7936)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7935,Vvar__2___24Anonymous__7936)
& ? [Vvar__2___24Anonymous__7950] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7950)
& ? [Vvar__3___24Anonymous__7951] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__3___24Anonymous__7951)
& ( cType___24t(V0__A)
=> ( c_24__type__7910___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__7935,V0__A)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,Vvar__2___24Anonymous__7936) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__7950,Vvar__3___24Anonymous__7951)
& ( ( happ(V1__f,Vvar__1___24Anonymous__7935) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7935,Vvar__2___24Anonymous__7950),Vvar__3___24Anonymous__7951) )
| ( happ(V1__f,Vvar__1___24Anonymous__7935) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__7950,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7935,Vvar__3___24Anonymous__7951)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.removelast',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7809] :
( t(Vvar__1___24Anonymous__7809,V0__A)
& ? [Vvar__2___24Anonymous__7810] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7810)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7810)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7809,Vvar__2___24Anonymous__7810)
& ( ( Vvar__2___24Anonymous__7810 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7821] :
( t(Vvar__1___24Anonymous__7821,V0__A)
& ? [Vvar__2___24Anonymous__7822] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7822)
& Vvar__2___24Anonymous__7810 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7821,Vvar__2___24Anonymous__7822)
& cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7809,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,Vvar__2___24Anonymous__7810)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.repeat',axiom,
! [V0__A,V2__x,V3__n] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__0___24Anonymous__8139] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8139)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8139)
& cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,V3__n) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V2__x,Vvar__0___24Anonymous__8139)) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__7831] :
( t(Vvar__1___24Anonymous__7831,V0__A)
& ? [Vvar__2___24Anonymous__7832] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7832)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7831,Vvar__2___24Anonymous__7832)
& cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,Vvar__2___24Anonymous__7832),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7831,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.rev_append',axiom,
! [V0__A,V2__l,V3__l_27] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = V3__l_27 )
| ? [Vvar__1___24Anonymous__38467] :
( t(Vvar__1___24Anonymous__38467,V0__A)
& ? [Vvar__2___24Anonymous__38468] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38468)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38467,Vvar__2___24Anonymous__38468)
& cCoq_2eLists_2eList_2erev__append___24a3(V0__A,V2__l,V3__l_27) = cCoq_2eLists_2eList_2erev__append___24a3(V0__A,Vvar__2___24Anonymous__38468,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38467,V3__l_27)) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.seq',axiom,
! [V1__start,V2__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__len)
=> ( ( V2__len = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__8134] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8134)
& V2__len = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8134)
& cCoq_2eLists_2eList_2eseq___24a2(V1__start,V2__len) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__start,cCoq_2eLists_2eList_2eseq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__start),Vvar__0___24Anonymous__8134)) ) ) ) ).
fof('$_def_Coq.Lists.List.skipn',axiom,
! [V0__A,V2__n,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = V3__l )
| ? [Vvar__0___24Anonymous__8080] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8080)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8080)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__8087] :
( t(Vvar__1___24Anonymous__8087,V0__A)
& ? [Vvar__2___24Anonymous__8088] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8088)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8087,Vvar__2___24Anonymous__8088)
& cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V2__n,V3__l) = cCoq_2eLists_2eList_2eskipn___24a3(V0__A,Vvar__0___24Anonymous__8080,Vvar__2___24Anonymous__8088) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.split',axiom,
! [V0__A,V1__B,V3__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B))
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) )
| ? [Vvar__1___24Anonymous__7969] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__7969)
& ? [Vvar__2___24Anonymous__7970] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__7970)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__7969)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__1___24Anonymous__7969,Vvar__2___24Anonymous__7970)
& ? [Vvar__2___24Anonymous__7988] :
( t(Vvar__2___24Anonymous__7988,V0__A)
& ? [Vvar__3___24Anonymous__7989] :
( t(Vvar__3___24Anonymous__7989,V1__B)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__7970)
=> ( Vvar__1___24Anonymous__7969 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__7988,Vvar__3___24Anonymous__7989)
& ? [Vvar__2___24Anonymous__8001] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8001)
& ? [Vvar__3___24Anonymous__8002] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__3___24Anonymous__8002)
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,Vvar__2___24Anonymous__7970) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),Vvar__2___24Anonymous__8001,Vvar__3___24Anonymous__8002)
& cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__2___24Anonymous__7988,Vvar__2___24Anonymous__8001),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__3___24Anonymous__7989,Vvar__3___24Anonymous__8002)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__22595] :
( t(Vvar__1___24Anonymous__22595,V0__A)
& ? [Vvar__2___24Anonymous__22596] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__22596)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__22595,Vvar__2___24Anonymous__22596)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__22596 ) ) ) ) ) ).
fof('$_def_Coq.Lists.ListDec.decidable_eq',axiom,
! [V0__A] :
( cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V0__A)
<=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__22802___24a3(V0__A,V1__x,V2__y)) ) ) ) ).
fof('$_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('$_def_Coq.Logic.FinFun.Finite',axiom,
! [V0__A] :
( cCoq_2eLogic_2eFinFun_2eFinite___24a1(V0__A)
<=> ? [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
& cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Full',axiom,
! [V0__A,V1__l] :
( cCoq_2eLogic_2eFinFun_2eFull___24a2(V0__A,V1__l)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V1__l) ) ) ).
fof('$_def_Coq.Logic.FinFun.Injective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Surjective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__B)
=> ? [V4__x] :
( t(V4__x,V0__A)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bFun',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebFun___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__x),V0__n)) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bInjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__x,V0__n))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__y,V0__n))
=> ( happ(V1__f,V2__x) = happ(V1__f,V3__y)
=> V2__x = V3__y ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bSurjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V0__n,V1__f)
<=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__y,V0__n))
=> ? [V4__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x)
& p(cCoq_2eInit_2ePeano_2elt___24a2(V4__x,V0__n))
& happ(V1__f,V4__x) = V2__y ) ) ) ) ).
fof('$_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__35678] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35678)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35678)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__35681] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35681)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35681)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__35678,Vvar__0___24Anonymous__35681)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__59499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59499)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__59499)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__59502] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__59502)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__59502)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__59499,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__37304] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37304)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37304)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37304)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__20033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20033)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20033)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__20034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20034)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20034)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__20037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20037)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20037)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__20034,Vvar__0___24Anonymous__20037) ) ) ) ) ) ) ) ).
fof('$_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__35685] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35685)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35685)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__35688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35688)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35688)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__35685,Vvar__0___24Anonymous__35688)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__20042] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20042)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20042)
& cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__20042)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__37303] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37303)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37303)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37303)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__20039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20039)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20039)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20039) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.Bv2N',axiom,
! [V1__n,V2__bv] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eBool_2eBvector_2eBvector___24t(V1__n,V2__bv)
=> ( ( V2__bv = cCoq_2eVectors_2eVectorDef_2enil___24a1(cCoq_2eInit_2eDatatypes_2ebool)
& cCoq_2eNArith_2eNdigits_2eBv2N___24a2(V1__n,V2__bv) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__1__h__69967] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1__h__69967)
& ? [Vvar__2__n__69968] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__69968)
& ? [Vvar__3___24Anonymous__69969] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vvar__2__n__69968,Vvar__3___24Anonymous__69969)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1__h__69967)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__69968)
=> ( V2__bv = cCoq_2eVectors_2eVectorDef_2econs___24a4(cCoq_2eInit_2eDatatypes_2ebool,Vvar__1__h__69967,Vvar__2__n__69968,Vvar__3___24Anonymous__69969)
& ( ( Vvar__1__h__69967 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eNArith_2eNdigits_2eBv2N___24a2(V1__n,V2__bv) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(cCoq_2eNArith_2eNdigits_2eBv2N___24a2(Vvar__2__n__69968,Vvar__3___24Anonymous__69969)) )
| ( Vvar__1__h__69967 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eNArith_2eNdigits_2eBv2N___24a2(V1__n,V2__bv) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(cCoq_2eNArith_2eNdigits_2eBv2N___24a2(Vvar__2__n__69968,Vvar__3___24Anonymous__69969)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.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.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__20118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20118)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20118)
& ( ? [Vvar__0___24Anonymous__20122] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20122)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20122)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__20117__1__add__carry___24a2(Vvar__0___24Anonymous__20118,Vvar__0___24Anonymous__20122)) )
| ? [Vvar__0___24Anonymous__20123] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20123)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20123)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__20118,Vvar__0___24Anonymous__20123)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20118)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__20124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20124)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20124)
& ( ? [Vvar__0___24Anonymous__20128] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20128)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20128)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__20124,Vvar__0___24Anonymous__20128)) )
| ? [Vvar__0___24Anonymous__20129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20129)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20129)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__20124,Vvar__0___24Anonymous__20129)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20124) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__20130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20130)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20130)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20130)) )
| ? [Vvar__0___24Anonymous__20131] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20131)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20131)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20131) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.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__60181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60181)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60181)
& 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__60181,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__60182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60182)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60182)
& 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__60182,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('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__20255] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20255)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20255)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20255)
& ( ( Vvar__0___24Anonymous__20255 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__20258] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20258)
& Vvar__0___24Anonymous__20255 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20258)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__20255)) ) ) ) ) ) ) ) ).
fof('$_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__20262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__20262)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__20262)
& 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__20262)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__39585] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__39585)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__39585)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__39585)) )
| ? [Vvar__0___24Anonymous__39586] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__39586)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__39586)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__39586)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_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__20227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20227)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__20227)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__20227 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__20115] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20115)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20115)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20115)) )
| ? [Vvar__0___24Anonymous__20116] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20116)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20116)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20116) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__60151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60151)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__60151)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__60164___24a1(Vvar__0___24Anonymous__60151) )
| ? [Vvar__0___24Anonymous__60155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__60155)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__60155)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__60171___24a1(Vvar__0___24Anonymous__60155) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__60175 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qminus',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V0__x,cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V1__y)) ).
fof('$_def_Coq.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__24051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24051)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__24051)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__24051) )
| ? [Vvar__0___24Anonymous__24052] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24052)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24052)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__24052)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rfunctions.sum_nat_f_O',axiom,
! [V1__f,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,V2__n) = happ(V1__f,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__71677] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__71677)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__71677)
& cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,V2__n) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V1__f,Vvar__0___24Anonymous__71677),happ(V1__f,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__71677))) ) ) ) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__34849] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34849)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34849)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__34849)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1116___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Strings.ByteVector.ByteVector',axiom,
cCoq_2eStrings_2eByteVector_2eByteVector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_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__77173] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__77173)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__77173) ) ).
fof('$_def_Coq.Vectors.Fin.L_R',axiom,
! [V0__m,V1__n,V2__p] : cCoq_2eVectors_2eFin_2eL__R___24a3(V0__m,V1__n,V2__p) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(c_24__lam__73615___24a1(V0__m),V2__p,c_24__lam__73670___24a1(V0__m),V1__n) ).
fof('$_def_Coq.Vectors.Fin.case0',axiom,
! [V0__P,V1__p] :
( cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eO,V1__p)
=> ( ? [Vvar__0__n__73445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__73445)
& V1__p = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__73445)
& cCoq_2eVectors_2eFin_2ecase0___24a2(V0__P,V1__p) = c_24__lam__73452 )
| ? [Vvar__0__n__73447] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__73447)
& ? [Vvar__1___24Anonymous__73448] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__73447,Vvar__1___24Anonymous__73448)
& V1__p = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__73447,Vvar__1___24Anonymous__73448)
& cCoq_2eVectors_2eFin_2ecase0___24a2(V0__P,V1__p) = c_24__lam__73454___24a1(Vvar__0__n__73447) ) ) ) ) ).
fof('$_def_Coq.Vectors.Fin.caseS',axiom,
! [V0__P,V1__P1,V2__PS,V3__n,V4__p] : cCoq_2eVectors_2eFin_2ecaseS___24a5(V0__P,V1__P1,V2__PS,V3__n,V4__p) = cCoq_2eVectors_2eFin_2ecaseS_27___24a5(V3__n,V4__p,happ(V0__P,V3__n),happ(V1__P1,V3__n),happ(V2__PS,V3__n)) ).
fof('$_def_Coq.Vectors.Fin.of_nat_lt',axiom,
! [V1__p,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V1__p,V2__n) = c_24__lam__35806___24a1(V1__p) )
| ? [Vvar__0___24Anonymous__35797] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35797)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35797)
& ( ( V1__p = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V1__p,V2__n) = c_24__lam__35808___24a1(Vvar__0___24Anonymous__35797) )
| ? [Vvar__0___24Anonymous__35803] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35803)
& V1__p = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35803)
& cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V1__p,V2__n) = c_24__lam__35811___24a2(Vvar__0___24Anonymous__35797,Vvar__0___24Anonymous__35803) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.append',axiom,
! [V1__A,V2__n,V3__p,V4__v,V5__w] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,V2__n,V4__v)
=> ( ( V4__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = V5__w )
| ? [Vvar__1__h__75038] :
( t(Vvar__1__h__75038,V1__A)
& ? [Vvar__2__n__75039] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75039)
& ? [Vvar__3___24Anonymous__75040] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__75039,Vvar__3___24Anonymous__75040)
& V4__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__75038,Vvar__2__n__75039,Vvar__3___24Anonymous__75040)
& cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__75038,cCoq_2eInit_2eNat_2eadd___24a2(Vvar__2__n__75039,V3__p),cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,Vvar__2__n__75039,V3__p,Vvar__3___24Anonymous__75040,V5__w)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.case0',axiom,
! [V0__A,V1__P,V2__H,V3__v] :
( cType___24t(V0__A)
=> ( c_24__type__73912___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eO,V3__v)
=> ( ( V3__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2ecase0___24a4(V0__A,V1__P,V2__H,V3__v) = V2__H )
| ? [Vvar__1__h__73900] :
( t(Vvar__1__h__73900,V0__A)
& ? [Vvar__2__n__73901] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__73901)
& ? [Vvar__3___24Anonymous__73902] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__73901,Vvar__3___24Anonymous__73902)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__73900,Vvar__2__n__73901,Vvar__3___24Anonymous__73902)
& cCoq_2eVectors_2eVectorDef_2ecase0___24a4(V0__A,V1__P,V2__H,V3__v) = c_24__lam__73918___24a3(V0__A,V1__P,Vvar__2__n__73901) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.caseS',axiom,
! [V0__A,V1__P,V2__H,V3__n,V4__v] :
( cType___24t(V0__A)
=> ( c_24__type__73950___24t(V0__A,V1__P,V3__n,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v)
=> ( ( V4__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2ecaseS___24a5(V0__A,V1__P,V2__H,V3__n,V4__v) = c_24__lam__73957___24a3(V0__A,V1__P,V3__n) )
| ? [Vvar__1__h__73935] :
( t(Vvar__1__h__73935,V0__A)
& ? [Vvar__2__n__73936] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__73936)
& ? [Vvar__3___24Anonymous__73937] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__73936,Vvar__3___24Anonymous__73937)
& V4__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__73935,Vvar__2__n__73936,Vvar__3___24Anonymous__73937)
& cCoq_2eVectors_2eVectorDef_2ecaseS___24a5(V0__A,V1__P,V2__H,V3__n,V4__v) = happ(happ(happ(V2__H,Vvar__1__h__73935),Vvar__2__n__73936),Vvar__3___24Anonymous__73937) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.caseS\'',axiom,
! [V0__A,V1__n,V2__v] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> ( ( V2__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a3(V0__A,V1__n,V2__v) = c_24__lam__74025___24a2(V0__A,V1__n) )
| ? [Vvar__1__h__74002] :
( t(Vvar__1__h__74002,V0__A)
& ? [Vvar__2__n__74003] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__74003)
& ? [Vvar__3___24Anonymous__74004] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__74003,Vvar__3___24Anonymous__74004)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__74002,Vvar__2__n__74003,Vvar__3___24Anonymous__74004)
& cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a3(V0__A,V1__n,V2__v) = c_24__lam__74055___24a5(V0__A,V1__n,Vvar__1__h__74002,Vvar__2__n__74003,Vvar__3___24Anonymous__74004) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.const',axiom,
! [V0__A,V1__a] : cCoq_2eVectors_2eVectorDef_2econst___24a2(V0__A,V1__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(cCoq_2eVectors_2eVectorDef_2et___24a1(V0__A),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A),c_24__lam__74432___24a2(V0__A,V1__a)) ).
fof('$_def_Coq.Vectors.VectorDef.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__b,V5__n,V6__v] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__v)
=> ( ( V6__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2efold__left___24a6(V0__A,V1__B,V2__f,V4__b,V5__n,V6__v) = V4__b )
| ? [Vvar__1__h__75444] :
( t(Vvar__1__h__75444,V0__A)
& ? [Vvar__2__n__75445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75445)
& ? [Vvar__3___24Anonymous__75446] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__75445,Vvar__3___24Anonymous__75446)
& V6__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__75444,Vvar__2__n__75445,Vvar__3___24Anonymous__75446)
& cCoq_2eVectors_2eVectorDef_2efold__left___24a6(V0__A,V1__B,V2__f,V4__b,V5__n,V6__v) = cCoq_2eVectors_2eVectorDef_2efold__left___24a6(V0__A,V1__B,V2__f,happ(happ(V2__f,V4__b),Vvar__1__h__75444),Vvar__2__n__75445,Vvar__3___24Anonymous__75446) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.fold_left2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V5__a,V6__n,V7__v] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V6__n,V7__v)
=> ( ( V7__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__B)
& cCoq_2eVectors_2eVectorDef_2efold__left2___24a7(V0__A,V1__B,V2__C,V3__f,V5__a,V6__n,V7__v) = c_24__lam__75675___24a5(V0__A,V1__B,V2__C,V5__a,V6__n) )
| ? [Vvar__1__h__75646] :
( t(Vvar__1__h__75646,V1__B)
& ? [Vvar__2__n__75647] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75647)
& ? [Vvar__3___24Anonymous__75648] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,Vvar__2__n__75647,Vvar__3___24Anonymous__75648)
& V7__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,Vvar__1__h__75646,Vvar__2__n__75647,Vvar__3___24Anonymous__75648)
& cCoq_2eVectors_2eVectorDef_2efold__left2___24a7(V0__A,V1__B,V2__C,V3__f,V5__a,V6__n,V7__v) = c_24__lam__75728___24a9(V0__A,V1__B,V2__C,V3__f,V5__a,V6__n,Vvar__1__h__75646,Vvar__2__n__75647,Vvar__3___24Anonymous__75648) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.fold_right',axiom,
! [V0__A,V1__B,V2__f,V4__n,V5__v,V6__b] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ( ( V5__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2efold__right___24a6(V0__A,V1__B,V2__f,V4__n,V5__v,V6__b) = V6__b )
| ? [Vvar__1__h__75484] :
( t(Vvar__1__h__75484,V0__A)
& ? [Vvar__2__n__75485] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75485)
& ? [Vvar__3___24Anonymous__75486] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__75485,Vvar__3___24Anonymous__75486)
& V5__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__75484,Vvar__2__n__75485,Vvar__3___24Anonymous__75486)
& cCoq_2eVectors_2eVectorDef_2efold__right___24a6(V0__A,V1__B,V2__f,V4__n,V5__v,V6__b) = happ(happ(V2__f,Vvar__1__h__75484),cCoq_2eVectors_2eVectorDef_2efold__right___24a6(V0__A,V1__B,V2__f,Vvar__2__n__75485,Vvar__3___24Anonymous__75486,V6__b)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.fold_right2',axiom,
! [V0__A,V1__B,V2__C,V3__g,V4__c] : cCoq_2eVectors_2eVectorDef_2efold__right2___24a5(V0__A,V1__B,V2__C,V3__g,V4__c) = cCoq_2eVectors_2eVectorDef_2erect2___24a5(V0__A,V1__B,c_24__lam__75535___24a3(V0__A,V1__B,V2__C),V4__c,c_24__lam__75584___24a4(V0__A,V1__B,V2__C,V3__g)) ).
fof('$_def_Coq.Vectors.VectorDef.hd',axiom,
! [V0__A] : cCoq_2eVectors_2eVectorDef_2ehd___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V0__A,c_24__lam__70821___24a1(V0__A),c_24__lam__74423___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.last',axiom,
! [V0__A] : cCoq_2eVectors_2eVectorDef_2elast___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2erectS___24a4(V0__A,c_24__lam__70821___24a1(V0__A),c_24__lam__38501___24a1(V0__A),c_24__lam__70833___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.map',axiom,
! [V0__A,V1__B,V2__f,V4__n,V5__v] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ( ( V5__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2emap___24a5(V0__A,V1__B,V2__f,V4__n,V5__v) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__B) )
| ? [Vvar__1__h__75322] :
( t(Vvar__1__h__75322,V0__A)
& ? [Vvar__2__n__75323] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75323)
& ? [Vvar__3___24Anonymous__75324] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__75323,Vvar__3___24Anonymous__75324)
& V5__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__75322,Vvar__2__n__75323,Vvar__3___24Anonymous__75324)
& cCoq_2eVectors_2eVectorDef_2emap___24a5(V0__A,V1__B,V2__f,V4__n,V5__v) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,happ(V2__f,Vvar__1__h__75322),Vvar__2__n__75323,cCoq_2eVectors_2eVectorDef_2emap___24a5(V0__A,V1__B,V2__f,Vvar__2__n__75323,Vvar__3___24Anonymous__75324)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.map2',axiom,
! [V0__A,V1__B,V2__C,V3__g] : cCoq_2eVectors_2eVectorDef_2emap2___24a4(V0__A,V1__B,V2__C,V3__g) = cCoq_2eVectors_2eVectorDef_2erect2___24a5(V0__A,V1__B,c_24__lam__75355___24a3(V0__A,V1__B,V2__C),cCoq_2eVectors_2eVectorDef_2enil___24a1(V2__C),c_24__lam__75401___24a4(V0__A,V1__B,V2__C,V3__g)) ).
fof('$_def_Coq.Vectors.VectorDef.nth',axiom,
! [V0__A,V2__m,V3__v_27,V4__p] : cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V2__m,V3__v_27,V4__p) = c_24__case__Coq_2eVectors_2eFin_2et_2474541___24a4(V0__A,V2__m,V4__p,V3__v_27) ).
fof('$_def_Coq.Vectors.VectorDef.nth_order',axiom,
! [V0__A,V1__n,V2__v,V3__p] : cCoq_2eVectors_2eVectorDef_2enth__order___24a4(V0__A,V1__n,V2__v,V3__p) = cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V1__n,V2__v,cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V3__p,V1__n)) ).
fof('$_def_Coq.Vectors.VectorDef.of_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__9346] :
( t(Vvar__1___24Anonymous__9346,V1__A)
& ? [Vvar__2___24Anonymous__9347] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__9347)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__9346,Vvar__2___24Anonymous__9347)
& cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__9346,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__9347),cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V1__A,Vvar__2___24Anonymous__9347)) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.rect2',axiom,
! [V0__A,V1__B,V2__P,V3__bas,V4__rect,V6__n,V7__v1] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( c_24__type__74137___24t(V0__A,V1__B,V2__P,V6__n,V2__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__v1)
=> ( ( V7__v1 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2erect2___24a7(V0__A,V1__B,V2__P,V3__bas,V4__rect,V6__n,V7__v1) = c_24__lam__74150___24a5(V0__A,V1__B,V2__P,V3__bas,V6__n) )
| ? [Vvar__1__h__74098] :
( t(Vvar__1__h__74098,V0__A)
& ? [Vvar__2__n__74099] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__74099)
& ? [Vvar__3___24Anonymous__74100] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__74099,Vvar__3___24Anonymous__74100)
& V7__v1 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__74098,Vvar__2__n__74099,Vvar__3___24Anonymous__74100)
& cCoq_2eVectors_2eVectorDef_2erect2___24a7(V0__A,V1__B,V2__P,V3__bas,V4__rect,V6__n,V7__v1) = c_24__lam__74221___24a9(V0__A,V1__B,V2__P,V3__bas,V4__rect,V6__n,Vvar__1__h__74098,Vvar__2__n__74099,Vvar__3___24Anonymous__74100) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.rectS',axiom,
! [V0__A,V1__P,V2__bas,V3__rect,V5__n,V6__v] :
( cType___24t(V0__A)
=> ( c_24__type__70412___24t(V0__A,V1__P,V5__n,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__n),V6__v)
=> ( ( V6__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2erectS___24a6(V0__A,V1__P,V2__bas,V3__rect,V5__n,V6__v) = c_24__lam__70419___24a3(V0__A,V1__P,V5__n) )
| ? [Vvar__1__h__70346] :
( t(Vvar__1__h__70346,V0__A)
& ? [Vvar__2__n__70347] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__70347)
& ? [Vvar__3___24Anonymous__70348] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__70347,Vvar__3___24Anonymous__70348)
& V6__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__70346,Vvar__2__n__70347,Vvar__3___24Anonymous__70348)
& cCoq_2eVectors_2eVectorDef_2erectS___24a6(V0__A,V1__P,V2__bas,V3__rect,V5__n,V6__v) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592___24a8(V0__A,V1__P,V2__bas,V3__rect,V5__n,Vvar__1__h__70346,Vvar__2__n__70347,Vvar__3___24Anonymous__70348) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.replace',axiom,
! [V1__A,V2__n,V3__v,V4__p,V5__a] : cCoq_2eVectors_2eVectorDef_2ereplace___24a5(V1__A,V2__n,V3__v,V4__p,V5__a) = c_24__case__Coq_2eVectors_2eFin_2et_2474763___24a5(V1__A,V2__n,V4__p,V5__a,V3__v) ).
fof('$_def_Coq.Vectors.VectorDef.replace_order',axiom,
! [V0__A,V1__n,V2__v,V3__p] : cCoq_2eVectors_2eVectorDef_2ereplace__order___24a4(V0__A,V1__n,V2__v,V3__p) = cCoq_2eVectors_2eVectorDef_2ereplace___24a4(V0__A,V1__n,V2__v,cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V3__p,V1__n)) ).
fof('$_def_Coq.Vectors.VectorDef.rev',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVectorDef_2erev___24a3(V0__A,V1__n,V2__v) = cCoq_2eInit_2eLogic_2eeq__rect__r___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2et___24a1(V0__A),cCoq_2eVectors_2eVectorDef_2erev__append___24a5(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eO,V2__v,cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)),V1__n,cCoq_2eInit_2ePeano_2eplus__n__O___24a1(V1__n)) ).
fof('$_def_Coq.Vectors.VectorDef.rev_append',axiom,
! [V0__A,V1__n,V2__p,V3__v,V4__w] : cCoq_2eVectors_2eVectorDef_2erev__append___24a5(V0__A,V1__n,V2__p,V3__v,V4__w) = cCoq_2eInit_2eLogic_2eeq__rect__r___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__p),cCoq_2eVectors_2eVectorDef_2et___24a1(V0__A),cCoq_2eVectors_2eVectorDef_2erev__append__tail___24a5(V0__A,V1__n,V2__p,V3__v,V4__w),cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p),cCoq_2eArith_2ePlus_2eplus__tail__plus___24a2(V1__n,V2__p)) ).
fof('$_def_Coq.Vectors.VectorDef.rev_append_tail',axiom,
! [V1__A,V2__n,V3__p,V4__v,V5__w] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,V2__n,V4__v)
=> ( ( V4__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2erev__append__tail___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = V5__w )
| ? [Vvar__1__h__75284] :
( t(Vvar__1__h__75284,V1__A)
& ? [Vvar__2__n__75285] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__75285)
& ? [Vvar__3___24Anonymous__75286] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__75285,Vvar__3___24Anonymous__75286)
& V4__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__75284,Vvar__2__n__75285,Vvar__3___24Anonymous__75286)
& cCoq_2eVectors_2eVectorDef_2erev__append__tail___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = cCoq_2eVectors_2eVectorDef_2erev__append__tail___24a5(V1__A,Vvar__2__n__75285,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__p),Vvar__3___24Anonymous__75286,cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__75284,V3__p,V5__w)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.shiftin',axiom,
! [V1__A,V2__n,V3__a,V4__v] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,V2__n,V4__v)
=> ( ( V4__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
& cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V1__A,V2__n,V3__a,V4__v) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,V3__a,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)) )
| ? [Vvar__1__h__74903] :
( t(Vvar__1__h__74903,V1__A)
& ? [Vvar__2__n__74904] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__74904)
& ? [Vvar__3___24Anonymous__74905] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__74904,Vvar__3___24Anonymous__74905)
& V4__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__74903,Vvar__2__n__74904,Vvar__3___24Anonymous__74905)
& cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V1__A,V2__n,V3__a,V4__v) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__74903,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__74904),cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V1__A,Vvar__2__n__74904,V3__a,Vvar__3___24Anonymous__74905)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.shiftout',axiom,
! [V0__A] : cCoq_2eVectors_2eVectorDef_2eshiftout___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2erectS___24a4(V0__A,c_24__lam__70842___24a1(V0__A),c_24__lam__70844___24a1(V0__A),c_24__lam__70855___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.shiftrepeat',axiom,
! [V0__A] : cCoq_2eVectors_2eVectorDef_2eshiftrepeat___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2erectS___24a4(V0__A,c_24__lam__70866___24a1(V0__A),c_24__lam__70868___24a1(V0__A),c_24__lam__70879___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.t_rec',axiom,
! [V0__A,V1__P] : cCoq_2eVectors_2eVectorDef_2et__rec___24a2(V0__A,V1__P) = cCoq_2eVectors_2eVectorDef_2et__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Vectors.VectorDef.t_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__n,V6__t] :
( cType___24t(V0__A)
=> ( c_24__type__73790___24t(V0__A,V1__P,V5__n,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__t)
=> ( ( V6__t = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorDef_2et__rect___24a6(V0__A,V1__P,V2__f,V3__f,V5__n,V6__t) = V2__f )
| ? [Vvar__1__h__73775] :
( t(Vvar__1__h__73775,V0__A)
& ? [Vvar__2__n__73776] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__73776)
& ? [Vvar__3___24Anonymous__73777] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__73776,Vvar__3___24Anonymous__73777)
& V6__t = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__73775,Vvar__2__n__73776,Vvar__3___24Anonymous__73777)
& cCoq_2eVectors_2eVectorDef_2et__rect___24a6(V0__A,V1__P,V2__f,V3__f,V5__n,V6__t) = happ(happ(happ(happ(V3__f,Vvar__1__h__73775),Vvar__2__n__73776),Vvar__3___24Anonymous__73777),cCoq_2eVectors_2eVectorDef_2et__rect___24a6(V0__A,V1__P,V2__f,V3__f,Vvar__2__n__73776,Vvar__3___24Anonymous__73777)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Vectors.VectorDef.take',axiom,
! [V1__A,V2__n,V3__p,V5__v] : cCoq_2eVectors_2eVectorDef_2etake___24a4(V1__A,V2__n,V3__p,V5__v) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984___24a4(V1__A,V2__n,V3__p,V5__v) ).
fof('$_def_Coq.Vectors.VectorDef.tl',axiom,
! [V0__A] : cCoq_2eVectors_2eVectorDef_2etl___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V0__A,c_24__lam__70842___24a1(V0__A),c_24__lam__74889___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.to_list',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V0__A,V1__n,V2__v) = c_24__fix__9407__v__CANONICAL__2___24a5(V0__A,V1__n,V1__n,V2__v,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ).
fof('$_def_Coq.Vectors.VectorDef.uncons',axiom,
! [V0__A,V1__n,V2__v] : cCoq_2eVectors_2eVectorDef_2euncons___24a3(V0__A,V1__n,V2__v) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V1__n),cCoq_2eVectors_2eVectorDef_2ehd___24a3(V0__A,V1__n,V2__v),cCoq_2eVectors_2eVectorDef_2etl___24a3(V0__A,V1__n,V2__v)) ).
fof('$_def_Coq.Vectors.VectorEq.eqb',axiom,
! [V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V5__v1)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v2)
=> ( V5__v1 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& ( ( V6__v2 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__1__h__76040] :
( t(Vvar__1__h__76040,V0__A)
& ? [Vvar__2__n__76041] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__76041)
& ? [Vvar__3___24Anonymous__76042] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__76041,Vvar__3___24Anonymous__76042)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__76040,Vvar__2__n__76041,Vvar__3___24Anonymous__76042)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1__h__76047] :
( t(Vvar__1__h__76047,V0__A)
& ? [Vvar__2__n__76048] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__76048)
& ? [Vvar__3___24Anonymous__76049] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__76048,Vvar__3___24Anonymous__76049)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v2)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__76048)
=> ( V5__v1 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__76047,Vvar__2__n__76048,Vvar__3___24Anonymous__76049)
& ( ( V6__v2 = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1__h__76072] :
( t(Vvar__1__h__76072,V0__A)
& ? [Vvar__2__n__76073] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__76073)
& ? [Vvar__3___24Anonymous__76074] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__76073,Vvar__3___24Anonymous__76074)
& V6__v2 = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__76072,Vvar__2__n__76073,Vvar__3___24Anonymous__76074)
& cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__m,V4__n,V5__v1,V6__v2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V1__A__beq,Vvar__1__h__76047),Vvar__1__h__76072),cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,Vvar__2__n__76048,Vvar__2__n__76073,Vvar__3___24Anonymous__76049,Vvar__3___24Anonymous__76074)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__20960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20960)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20960)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20960) )
| ? [Vvar__0___24Anonymous__20961] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20961)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20961)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20961) ) ) ) ).
fof('$_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__367] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__367)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__367)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__371)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__371)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__367,Vvar__0___24Anonymous__371)) )
| ? [Vvar__0___24Anonymous__372] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__372)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__372)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__367,Vvar__0___24Anonymous__372) ) ) ) ) )
| ? [Vvar__0___24Anonymous__373] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__373)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__373)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__377] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__377)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__377)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__377,Vvar__0___24Anonymous__373) )
| ? [Vvar__0___24Anonymous__378] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__378)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__378)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__373,Vvar__0___24Anonymous__378)) ) ) ) ) ) ) ) ).
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__1256] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1256)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1256)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1257] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1257)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1257)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__1258] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1258)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1258)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__1262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1262)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1262)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1258,Vvar__0___24Anonymous__1262) )
| ? [Vvar__0___24Anonymous__1263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1263)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1263)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__1264] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1264)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1264)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1268)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1268)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1269)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1269)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1264,Vvar__0___24Anonymous__1269)) ) ) ) ) ) ) ) ).
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.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__386] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__386)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__386)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__390)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__390)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__386,Vvar__0___24Anonymous__390)) )
| ? [Vvar__0___24Anonymous__391] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__391)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__391)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__386,Vvar__0___24Anonymous__391)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__392] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__392)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__392)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__396)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__396)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__392,Vvar__0___24Anonymous__396)) )
| ? [Vvar__0___24Anonymous__397] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__397)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__397)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__392,Vvar__0___24Anonymous__397)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__20972] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20972)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20972)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20972) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1273] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1273)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1273)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__1273)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__382] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__382)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__382)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__382) )
| ? [Vvar__0___24Anonymous__383] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__383)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__383)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__383) ) ) ) ).
fof('$_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__35724] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35724)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35724)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__35724) )
| ? [Vvar__0___24Anonymous__35725] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35725)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35725)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__20979] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20979)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20979)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__20989] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20989)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20979)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20989)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20989)
& ? [Vvar__2___24Anonymous__20997] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__20997)
& ? [Vvar__3___24Anonymous__20998] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__20998)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__20979,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__20989)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__20997,Vvar__3___24Anonymous__20998)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__20997),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__20998)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21000)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20979)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21000)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21000)
& ? [Vvar__2___24Anonymous__21008] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21008)
& ? [Vvar__3___24Anonymous__21009] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21009)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__20979,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21000)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21008,Vvar__3___24Anonymous__21009)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21008)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21009)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21011] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21011)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21011)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__21021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21021)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21011)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21021)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21021)
& ? [Vvar__2___24Anonymous__21029] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21029)
& ? [Vvar__3___24Anonymous__21030] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21030)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21011,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21021)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21029,Vvar__3___24Anonymous__21030)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21029)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21030))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21032] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21032)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21011)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21032)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21032)
& ? [Vvar__2___24Anonymous__21040] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21040)
& ? [Vvar__3___24Anonymous__21041] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__21041)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__21011,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21032)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__21040,Vvar__3___24Anonymous__21041)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__21040),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__21041))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_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__20968] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20968)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__20968)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__20968) )
| ? [Vvar__0___24Anonymous__20969] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20969)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__20969)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength',axiom,
cCoq_2eZArith_2eZcomplements_2eZlength = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_def_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
! [V1__acc,V2__A,V3__l] :
( cType___24t(V2__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__A)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = V1__acc )
| ? [Vvar__1___24Anonymous__10886] :
( t(Vvar__1___24Anonymous__10886,V2__A)
& ? [Vvar__2___24Anonymous__10887] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__A,Vvar__2___24Anonymous__10887)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__A,Vvar__1___24Anonymous__10886,Vvar__2___24Anonymous__10887)
& cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V1__acc,V2__A,V3__l) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__acc),V2__A,Vvar__2___24Anonymous__10887) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znat.neq',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.Zpower.shift_nat',axiom,
! [V0__n,V1__z] : cCoq_2eZArith_2eZpower_2eshift__nat___24a2(V0__n,V1__z) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(c_24__lam__77166,V1__z,c_24__lam__77167,V0__n) ).
fof('$_def_Coq.funind.Recdef.iter',axiom,
! [V0__A,V2__n,V3__fl,V4__def] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2efunind_2eRecdef_2eiter___24a4(V0__A,V2__n,V3__fl,V4__def) = V4__def )
| ? [Vvar__0___24Anonymous__8296] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8296)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8296)
& cCoq_2efunind_2eRecdef_2eiter___24a4(V0__A,V2__n,V3__fl,V4__def) = happ(V3__fl,cCoq_2efunind_2eRecdef_2eiter___24a4(V0__A,Vvar__0___24Anonymous__8296,V3__fl,V4__def)) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__21145___24a1(V0__D) ).
fof('$_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__24078] :
( t(Vvar__1___24Anonymous__24078,V1__A)
& ? [Vvar__2___24Anonymous__24079] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__24079)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__24079)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__24078,Vvar__2___24Anonymous__24079)
& ( ( Vvar__2___24Anonymous__24079 = 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__24078)) ) )
| ? [Vvar__1___24Anonymous__24090] :
( t(Vvar__1___24Anonymous__24090,V1__A)
& ? [Vvar__2___24Anonymous__24091] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__24091)
& Vvar__2___24Anonymous__24079 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__24090,Vvar__2___24Anonymous__24091)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__24078))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__24079) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__24059] :
( t(Vvar__1___24Anonymous__24059,V1__A)
& ? [Vvar__2___24Anonymous__24060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__24060)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__24059,Vvar__2___24Anonymous__24060)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__24059))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__24060,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30111] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30111)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30111)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__30112] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30112)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30112)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30115] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30115)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30115)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__30112,Vvar__0___24Anonymous__30115) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
! [V0__A,V1__B,V2__f,V3__o] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
=> ( ? [Vvar__1___24Anonymous__50037] :
( t(Vvar__1___24Anonymous__50037,V0__A)
& V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__50037)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__50037) )
| ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
& cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__35587] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__35587)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__35587) ) ).
fof('$_def_Coq.micromega.ZMicromega.make_conj',axiom,
cCoq_2emicromega_2eZMicromega_2emake__conj = cCoq_2emicromega_2eRefl_2emake__conj ).
fof('$_def_Coq.micromega.ZMicromega.make_impl',axiom,
cCoq_2emicromega_2eZMicromega_2emake__impl = cCoq_2emicromega_2eRefl_2emake__impl ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.setoid_ring.BinList.jump',axiom,
! [V0__A,V2__p,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( ? [Vvar__0___24Anonymous__21073] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21073)
& V2__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21073)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__21073,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__21073,cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l))) )
| ? [Vvar__0___24Anonymous__21074] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21074)
& V2__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21074)
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__21074,cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,Vvar__0___24Anonymous__21074,V3__l)) )
| ( V2__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V0__A,V2__p,V3__l) = cCoq_2eLists_2eList_2etl___24a2(V0__A,V3__l) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.FEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V9__C)
=> ( cType___24t(V11__Cpow)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,V16__pe)
=> ( ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V1__rO )
| ( V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V9__C)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__37765] :
( t(Vvar__1___24Anonymous__37765,V9__C)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V9__C,Vvar__1___24Anonymous__37765)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V10__phi,Vvar__1___24Anonymous__37765) )
| ? [Vvar__1___24Anonymous__37767] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__37767)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V9__C,Vvar__1___24Anonymous__37767)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__37767,V15__l) )
| ? [Vvar__1___24Anonymous__37769] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37769)
& ? [Vvar__2___24Anonymous__37770] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__37770)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V9__C,Vvar__1___24Anonymous__37769,Vvar__2___24Anonymous__37770)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37769)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__37770)) ) )
| ? [Vvar__1___24Anonymous__37773] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37773)
& ? [Vvar__2___24Anonymous__37774] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__37774)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V9__C,Vvar__1___24Anonymous__37773,Vvar__2___24Anonymous__37774)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37773)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__37774)) ) )
| ? [Vvar__1___24Anonymous__37777] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37777)
& ? [Vvar__2___24Anonymous__37778] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__37778)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V9__C,Vvar__1___24Anonymous__37777,Vvar__2___24Anonymous__37778)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37777)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__37778)) ) )
| ? [Vvar__1___24Anonymous__37781] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37781)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V9__C,Vvar__1___24Anonymous__37781)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37781)) )
| ? [Vvar__1___24Anonymous__37783] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37783)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V9__C,Vvar__1___24Anonymous__37783)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(V8__rinv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37783)) )
| ? [Vvar__1___24Anonymous__37785] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37785)
& ? [Vvar__2___24Anonymous__37786] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__2___24Anonymous__37786)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V9__C,Vvar__1___24Anonymous__37785,Vvar__2___24Anonymous__37786)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37785)),cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__2___24Anonymous__37786)) ) )
| ? [Vvar__1___24Anonymous__37789] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V9__C,Vvar__1___24Anonymous__37789)
& ? [Vvar__2___24Anonymous__37790] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__37790)
& V16__pe = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V9__C,Vvar__1___24Anonymous__37789,Vvar__2___24Anonymous__37790)
& cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,V16__pe) = happ(happ(V13__rpow,cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow,V15__l,Vvar__1___24Anonymous__37789)),happ(V12__Cp__phi,Vvar__2___24Anonymous__37790)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__22488] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__22488)
& ? [Vvar__2___24Anonymous__22489] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__22489)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__22488,Vvar__2___24Anonymous__22489)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__22488),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__22489,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__38080] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__38080)
& ? [Vvar__2___24Anonymous__38081] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__38081)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__38081)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__38080,Vvar__2___24Anonymous__38081)
& ( ( Vvar__2___24Anonymous__38081 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__38080)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__38092] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__38092)
& ? [Vvar__2___24Anonymous__38093] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__38093)
& Vvar__2___24Anonymous__38081 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__38092,Vvar__2___24Anonymous__38093)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__38080)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__38081) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__38067] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__38067)
& ? [Vvar__2__denum__38068] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__38068)
& ? [Vvar__3__condition__38069] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__38069)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__38067,Vvar__2__denum__38068,Vvar__3__condition__38069)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__38069 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__38058] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__38058)
& ? [Vvar__2__denum__38059] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__38059)
& ? [Vvar__3__condition__38060] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__38060)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__38058,Vvar__2__denum__38059,Vvar__3__condition__38060)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__38059 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__38047] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__38047)
& ? [Vvar__2__denum__38048] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__38048)
& ? [Vvar__3__condition__38049] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__38049)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__38047,Vvar__2__denum__38048,Vvar__3__condition__38049)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__38047 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__44919] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__44919)
& ? [Vvar__2__rsplit__common__44920] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__44920)
& ? [Vvar__3__rsplit__right__44921] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__44921)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__44919,Vvar__2__rsplit__common__44920,Vvar__3__rsplit__right__44921)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__44919 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__44939] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__44939)
& ? [Vvar__2__rsplit__common__44940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__44940)
& ? [Vvar__3__rsplit__right__44941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__44941)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__44939,Vvar__2__rsplit__common__44940,Vvar__3__rsplit__right__44941)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__44941 ) ) ) ) ) ).
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.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__38367] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38367)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38367)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__38367) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__22528] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22528)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22528)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__22528) )
| ? [Vvar__0___24Anonymous__22529] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22529)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22529)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__22529)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__8531___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__30170] :
( t(Vvar__1___24Anonymous__30170,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__30170)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__30170) )
| ? [Vvar__1___24Anonymous__30172] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__30172)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__30172)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__30172,V13__l) )
| ? [Vvar__1___24Anonymous__30174] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__30174)
& ? [Vvar__2___24Anonymous__30175] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__30175)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__30174,Vvar__2___24Anonymous__30175)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__30174)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__30175)) ) )
| ? [Vvar__1___24Anonymous__30178] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__30178)
& ? [Vvar__2___24Anonymous__30179] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__30179)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__30178,Vvar__2___24Anonymous__30179)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__30178)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__30179)) ) )
| ? [Vvar__1___24Anonymous__30182] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__30182)
& ? [Vvar__2___24Anonymous__30183] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__30183)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__30182,Vvar__2___24Anonymous__30183)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__30182)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__30183)) ) )
| ? [Vvar__1___24Anonymous__30186] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__30186)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__30186)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__30186)) )
| ? [Vvar__1___24Anonymous__30188] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__30188)
& ? [Vvar__2___24Anonymous__30189] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__30189)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__30188,Vvar__2___24Anonymous__30189)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__30188)),happ(V10__Cp__phi,Vvar__2___24Anonymous__30189)) ) ) ) ) ) ) ) ).
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__8416] :
( t(Vvar__1___24Anonymous__8416,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__8416)
& ( ? [Vvar__1___24Anonymous__8426] :
( t(Vvar__1___24Anonymous__8426,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__8426)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__8416),Vvar__1___24Anonymous__8426) )
| ? [Vvar__1___24Anonymous__8428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8428)
& ? [Vvar__2___24Anonymous__8429] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__8429)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__8428,Vvar__2___24Anonymous__8429)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8432] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8432)
& ? [Vvar__2___24Anonymous__8433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8433)
& ? [Vvar__3___24Anonymous__8434] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__8434)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__8432,Vvar__2___24Anonymous__8433,Vvar__3___24Anonymous__8434)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8439)
& ? [Vvar__2___24Anonymous__8440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__8440)
& ( 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__8439,Vvar__2___24Anonymous__8440)
& ( ? [Vvar__1___24Anonymous__8460] :
( t(Vvar__1___24Anonymous__8460,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__8460)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8462] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8462)
& ? [Vvar__2___24Anonymous__8463] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__8463)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8439)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8462)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__8462,Vvar__2___24Anonymous__8463)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__8439,Vvar__1___24Anonymous__8462) = 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__8440,Vvar__2___24Anonymous__8463) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__8439,Vvar__1___24Anonymous__8462) = 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__8439,Vvar__1___24Anonymous__8462) = 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__8468] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8468)
& ? [Vvar__2___24Anonymous__8469] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8469)
& ? [Vvar__3___24Anonymous__8470] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__8470)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__8468,Vvar__2___24Anonymous__8469,Vvar__3___24Anonymous__8470)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__8475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8475)
& ? [Vvar__2___24Anonymous__8476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8476)
& ? [Vvar__3___24Anonymous__8477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__8477)
& ( 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__8475,Vvar__2___24Anonymous__8476,Vvar__3___24Anonymous__8477)
& ( ? [Vvar__1___24Anonymous__8510] :
( t(Vvar__1___24Anonymous__8510,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__8510)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__8512] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8512)
& ? [Vvar__2___24Anonymous__8513] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__8513)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__8512,Vvar__2___24Anonymous__8513)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__8516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8516)
& ? [Vvar__2___24Anonymous__8517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8517)
& ? [Vvar__3___24Anonymous__8518] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__8518)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8476)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8517)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__8516,Vvar__2___24Anonymous__8517,Vvar__3___24Anonymous__8518)
& ( ( cType___24t(V0__C)
=> ( c_24__type__8531___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8475)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__8516)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__8476,Vvar__2___24Anonymous__8517) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8475,Vvar__1___24Anonymous__8516) = 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__8477,Vvar__3___24Anonymous__8518) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__8475,Vvar__1___24Anonymous__8516) = 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__8476,Vvar__2___24Anonymous__8517) = 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__8476,Vvar__2___24Anonymous__8517) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign] : cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V12__Cpow,V13__Cp__phi,V14__rpow,V15__get__sign) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V0__R,V1__rO,V2__rI,V3__radd,V5__rsub,V6__ropp,V7__C,V8__cO,V9__cI,V10__ceqb,V11__phi,V15__get__sign,c_24__let__16__mkpow__55942___24a5(V0__R,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__17__mkopp__pow__55943___24a6(V0__R,V6__ropp,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow),c_24__let__18__mkmult__pow__55944___24a6(V0__R,V4__rmul,V7__C,V12__Cpow,V13__Cp__phi,V14__rpow)) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__54263] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__54263)
& ? [Vvar__2___24Anonymous__54264] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__54264)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__54263)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__54263,Vvar__2___24Anonymous__54264)
& ? [Vvar__2___24Anonymous__54282] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__54282)
& ? [Vvar__3___24Anonymous__54283] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__54283)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__54264)
=> ( Vvar__1___24Anonymous__54263 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__54282,Vvar__3___24Anonymous__54283)
& ( ( Vvar__2___24Anonymous__54264 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__54282)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__54283))) ) )
| ? [Vvar__1___24Anonymous__54294] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__54294)
& ? [Vvar__2___24Anonymous__54295] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__54295)
& Vvar__2___24Anonymous__54264 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__54294,Vvar__2___24Anonymous__54295)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__54282)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__54283)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__54264) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__38781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38781)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38781)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__38781),V4__x,Vvar__0___24Anonymous__38781) )
| ? [Vvar__0___24Anonymous__38782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38782)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38782)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__38782),V4__x,Vvar__0___24Anonymous__38782) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__8872___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__30405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30405)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30405)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__30405) ) ) ) ) ).
fof('$_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__30385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30385)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30385)
& 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__30386__30389___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30385)),c_24__let__var__6__p__30386__30389___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30385))) )
| ? [Vvar__0___24Anonymous__30387] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30387)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30387)
& 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__30388__30390___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30387)),c_24__let__var__6__p__30388__30390___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__30387)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_QuicksortComplexity.arith_lems.log2ceil',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2earith__lems_2elog2ceil___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__39511] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__39511)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__39511)
& cQuicksortComplexity_2earith__lems_2elog2ceil___24a1(V0__n) = cQuicksortComplexity_2earith__lems_2eceil__log2__S___24a1(Vvar__0___24Anonymous__39511) ) ) ) ).
fof('$_def_QuicksortComplexity.arith_lems.pow',axiom,
! [V1__b,V2__e] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__e)
=> ( ( V2__e = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2earith__lems_2epow___24a2(V1__b,V2__e) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__35632] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35632)
& V2__e = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35632)
& cQuicksortComplexity_2earith__lems_2epow___24a2(V1__b,V2__e) = cCoq_2eInit_2eNat_2emul___24a2(V1__b,cQuicksortComplexity_2earith__lems_2epow___24a2(V1__b,Vvar__0___24Anonymous__35632)) ) ) ) ).
fof('$_def_QuicksortComplexity.arith_lems.sqrd',axiom,
! [V0__n] : cQuicksortComplexity_2earith__lems_2esqrd___24a1(V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V0__n,V0__n) ).
fof('$_def_QuicksortComplexity.list_utils.Partitioning',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T) = c_24__type__2690___24a1(V0__T) ).
fof('$_def_QuicksortComplexity.list_utils.add',axiom,
cQuicksortComplexity_2elist__utils_2eadd = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_QuicksortComplexity.list_utils.concat',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2econcat___24a1(V0__T) = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2eapp___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) ).
fof('$_def_QuicksortComplexity.list_utils.count',axiom,
! [V0__X,V1__p,V3__l] :
( cType___24t(V0__X)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X)
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__15049] :
( t(Vvar__1___24Anonymous__15049,V0__X)
& ? [Vvar__2___24Anonymous__15050] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,Vvar__2___24Anonymous__15050)
& ( cType___24t(V0__X)
=> ( c_24__type__7910___24t(V0__X,V1__p)
=> ( t(Vvar__1___24Anonymous__15049,V0__X)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,Vvar__1___24Anonymous__15049,Vvar__2___24Anonymous__15050)
& ( ( happ(V1__p,Vvar__1___24Anonymous__15049) = cCoq_2eInit_2eDatatypes_2etrue
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__15050)) )
| ( happ(V1__p,Vvar__1___24Anonymous__15049) = cCoq_2eInit_2eDatatypes_2efalse
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__15050) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.list_utils.insert_everywhere',axiom,
! [V0__T,V2__x,V3__l] :
( cType___24t(V0__T)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)
& cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a3(V0__T,V2__x,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T))) )
| ? [Vvar__1___24Anonymous__18592] :
( t(Vvar__1___24Anonymous__18592,V0__T)
& ? [Vvar__2___24Anonymous__18593] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2___24Anonymous__18593)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,Vvar__1___24Anonymous__18592,Vvar__2___24Anonymous__18593)
& cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a3(V0__T,V2__x,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,Vvar__1___24Anonymous__18592,Vvar__2___24Anonymous__18593)),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2econs___24a2(V0__T,Vvar__1___24Anonymous__18592),cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a3(V0__T,V2__x,Vvar__2___24Anonymous__18593))) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.list_utils.me',axiom,
! [V0__T,V1__ab] : cQuicksortComplexity_2elist__utils_2eme___24a2(V0__T,V1__ab) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__ab)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__ab))) ).
fof('$_def_QuicksortComplexity.list_utils.merges',axiom,
! [V0__T,V1__a,V2__b] : cQuicksortComplexity_2elist__utils_2emerges___24a3(V0__T,V1__a,V2__b) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cQuicksortComplexity_2elist__utils_2emerges__spec___24a3(V0__T,cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__a,V2__b)),cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__a,V2__b))),cQuicksortComplexity_2elist__utils_2emerges__ex___24a2(V0__T,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__a,V2__b))) ).
fof('$_def_QuicksortComplexity.list_utils.perms',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2eperms___24a1(V0__T) = cCoq_2eLists_2eList_2efold__right___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),V0__T,c_24__lam__18601___24a1(V0__T),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)))) ).
fof('$_def_QuicksortComplexity.list_utils.product',axiom,
! [V0__A,V1__B,V2__aa,V3__bb] : cQuicksortComplexity_2elist__utils_2eproduct___24a4(V0__A,V1__B,V2__aa,V3__bb) = cQuicksortComplexity_2elist__utils_2econcat___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2emap___24a4(V0__A,cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)),c_24__lam__15194___24a3(V0__A,V1__B,V3__bb),V2__aa)) ).
fof('$_def_QuicksortComplexity.list_utils.repeat',axiom,
! [V1__T,V2__n,V3__x] :
( cType___24t(V1__T)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T) )
| ? [Vvar__0___24Anonymous__15095] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15095)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__15095)
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V3__x,cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,Vvar__0___24Anonymous__15095,V3__x)) ) ) ) ) ).
fof('$_def_QuicksortComplexity.list_utils.splits',axiom,
! [V0__T,V2__l] :
( cType___24t(V0__T)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)
& cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T))) )
| ? [Vvar__1___24Anonymous__18577] :
( t(Vvar__1___24Anonymous__18577,V0__T)
& ? [Vvar__2___24Anonymous__18578] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2___24Anonymous__18578)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,Vvar__1___24Anonymous__18577,Vvar__2___24Anonymous__18578)
& cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),Vvar__1___24Anonymous__18577,Vvar__2___24Anonymous__18578),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),c_24__lam__18584___24a2(V0__T,Vvar__1___24Anonymous__18577),cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,Vvar__2___24Anonymous__18578))) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_below.Snb',axiom,
! [V0__n,V1__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__nb)
=> ? [Vvar__0__v__447] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__447)
& ? [Vvar__1__p__448] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__448)
& V1__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__447,Vvar__1__p__448)
& cQuicksortComplexity_2enat__below_2eSnb___24a2(V0__n,V1__nb) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__v__447),Vvar__1__p__448) ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_below.natBelow_rec',axiom,
! [V0__P] : cQuicksortComplexity_2enat__below_2enatBelow__rec___24a1(V0__P) = cQuicksortComplexity_2enat__below_2enatBelow__rect___24a1(V0__P) ).
fof('$_def_QuicksortComplexity.nat_below.natBelow_rect',axiom,
! [V0__P,V1__f,V2__n,V3__n] :
( c_24__type__76776___24t(V0__P,V2__n,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V2__n,V3__n)
=> ? [Vvar__0__v__76767] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__76767)
& ? [Vvar__1__p__76768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__76768)
& V3__n = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__76767,Vvar__1__p__76768)
& cQuicksortComplexity_2enat__below_2enatBelow__rect___24a4(V0__P,V1__f,V2__n,V3__n) = happ(happ(V1__f,Vvar__0__v__76767),Vvar__1__p__76768) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_below.nb0',axiom,
! [V0__n] : cQuicksortComplexity_2enat__below_2enb0___24a1(V0__n) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ).
fof('$_def_QuicksortComplexity.nat_below.nb_val',axiom,
! [V0__n,V1__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__nb)
=> ? [Vvar__0__v__165] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__165)
& ? [Vvar__1__p__166] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__166)
& V1__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__165,Vvar__1__p__166)
& cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__nb) = Vvar__0__v__165 ) ) ) ) ).
fof('$_def_QuicksortComplexity.nat_seqs.nats',axiom,
! [V1__b,V2__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__w)
=> ( ( V2__w = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V2__w) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat) )
| ? [Vvar__0___24Anonymous__19874] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19874)
& V2__w = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19874)
& cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V2__w) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,V1__b,cQuicksortComplexity_2enat__seqs_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__b),Vvar__0___24Anonymous__19874)) ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Ec',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ? [Vvar__0__Ec__173] :
( cType___24t(Vvar__0__Ec__173)
& ? [Vvar__1__Ecmp__174] :
( c_24__type__271___24t(Vvar__0__Ec__173,Vvar__1__Ecmp__174)
& ! [Vvar__var__2__x__180__182] :
( t(Vvar__var__2__x__180__182,Vvar__0__Ec__173)
=> ! [Vvar__var__3__y__181__183] :
( t(Vvar__var__3__y__181__183,Vvar__0__Ec__173)
=> happ(happ(Vvar__1__Ecmp__174,Vvar__var__2__x__180__182),Vvar__var__3__y__181__183) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vvar__1__Ecmp__174,Vvar__var__3__y__181__183),Vvar__var__2__x__180__182)) ) )
& ! [Vvar__var__3__x__185__191] :
( t(Vvar__var__3__x__185__191,Vvar__0__Ec__173)
=> ! [Vvar__var__4__y__186__192] :
( t(Vvar__var__4__y__186__192,Vvar__0__Ec__173)
=> ! [Vvar__var__5__z__188__194] :
( t(Vvar__var__5__z__188__194,Vvar__0__Ec__173)
=> ! [Vvar__var__6__c__187__193] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__6__c__187__193)
=> ( happ(happ(Vvar__1__Ecmp__174,Vvar__var__3__x__185__191),Vvar__var__4__y__186__192) = Vvar__var__6__c__187__193
=> ( happ(happ(Vvar__1__Ecmp__174,Vvar__var__4__y__186__192),Vvar__var__5__z__188__194) = Vvar__var__6__c__187__193
=> happ(happ(Vvar__1__Ecmp__174,Vvar__var__3__x__185__191),Vvar__var__5__z__188__194) = Vvar__var__6__c__187__193 ) ) ) ) ) )
& ! [Vvar__var__4__x__198__204] :
( t(Vvar__var__4__x__198__204,Vvar__0__Ec__173)
=> ! [Vvar__var__5__y__199__205] :
( t(Vvar__var__5__y__199__205,Vvar__0__Ec__173)
=> ! [Vvar__var__6__z__200__206] :
( t(Vvar__var__6__z__200__206,Vvar__0__Ec__173)
=> ! [Vvar__var__7__c__201__207] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__7__c__201__207)
=> ( happ(happ(Vvar__1__Ecmp__174,Vvar__var__4__x__198__204),Vvar__var__5__y__199__205) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vvar__1__Ecmp__174,Vvar__var__5__y__199__205),Vvar__var__6__z__200__206) = Vvar__var__7__c__201__207
=> happ(happ(Vvar__1__Ecmp__174,Vvar__var__4__x__198__204),Vvar__var__6__z__200__206) = Vvar__var__7__c__201__207 ) ) ) ) ) )
& V0__e = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__173,Vvar__1__Ecmp__174)
& cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e) = Vvar__0__Ec__173 ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Ecmp',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ? [Vvar__0__Ec__520] :
( cType___24t(Vvar__0__Ec__520)
& ? [Vvar__1__Ecmp__521] :
( c_24__type__271___24t(Vvar__0__Ec__520,Vvar__1__Ecmp__521)
& ! [Vvar__var__2__x__527__529] :
( t(Vvar__var__2__x__527__529,Vvar__0__Ec__520)
=> ! [Vvar__var__3__y__528__530] :
( t(Vvar__var__3__y__528__530,Vvar__0__Ec__520)
=> happ(happ(Vvar__1__Ecmp__521,Vvar__var__2__x__527__529),Vvar__var__3__y__528__530) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vvar__1__Ecmp__521,Vvar__var__3__y__528__530),Vvar__var__2__x__527__529)) ) )
& ! [Vvar__var__3__x__532__538] :
( t(Vvar__var__3__x__532__538,Vvar__0__Ec__520)
=> ! [Vvar__var__4__y__533__539] :
( t(Vvar__var__4__y__533__539,Vvar__0__Ec__520)
=> ! [Vvar__var__5__z__535__541] :
( t(Vvar__var__5__z__535__541,Vvar__0__Ec__520)
=> ! [Vvar__var__6__c__534__540] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__6__c__534__540)
=> ( happ(happ(Vvar__1__Ecmp__521,Vvar__var__3__x__532__538),Vvar__var__4__y__533__539) = Vvar__var__6__c__534__540
=> ( happ(happ(Vvar__1__Ecmp__521,Vvar__var__4__y__533__539),Vvar__var__5__z__535__541) = Vvar__var__6__c__534__540
=> happ(happ(Vvar__1__Ecmp__521,Vvar__var__3__x__532__538),Vvar__var__5__z__535__541) = Vvar__var__6__c__534__540 ) ) ) ) ) )
& ! [Vvar__var__4__x__545__551] :
( t(Vvar__var__4__x__545__551,Vvar__0__Ec__520)
=> ! [Vvar__var__5__y__546__552] :
( t(Vvar__var__5__y__546__552,Vvar__0__Ec__520)
=> ! [Vvar__var__6__z__547__553] :
( t(Vvar__var__6__z__547__553,Vvar__0__Ec__520)
=> ! [Vvar__var__7__c__548__554] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__7__c__548__554)
=> ( happ(happ(Vvar__1__Ecmp__521,Vvar__var__4__x__545__551),Vvar__var__5__y__546__552) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vvar__1__Ecmp__521,Vvar__var__5__y__546__552),Vvar__var__6__z__547__553) = Vvar__var__7__c__548__554
=> happ(happ(Vvar__1__Ecmp__521,Vvar__var__4__x__545__551),Vvar__var__6__z__547__553) = Vvar__var__7__c__548__554 ) ) ) ) ) )
& V0__e = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__520,Vvar__1__Ecmp__521)
& cQuicksortComplexity_2esort__order_2eEcmp___24a1(V0__e) = Vvar__1__Ecmp__521 ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Ege',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eEge___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_QuicksortComplexity.sort_order.Egeb',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eEq
& cQuicksortComplexity_2esort__order_2eEgeb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt
& cQuicksortComplexity_2esort__order_2eEgeb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eGt
& cQuicksortComplexity_2esort__order_2eEgeb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Egt',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eEgt___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_QuicksortComplexity.sort_order.Egtb',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eEq
& cQuicksortComplexity_2esort__order_2eEgtb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt
& cQuicksortComplexity_2esort__order_2eEgtb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eGt
& cQuicksortComplexity_2esort__order_2eEgtb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Ele',axiom,
! [V0__e,V1__x,V2__y] :
( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
<=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_QuicksortComplexity.sort_order.Eleb',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eEq
& cQuicksortComplexity_2esort__order_2eEleb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt
& cQuicksortComplexity_2esort__order_2eEleb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eGt
& cQuicksortComplexity_2esort__order_2eEleb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.sort_order.Elt',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eElt___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_QuicksortComplexity.sort_order.Eltb',axiom,
! [V0__e,V1__x,V2__y] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eEq
& cQuicksortComplexity_2esort__order_2eEltb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt
& cQuicksortComplexity_2esort__order_2eEltb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eGt
& cQuicksortComplexity_2esort__order_2eEltb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.util.decision',axiom,
! [V0__P] : cQuicksortComplexity_2eutil_2edecision___24a1(V0__P) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V0__P,c_24__prop__4272___24a1(V0__P)) ).
fof('$_def_QuicksortComplexity.util.ext_eq',axiom,
! [V0__A,V1__B,V2__f,V3__g] :
( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__f,V3__g)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) ) ) ).
fof('$_def_QuicksortComplexity.util.on',axiom,
! [V0__A,V1__B,V2__C,V3__g,V4__f,V5__x,V6__y] : cQuicksortComplexity_2eutil_2eon___24a7(V0__A,V1__B,V2__C,V3__g,V4__f,V5__x,V6__y) = happ(happ(V4__f,happ(V3__g,V5__x)),happ(V3__g,V6__y)) ).
fof('$_def_QuicksortComplexity.util.uncurry',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__ab] : cQuicksortComplexity_2eutil_2euncurry___24a5(V0__A,V1__B,V2__C,V3__f,V4__ab) = happ(happ(V3__f,cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V4__ab)),cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V4__ab)) ).
fof('$_def_QuicksortComplexity.util.unsum_bool',axiom,
! [V0__A,V1__B,V2__sb] :
( cProp___24t(V0__A)
=> ( cProp___24t(V1__B)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V2__sb)
=> ( ( p(V0__A)
& V2__sb = cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B)
& cQuicksortComplexity_2eutil_2eunsum__bool___24a3(V0__A,V1__B,V2__sb) = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(V1__B)
& V2__sb = cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B)
& cQuicksortComplexity_2eutil_2eunsum__bool___24a3(V0__A,V1__B,V2__sb) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.R',axiom,
! [V0__P,V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2eR___24a2(V0__P,V1__n) = c_24__lam__76838 )
| ? [Vvar__0___24Anonymous__76837] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76837)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76837)
& cQuicksortComplexity_2evec_2eR___24a2(V0__P,V1__n) = happ(V0__P,Vvar__0___24Anonymous__76837) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.Xlt',axiom,
! [V0__X,V1__Xle,V2__x,V3__y] :
( cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,V2__x,V3__y)
<=> ( p(happ(happ(V1__Xle,V2__x),V3__y))
& ~ p(happ(happ(V1__Xle,V3__y),V2__x)) ) ) ).
fof('$_def_QuicksortComplexity.vec.app',axiom,
! [V1__A,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2eapp___24a2(V1__A,V2__n) = c_24__lam__73002___24a1(V1__A) )
| ? [Vvar__0___24Anonymous__72992] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__72992)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__72992)
& cQuicksortComplexity_2evec_2eapp___24a2(V1__A,V2__n) = c_24__lam__73012___24a2(V1__A,Vvar__0___24Anonymous__72992) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.drop',axiom,
! [V1__A,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2edrop___24a2(V1__A,V2__n) = c_24__lam__77034___24a1(V1__A) )
| ? [Vvar__0___24Anonymous__77021] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77021)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77021)
& cQuicksortComplexity_2evec_2edrop___24a2(V1__A,V2__n) = c_24__lam__77078___24a2(V1__A,Vvar__0___24Anonymous__77021) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.from_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__690] :
( t(Vvar__1___24Anonymous__690,V1__A)
& ? [Vvar__2___24Anonymous__691] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__691)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__690,Vvar__2___24Anonymous__691)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__690,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__691),cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,Vvar__2___24Anonymous__691)) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.head',axiom,
! [V0__A,V1__n,V2__v] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> ( ( V2__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)
& cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v) = cCoq_2eInit_2eLogic_2eI )
| ? [Vvar__1__h__660] :
( t(Vvar__1__h__660,V0__A)
& ? [Vvar__2__n__661] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__661)
& ? [Vvar__3___24Anonymous__662] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,Vvar__2__n__661,Vvar__3___24Anonymous__662)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,Vvar__1__h__660,Vvar__2__n__661,Vvar__3___24Anonymous__662)
& cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v) = Vvar__1__h__660 ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.insert_ordered',axiom,
! [V0__X,V1__Xle,V2__XleDec,V4__x,V5__n] :
( cType___24t(V0__X)
=> ( c_24__type__73256___24t(V0__X,V1__Xle,V1__Xle)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( ( V5__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2einsert__ordered___24a5(V0__X,V1__Xle,V2__XleDec,V4__x,V5__n) = c_24__lam__73263___24a3(V0__X,V1__Xle,V4__x) )
| ? [Vvar__0___24Anonymous__73244] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__73244)
& V5__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__73244)
& cQuicksortComplexity_2evec_2einsert__ordered___24a5(V0__X,V1__Xle,V2__XleDec,V4__x,V5__n) = c_24__lam__73293___24a5(V0__X,V1__Xle,V2__XleDec,V4__x,Vvar__0___24Anonymous__73244) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.insertion_sort',axiom,
! [V0__X,V1__Xle,V2__XleDec,V4__n] :
( cType___24t(V0__X)
=> ( c_24__type__1206___24t(V0__X,V1__Xle,V1__Xle)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2einsertion__sort___24a4(V0__X,V1__Xle,V2__XleDec,V4__n) = c_24__lam__1212___24a2(V0__X,V1__Xle) )
| ? [Vvar__0___24Anonymous__1197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1197)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1197)
& cQuicksortComplexity_2evec_2einsertion__sort___24a4(V0__X,V1__Xle,V2__XleDec,V4__n) = c_24__lam__1223___24a4(V0__X,V1__Xle,V2__XleDec,Vvar__0___24Anonymous__1197) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.map',axiom,
! [V1__X,V2__Y,V3__f,V4__n,V5__v] :
( cType___24t(V1__X)
=> ( cType___24t(V2__Y)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,V4__n,V5__v)
=> ( ( V5__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__X)
& cQuicksortComplexity_2evec_2emap___24a5(V1__X,V2__Y,V3__f,V4__n,V5__v) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V2__Y) )
| ? [Vvar__1__h__331] :
( t(Vvar__1__h__331,V1__X)
& ? [Vvar__2__n__332] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__332)
& ? [Vvar__3___24Anonymous__333] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__332,Vvar__3___24Anonymous__333)
& V5__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__331,Vvar__2__n__332,Vvar__3___24Anonymous__333)
& cQuicksortComplexity_2evec_2emap___24a5(V1__X,V2__Y,V3__f,V4__n,V5__v) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V2__Y,happ(V3__f,Vvar__1__h__331),Vvar__2__n__332,cQuicksortComplexity_2evec_2emap___24a5(V1__X,V2__Y,V3__f,Vvar__2__n__332,Vvar__3___24Anonymous__333)) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.natBelow_S_bla',axiom,
! [V0__T,V1__n,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__n,V2__b)
=> ? [Vvar__0__v__73065] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__73065)
& ? [Vvar__1__p__73066] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__73066)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__73065)
=> ( V2__b = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__73065,Vvar__1__p__73066)
& ( ( Vvar__0__v__73065 = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2enatBelow__S__bla___24a3(V0__T,V1__n,V2__b) = c_24__lam__73107___24a3(V0__T,V1__n,Vvar__1__p__73066) )
| ? [Vvar__0___24Anonymous__73092] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__73092)
& Vvar__0__v__73065 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__73092)
& cQuicksortComplexity_2evec_2enatBelow__S__bla___24a3(V0__T,V1__n,V2__b) = c_24__lam__73122___24a4(V0__T,V1__n,Vvar__1__p__73066,Vvar__0___24Anonymous__73092) ) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.natBelow_rect',axiom,
! [V0__P,V1__Pz,V2__Ps,V4__n] :
( c_24__type__716___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2enatBelow__rect___24a4(V0__P,V1__Pz,V2__Ps,V4__n) = c_24__lam__719___24a1(V0__P) )
| ? [Vvar__0___24Anonymous__697] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__697)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__697)
& cQuicksortComplexity_2evec_2enatBelow__rect___24a4(V0__P,V1__Pz,V2__Ps,V4__n) = c_24__lam__827___24a4(V0__P,V1__Pz,V2__Ps,Vvar__0___24Anonymous__697) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.natBelow_rect_S',axiom,
! [V0__P,V1__Pz,V2__Ps,V3__n,V4__nb] : cQuicksortComplexity_2evec_2enatBelow__rect__S___24a5(V0__P,V1__Pz,V2__Ps,V3__n,V4__nb) = cQuicksortComplexity_2evec_2enatBelow__rect___24a5(cQuicksortComplexity_2evec_2eR___24a1(V0__P),V1__Pz,V2__Ps,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__nb) ).
fof('$_def_QuicksortComplexity.vec.nats',axiom,
! [V1__x,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2enats___24a2(V1__x,V2__n) = cCoq_2eVectors_2eVectorDef_2enil___24a1(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__359] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__359)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__359)
& cQuicksortComplexity_2evec_2enats___24a2(V1__x,V2__n) = cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,Vvar__0___24Anonymous__359))),cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__359))),c_24__lam__363___24a2(V1__x,Vvar__0___24Anonymous__359),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__359),cCoq_2eVectors_2eVectorDef_2econs___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,Vvar__0___24Anonymous__359))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V1__x,Vvar__0___24Anonymous__359),Vvar__0___24Anonymous__359,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__x),Vvar__0___24Anonymous__359))) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.nb_nats',axiom,
! [V0__x,V1__n] : cQuicksortComplexity_2evec_2enb__nats___24a2(V0__x,V1__n) = cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V1__n)),cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__below_2enb__val___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V1__n)),V1__n,cQuicksortComplexity_2evec_2enats___24a2(V0__x,V1__n)) ).
fof('$_def_QuicksortComplexity.vec.nof',axiom,
! [V0__n,V1___24Anonymous] : cQuicksortComplexity_2evec_2enof___24a2(V0__n,V1___24Anonymous) = V0__n ).
fof('$_def_QuicksortComplexity.vec.nth',axiom,
! [V1__X,V2__n,V3__v] :
( cType___24t(V1__X)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,V2__n,V3__v)
=> ( ( V3__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__X)
& cQuicksortComplexity_2evec_2enth___24a3(V1__X,V2__n,V3__v) = c_24__lam__1070___24a2(V1__X,V2__n) )
| ? [Vvar__1__h__1059] :
( t(Vvar__1__h__1059,V1__X)
& ? [Vvar__2__n__1060] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__1060)
& ? [Vvar__3___24Anonymous__1061] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__1060,Vvar__3___24Anonymous__1061)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__1059,Vvar__2__n__1060,Vvar__3___24Anonymous__1061)
& cQuicksortComplexity_2evec_2enth___24a3(V1__X,V2__n,V3__v) = c_24__lam__1076___24a5(V1__X,V2__n,Vvar__1__h__1059,Vvar__2__n__1060,Vvar__3___24Anonymous__1061) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.plusnb',axiom,
! [V0__y,V1__x,V2__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__x,V2__nb)
=> ? [Vvar__0__v__1092] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__1092)
& ? [Vvar__1__p__1093] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__1093)
& V2__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__1092,Vvar__1__p__1093)
& cQuicksortComplexity_2evec_2eplusnb___24a3(V0__y,V1__x,V2__nb) = cCoq_2eInit_2eLogic_2eeq__rec__r___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0__v__1092,cCoq_2eInit_2eNat_2eadd___24a2(Vvar__1__p__1093,V0__y))),cQuicksortComplexity_2enat__below_2enatBelow,cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__1092,cCoq_2eInit_2eNat_2eadd___24a2(Vvar__1__p__1093,V0__y)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0__v__1092,Vvar__1__p__1093),V0__y)),cCoq_2eInit_2ePeano_2eeq__S___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0__v__1092,Vvar__1__p__1093),V0__y),cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0__v__1092,cCoq_2eInit_2eNat_2eadd___24a2(Vvar__1__p__1093,V0__y)),cCoq_2eArith_2ePlus_2eplus__assoc__reverse___24a3(Vvar__0__v__1092,Vvar__1__p__1093,V0__y))) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.remove',axiom,
! [V0__T,V1__n,V2__v,V3__nb] : cQuicksortComplexity_2evec_2eremove___24a4(V0__T,V1__n,V2__v,V3__nb) = cQuicksortComplexity_2evec_2enatBelow__rect__S___24a6(c_24__lam__73155___24a2(V0__T,V1__n),c_24__lam__73162___24a2(V0__T,V1__n),c_24__lam__73181___24a2(V0__T,V1__n),V1__n,V3__nb,V2__v) ).
fof('$_def_QuicksortComplexity.vec.tail',axiom,
! [V0__n,V1__A,V2__v] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cType___24t(V1__A)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V2__v)
=> ( ( V2__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
& cQuicksortComplexity_2evec_2etail___24a3(V0__n,V1__A,V2__v) = cCoq_2eInit_2eLogic_2eI )
| ? [Vvar__1__h__675] :
( t(Vvar__1__h__675,V1__A)
& ? [Vvar__2__n__676] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__676)
& ? [Vvar__3___24Anonymous__677] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__676,Vvar__3___24Anonymous__677)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__675,Vvar__2__n__676,Vvar__3___24Anonymous__677)
& cQuicksortComplexity_2evec_2etail___24a3(V0__n,V1__A,V2__v) = Vvar__3___24Anonymous__677 ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.take',axiom,
! [V1__A,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2etake___24a2(V1__A,V2__n) = c_24__lam__76867___24a1(V1__A) )
| ? [Vvar__0___24Anonymous__76847] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76847)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76847)
& cQuicksortComplexity_2evec_2etake___24a2(V1__A,V2__n) = c_24__lam__76949___24a2(V1__A,Vvar__0___24Anonymous__76847) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.to_list',axiom,
! [V1__X,V2__n,V3__v] :
( cType___24t(V1__X)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,V2__n,V3__v)
=> ( ( V3__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__X)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__X) )
| ? [Vvar__1__h__315] :
( t(Vvar__1__h__315,V1__X)
& ? [Vvar__2__n__316] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__316)
& ? [Vvar__3___24Anonymous__317] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__316,Vvar__3___24Anonymous__317)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__315,Vvar__2__n__316,Vvar__3___24Anonymous__317)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__X,Vvar__1__h__315,cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,Vvar__2__n__316,Vvar__3___24Anonymous__317)) ) ) ) ) ) ) ) ).
fof('$_def_indices.contents.Index',axiom,
! [Vvar__292] :
( cindices_2econtents_2eIndex___24t(Vvar__292)
<=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),Vvar__292) ) ).
fof('$_def_indices.contents.IndexIn',axiom,
! [V0__i,V1__l] :
( cindices_2econtents_2eIndexIn___24a2(V0__i,V1__l)
<=> cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V0__i,cCoq_2eLists_2eList_2emap___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col)),cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__below_2enb__val___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col)),V1__l)) ) ).
fof('$_def_indices.contents.IndexSeq',axiom,
! [V0__b,V1__l] :
( cindices_2econtents_2eIndexSeq___24a2(V0__b,V1__l)
<=> ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__b,V2__i))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__i,cCoq_2eInit_2eNat_2eadd___24a2(V0__b,cCoq_2eInit_2eDatatypes_2elength___24a2(cindices_2econtents_2eIndex,V1__l))))
=> cindices_2econtents_2eIndexIn___24a2(V2__i,V1__l) ) ) ) ) ).
fof('$_def_indices.contents.IndexSeq_above',axiom,
! [V0__b,V1__l] :
( cindices_2econtents_2eIndexSeq__above___24a2(V0__b,V1__l)
<=> cindices_2econtents_2eIndexSeq___24a2(cCoq_2eInit_2eNat_2esub___24a2(V0__b,cCoq_2eInit_2eDatatypes_2elength___24a2(cindices_2econtents_2eIndex,V1__l)),V1__l) ) ).
fof('$_def_indices.contents.UE',axiom,
cindices_2econtents_2eUE = cQuicksortComplexity_2esort__order_2eBuild__E___24a5(cindices_2econtents_2eIndex,c_24__lam__4830,c_24__lam__4832,c_24__lam__7070,c_24__lam__7074) ).
fof('$_def_indices.contents.subscript',axiom,
cindices_2econtents_2esubscript = cQuicksortComplexity_2evec_2enth___24a3(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),cQuicksortComplexity_2evec_2einsertion__sort___24a5(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),cQuicksortComplexity_2esort__order_2eEle___24a1(cT),cQuicksortComplexity_2esort__order_2eEle__le__dec___24a1(cT),cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),cQuicksortComplexity_2evec_2efrom__list___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col))) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__21090,Vvar__1___24Anonymous__21091,Vvar__0__P__21092,Vvar__1___24Anonymous__21093] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__21090) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__21092) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__20280,Vvar__1___24Anonymous__20281,Vvar__2___24Anonymous__20282] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20280,Vvar__1___24Anonymous__20281,Vvar__2___24Anonymous__20282) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__5] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__7274,Vvar__1___24Anonymous__7275,Vvar__0__A__7276] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7274,Vvar__1___24Anonymous__7275) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7276) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__21124,Vvar__1__B__21125,Vvar__2___24Anonymous__21126,Vvar__0__A__21127,Vvar__1__B__21128,Vvar__2___24Anonymous__21129] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21124,Vvar__1__B__21125,Vvar__2___24Anonymous__21126) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21127,Vvar__1__B__21128,Vvar__2___24Anonymous__21129) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__22,Vvar__0__A__23,Vvar__1___24Anonymous__24,Vvar__2___24Anonymous__25] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__23,Vvar__1___24Anonymous__24,Vvar__2___24Anonymous__25) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__59688] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__59688) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__59712,Vvar__0__d__59713] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__59712) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__59713) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2276,Vvar__1__B__2277,Vvar__2___24Anonymous__2278,Vvar__0__A__2279,Vvar__1__B__2280,Vvar__2___24Anonymous__2281] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2276,Vvar__1__B__2277,Vvar__2___24Anonymous__2278) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2279,Vvar__1__B__2280) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2236,Vvar__1__B__2237,Vvar__2___24Anonymous__2238,Vvar__0__A__2239,Vvar__1__B__2240,Vvar__2___24Anonymous__2241] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2236,Vvar__1__B__2237) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2239,Vvar__1__B__2240) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1325] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1325) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1334] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1334) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1317,Vvar__0___24Anonymous__1318] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1317) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1318) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__59824,Vvar__1___24Anonymous__59825,Vvar__0__x__59826,Vvar__1__n__59827,Vvar__2___24Anonymous__59828] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__59824) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__59826,Vvar__1__n__59827) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__2307,Vvar__1___24Anonymous__2308] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__2307,Vvar__1___24Anonymous__2308) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__1992,Vvar__1__lt__1993,Vvar__2__eq__1994,Vvar__3__x__1995,Vvar__4__y__1996,Vvar__5___24Anonymous__1997,Vvar__0__X__1998,Vvar__1__lt__1999,Vvar__2__eq__2000,Vvar__3__x__2001,Vvar__4__y__2002,Vvar__5___24Anonymous__2003] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__1992,Vvar__1__lt__1993,Vvar__2__eq__1994,Vvar__3__x__1995,Vvar__4__y__1996) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__1998,Vvar__1__lt__1999,Vvar__2__eq__2000,Vvar__3__x__2001,Vvar__4__y__2002) ).
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__22512,Vvar__0__n__22513,Vvar__1___24Anonymous__22514] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__22512) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__22513,Vvar__1___24Anonymous__22514) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__419,Vvar__0__A__420,Vvar__1__h__421,Vvar__2__n__422,Vvar__3___24Anonymous__423] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__419) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__420,Vvar__1__h__421,Vvar__2__n__422,Vvar__3___24Anonymous__423) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__21271,Vvar__1___24Anonymous__21272,Vvar__0__C__21273,Vvar__1___24Anonymous__21274] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__21271,Vvar__1___24Anonymous__21272) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__21273,Vvar__1___24Anonymous__21274) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__21335,Vvar__1___24Anonymous__21336,Vvar__0__C__21337,Vvar__1___24Anonymous__21338,Vvar__2___24Anonymous__21339] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__21335,Vvar__1___24Anonymous__21336) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__21337,Vvar__1___24Anonymous__21338,Vvar__2___24Anonymous__21339) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__21372,Vvar__1___24Anonymous__21373] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__21372,Vvar__1___24Anonymous__21373) ).
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('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__30074,Vvar__1___24Anonymous__30075,Vvar__0__C__30076,Vvar__1___24Anonymous__30077] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__30074,Vvar__1___24Anonymous__30075) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__30076,Vvar__1___24Anonymous__30077) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__35491,Vvar__1__TX__35492,Vvar__2__AA__35493,Vvar__3__AF__35494,Vvar__0__TA__35495,Vvar__1__TX__35496,Vvar__2__AA__35497,Vvar__3__AF__35498] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__35491,Vvar__1__TX__35492,Vvar__2__AA__35493,Vvar__3__AF__35494) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__35495,Vvar__1__TX__35496,Vvar__2__AA__35497,Vvar__3__AF__35498) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__35615,Vvar__1___24Anonymous__35616] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35615,Vvar__1___24Anonymous__35616) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__22393,Vvar__0__C__22394] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__22393) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__22394) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__8748,Vvar__0__C__8749] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__8748) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__8749) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__8390,Vvar__1___24Anonymous__8391,Vvar__0__C__8392,Vvar__1___24Anonymous__8393,Vvar__2___24Anonymous__8394] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__8390,Vvar__1___24Anonymous__8391) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__8392,Vvar__1___24Anonymous__8393,Vvar__2___24Anonymous__8394) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__8558,Vvar__1___24Anonymous__8559] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__8558,Vvar__1___24Anonymous__8559) ).
fof('$_discrim_QuicksortComplexity.arith_lems.R_ceil_log2_S_0$QuicksortComplexity.arith_lems.R_ceil_log2_S_1',axiom,
! [Vvar__0__n__60044,Vvar__1___24Anonymous__60045,Vvar__0__n__60046,Vvar__1____x__60047,Vvar__2___24Anonymous__60048,Vvar__3____res__60049,Vvar__4___24Anonymous__60050] : cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__60044) != cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__60046,Vvar__1____x__60047,Vvar__3____res__60049,Vvar__4___24Anonymous__60050) ).
fof('$_discrim_QuicksortComplexity.arith_lems.R_floor_log2_S_0$QuicksortComplexity.arith_lems.R_floor_log2_S_1',axiom,
! [Vvar__0__n__60076,Vvar__1___24Anonymous__60077,Vvar__0__n__60078,Vvar__1__n_27__60079,Vvar__2___24Anonymous__60080,Vvar__3____res__60081,Vvar__4___24Anonymous__60082] : cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__60076) != cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__60078,Vvar__1__n_27__60079,Vvar__3____res__60081,Vvar__4___24Anonymous__60082) ).
fof('$_fix_156_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__156__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__157)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__157)
& c_24__fix__156__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__156__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__157,Vv__CANONICAL__2)) ) ) ) ).
fof('$_fix_19265_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__fix__19265__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__19269] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__19269)
& ? [Vvar__2___24Anonymous__19270] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__19270)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19269,Vvar__2___24Anonymous__19270)
& c_24__fix__19265__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__19269),c_24__fix__19265__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__19270)) ) ) ) ) ) ).
fof('$_fix_19362_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__fix__19362__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__19366] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__19366)
& ? [Vvar__2___24Anonymous__19367] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__19367)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19366,Vvar__2___24Anonymous__19367)
& c_24__fix__19362__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__19366,c_24__fix__19362__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19367,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_20117_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__20132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20132)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20132)
& ( ? [Vvar__0___24Anonymous__20136] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20136)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20136)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__20117__1__add__carry___24a2(Vvar__0___24Anonymous__20132,Vvar__0___24Anonymous__20136)) )
| ? [Vvar__0___24Anonymous__20137] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20137)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20137)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__20117__1__add__carry___24a2(Vvar__0___24Anonymous__20132,Vvar__0___24Anonymous__20137)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20132)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__20138] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20138)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20138)
& ( ? [Vvar__0___24Anonymous__20142] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20142)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20142)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__20117__1__add__carry___24a2(Vvar__0___24Anonymous__20138,Vvar__0___24Anonymous__20142)) )
| ? [Vvar__0___24Anonymous__20143] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20143)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20143)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__20138,Vvar__0___24Anonymous__20143)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20138)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__20144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20144)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20144)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20144)) )
| ? [Vvar__0___24Anonymous__20145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20145)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20145)
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__20145)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__20117__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_24577_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__24577__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__24581] :
( t(Vvar__1___24Anonymous__24581,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__24582] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__24582)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24581,Vvar__2___24Anonymous__24582)
& c_24__fix__24577__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__24581,c_24__fix__24577__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__24582,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_73712_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( ? [Vvar__0__n__73714] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__73714)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__73714)
& c_24__fix__73712__v__CANONICAL__2___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eFin_2eF1___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__73714)) )
| ? [Vvar__0__n__73715] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__73715)
& ? [Vvar__1___24Anonymous__73716] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__73715,Vvar__1___24Anonymous__73716)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__73715,Vvar__1___24Anonymous__73716)
& c_24__fix__73712__v__CANONICAL__2___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eFin_2eFS___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__73715),c_24__fix__73712__v__CANONICAL__2___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__0__n__73715,Vvar__1___24Anonymous__73716)) ) ) ) ) ) ).
fof('$_fix_75238_v_CANONICAL_3',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
& c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__0___24Anonymous__75239] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75239)
& Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__75239)
& c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__75239,Vv__CANONICAL__5)) ) ) ) ).
fof('$_fix_9407_v_CANONICAL_2',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__9407__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__5 )
| ? [Vvar__1__h__9412] :
( t(Vvar__1__h__9412,Vv__CANONICAL__0)
& ? [Vvar__2__n__9413] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__9413)
& ? [Vvar__3___24Anonymous__9414] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__9413,Vvar__3___24Anonymous__9414)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__9412,Vvar__2__n__9413,Vvar__3___24Anonymous__9414)
& c_24__fix__9407__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1__h__9412,c_24__fix__9407__v__CANONICAL__2___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__9413,Vvar__3___24Anonymous__9414,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__21098,Vvar__0__P__21099,Vvar__1___24Anonymous__21100,Vvar__1___24Anonymous__21101] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__21098) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__21099)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__21098 = Vvar__0__P__21099 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__21094,Vvar__0__P__21095,Vvar__1___24Anonymous__21096,Vvar__1___24Anonymous__21097] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__21094) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__21095)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__21094 = Vvar__0__P__21095 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__20283,Vvar__0___24Anonymous__20284,Vvar__1___24Anonymous__20285,Vvar__1___24Anonymous__20286,Vvar__2___24Anonymous__20287,Vvar__2___24Anonymous__20288] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20283,Vvar__1___24Anonymous__20285,Vvar__2___24Anonymous__20287) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20284,Vvar__1___24Anonymous__20286,Vvar__2___24Anonymous__20288)
=> ( Vvar__2___24Anonymous__20287 = Vvar__2___24Anonymous__20288
& Vvar__1___24Anonymous__20285 = Vvar__1___24Anonymous__20286
& Vvar__0___24Anonymous__20283 = Vvar__0___24Anonymous__20284 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__7281,Vvar__0__A__7282] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7281) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7282)
=> Vvar__0__A__7281 = Vvar__0__A__7282 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__6,Vvar__0___24Anonymous__7] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7)
=> Vvar__0___24Anonymous__6 = Vvar__0___24Anonymous__7 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__7277,Vvar__0__A__7278,Vvar__1___24Anonymous__7279,Vvar__1___24Anonymous__7280] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7277,Vvar__1___24Anonymous__7279) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7278,Vvar__1___24Anonymous__7280)
=> ( Vvar__1___24Anonymous__7279 = Vvar__1___24Anonymous__7280
& Vvar__0__A__7277 = Vvar__0__A__7278 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__28,Vvar__0__A__29,Vvar__1___24Anonymous__30,Vvar__1___24Anonymous__31,Vvar__2___24Anonymous__32,Vvar__2___24Anonymous__33] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28,Vvar__1___24Anonymous__30,Vvar__2___24Anonymous__32) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29,Vvar__1___24Anonymous__31,Vvar__2___24Anonymous__33)
=> ( Vvar__2___24Anonymous__32 = Vvar__2___24Anonymous__33
& Vvar__1___24Anonymous__30 = Vvar__1___24Anonymous__31
& Vvar__0__A__28 = Vvar__0__A__29 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__21130,Vvar__0__A__21131,Vvar__1__B__21132,Vvar__1__B__21133,Vvar__2___24Anonymous__21134,Vvar__2___24Anonymous__21135] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21130,Vvar__1__B__21132,Vvar__2___24Anonymous__21134) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21131,Vvar__1__B__21133,Vvar__2___24Anonymous__21135)
=> ( Vvar__2___24Anonymous__21134 = Vvar__2___24Anonymous__21135
& Vvar__1__B__21132 = Vvar__1__B__21133
& Vvar__0__A__21130 = Vvar__0__A__21131 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__21136,Vvar__0__A__21137,Vvar__1__B__21138,Vvar__1__B__21139,Vvar__2___24Anonymous__21140,Vvar__2___24Anonymous__21141] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21136,Vvar__1__B__21138,Vvar__2___24Anonymous__21140) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21137,Vvar__1__B__21139,Vvar__2___24Anonymous__21141)
=> ( Vvar__2___24Anonymous__21140 = Vvar__2___24Anonymous__21141
& Vvar__1__B__21138 = Vvar__1__B__21139
& Vvar__0__A__21136 = Vvar__0__A__21137 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__26,Vvar__0__A__27] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27)
=> Vvar__0__A__26 = Vvar__0__A__27 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__7298,Vvar__0__A__7299,Vvar__1__B__7300,Vvar__1__B__7301,Vvar__2___24Anonymous__7302,Vvar__2___24Anonymous__7303,Vvar__3___24Anonymous__7304,Vvar__3___24Anonymous__7305] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7298,Vvar__1__B__7300,Vvar__2___24Anonymous__7302,Vvar__3___24Anonymous__7304) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7299,Vvar__1__B__7301,Vvar__2___24Anonymous__7303,Vvar__3___24Anonymous__7305)
=> ( Vvar__3___24Anonymous__7304 = Vvar__3___24Anonymous__7305
& Vvar__2___24Anonymous__7302 = Vvar__2___24Anonymous__7303
& Vvar__1__B__7300 = Vvar__1__B__7301
& Vvar__0__A__7298 = Vvar__0__A__7299 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__59689,Vvar__0___24Anonymous__59690] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__59689) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__59690)
=> Vvar__0___24Anonymous__59689 = Vvar__0___24Anonymous__59690 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__59691,Vvar__0___24Anonymous__59692] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__59691) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__59692)
=> Vvar__0___24Anonymous__59691 = Vvar__0___24Anonymous__59692 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__59693,Vvar__0___24Anonymous__59694] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__59693) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__59694)
=> Vvar__0___24Anonymous__59693 = Vvar__0___24Anonymous__59694 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__59695,Vvar__0___24Anonymous__59696] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__59695) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__59696)
=> Vvar__0___24Anonymous__59695 = Vvar__0___24Anonymous__59696 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__59697,Vvar__0___24Anonymous__59698] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__59697) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__59698)
=> Vvar__0___24Anonymous__59697 = Vvar__0___24Anonymous__59698 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__59699,Vvar__0___24Anonymous__59700] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__59699) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__59700)
=> Vvar__0___24Anonymous__59699 = Vvar__0___24Anonymous__59700 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__59701,Vvar__0___24Anonymous__59702] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__59701) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__59702)
=> Vvar__0___24Anonymous__59701 = Vvar__0___24Anonymous__59702 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__59703,Vvar__0___24Anonymous__59704] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__59703) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__59704)
=> Vvar__0___24Anonymous__59703 = Vvar__0___24Anonymous__59704 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__59705,Vvar__0___24Anonymous__59706] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__59705) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__59706)
=> Vvar__0___24Anonymous__59705 = Vvar__0___24Anonymous__59706 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__59707,Vvar__0___24Anonymous__59708] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__59707) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__59708)
=> Vvar__0___24Anonymous__59707 = Vvar__0___24Anonymous__59708 ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__59716,Vvar__0__d__59717] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__59716) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__59717)
=> Vvar__0__d__59716 = Vvar__0__d__59717 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__59714,Vvar__0__d__59715] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__59714) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__59715)
=> Vvar__0__d__59714 = Vvar__0__d__59715 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__2183,Vvar__0__A__2184,Vvar__1__P__2185,Vvar__1__P__2186,Vvar__2__x__2187,Vvar__2__x__2188,Vvar__3___24Anonymous__2189,Vvar__3___24Anonymous__2190] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2183,Vvar__1__P__2185,Vvar__2__x__2187) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2184,Vvar__1__P__2186,Vvar__2__x__2188)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__2187 = Vvar__2__x__2188
& Vvar__1__P__2185 = Vvar__1__P__2186
& Vvar__0__A__2183 = Vvar__0__A__2184 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__35074,Vvar__0__A__35075,Vvar__1__P__35076,Vvar__1__P__35077,Vvar__2__x__35078,Vvar__2__x__35079,Vvar__3___24Anonymous__35080,Vvar__3___24Anonymous__35081] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__35074,Vvar__1__P__35076,Vvar__2__x__35078,Vvar__3___24Anonymous__35080) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__35075,Vvar__1__P__35077,Vvar__2__x__35079,Vvar__3___24Anonymous__35081)
=> ( Vvar__3___24Anonymous__35080 = Vvar__3___24Anonymous__35081
& Vvar__2__x__35078 = Vvar__2__x__35079
& Vvar__1__P__35076 = Vvar__1__P__35077
& Vvar__0__A__35074 = Vvar__0__A__35075 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__2282,Vvar__0__A__2283,Vvar__1__B__2284,Vvar__1__B__2285,Vvar__2___24Anonymous__2286,Vvar__2___24Anonymous__2287] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2282,Vvar__1__B__2284,Vvar__2___24Anonymous__2286) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2283,Vvar__1__B__2285,Vvar__2___24Anonymous__2287)
=> ( Vvar__2___24Anonymous__2286 = Vvar__2___24Anonymous__2287
& Vvar__1__B__2284 = Vvar__1__B__2285
& Vvar__0__A__2282 = Vvar__0__A__2283 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__2288,Vvar__0__A__2289,Vvar__1__B__2290,Vvar__1__B__2291,Vvar__2___24Anonymous__2292,Vvar__2___24Anonymous__2293] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2288,Vvar__1__B__2290) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2289,Vvar__1__B__2291)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2290 = Vvar__1__B__2291
& Vvar__0__A__2288 = Vvar__0__A__2289 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__2242,Vvar__0__A__2243,Vvar__1__B__2244,Vvar__1__B__2245,Vvar__2___24Anonymous__2246,Vvar__2___24Anonymous__2247] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2242,Vvar__1__B__2244) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2243,Vvar__1__B__2245)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2244 = Vvar__1__B__2245
& Vvar__0__A__2242 = Vvar__0__A__2243 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2248,Vvar__0__A__2249,Vvar__1__B__2250,Vvar__1__B__2251,Vvar__2___24Anonymous__2252,Vvar__2___24Anonymous__2253] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2248,Vvar__1__B__2250) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2249,Vvar__1__B__2251)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2250 = Vvar__1__B__2251
& Vvar__0__A__2248 = Vvar__0__A__2249 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1326,Vvar__0___24Anonymous__1327] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1326) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1327)
=> Vvar__0___24Anonymous__1326 = Vvar__0___24Anonymous__1327 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1337,Vvar__0___24Anonymous__1338] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1337) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1338)
=> Vvar__0___24Anonymous__1337 = Vvar__0___24Anonymous__1338 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1335,Vvar__0___24Anonymous__1336] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1335) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1336)
=> Vvar__0___24Anonymous__1335 = Vvar__0___24Anonymous__1336 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1319,Vvar__0___24Anonymous__1320] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1319) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1320)
=> Vvar__0___24Anonymous__1319 = Vvar__0___24Anonymous__1320 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1321,Vvar__0___24Anonymous__1322] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1321) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1322)
=> Vvar__0___24Anonymous__1321 = Vvar__0___24Anonymous__1322 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__8249,Vvar__0__Qnum__8250,Vvar__1__Qden__8251,Vvar__1__Qden__8252] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__8249,Vvar__1__Qden__8251) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__8250,Vvar__1__Qden__8252)
=> ( Vvar__1__Qden__8251 = Vvar__1__Qden__8252
& Vvar__0__Qnum__8249 = Vvar__0__Qnum__8250 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__59839,Vvar__0__x__59840,Vvar__1__n__59841,Vvar__1__n__59842,Vvar__2___24Anonymous__59843,Vvar__2___24Anonymous__59844] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__59839,Vvar__1__n__59841) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__59840,Vvar__1__n__59842)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__59841 = Vvar__1__n__59842
& Vvar__0__x__59839 = Vvar__0__x__59840 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__59829,Vvar__0__x__59830,Vvar__1___24Anonymous__59831,Vvar__1___24Anonymous__59832] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__59829) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__59830)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__59829 = Vvar__0__x__59830 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__59833,Vvar__0__x__59834,Vvar__1__n__59835,Vvar__1__n__59836,Vvar__2___24Anonymous__59837,Vvar__2___24Anonymous__59838] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__59833,Vvar__1__n__59835) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__59834,Vvar__1__n__59836)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__59835 = Vvar__1__n__59836
& Vvar__0__x__59833 = Vvar__0__x__59834 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__1291,Vvar__0___24Anonymous__1292,Vvar__1___24Anonymous__1293,Vvar__1___24Anonymous__1294,Vvar__2___24Anonymous__1295,Vvar__2___24Anonymous__1296,Vvar__3___24Anonymous__1297,Vvar__3___24Anonymous__1298,Vvar__4___24Anonymous__1299,Vvar__4___24Anonymous__1300,Vvar__5___24Anonymous__1301,Vvar__5___24Anonymous__1302,Vvar__6___24Anonymous__1303,Vvar__6___24Anonymous__1304,Vvar__7___24Anonymous__1305,Vvar__7___24Anonymous__1306] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1291,Vvar__1___24Anonymous__1293,Vvar__2___24Anonymous__1295,Vvar__3___24Anonymous__1297,Vvar__4___24Anonymous__1299,Vvar__5___24Anonymous__1301,Vvar__6___24Anonymous__1303,Vvar__7___24Anonymous__1305) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1292,Vvar__1___24Anonymous__1294,Vvar__2___24Anonymous__1296,Vvar__3___24Anonymous__1298,Vvar__4___24Anonymous__1300,Vvar__5___24Anonymous__1302,Vvar__6___24Anonymous__1304,Vvar__7___24Anonymous__1306)
=> ( Vvar__7___24Anonymous__1305 = Vvar__7___24Anonymous__1306
& Vvar__6___24Anonymous__1303 = Vvar__6___24Anonymous__1304
& Vvar__5___24Anonymous__1301 = Vvar__5___24Anonymous__1302
& Vvar__4___24Anonymous__1299 = Vvar__4___24Anonymous__1300
& Vvar__3___24Anonymous__1297 = Vvar__3___24Anonymous__1298
& Vvar__2___24Anonymous__1295 = Vvar__2___24Anonymous__1296
& Vvar__1___24Anonymous__1293 = Vvar__1___24Anonymous__1294
& Vvar__0___24Anonymous__1291 = Vvar__0___24Anonymous__1292 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__2309,Vvar__0___24Anonymous__2310,Vvar__1___24Anonymous__2311,Vvar__1___24Anonymous__2312] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__2309,Vvar__1___24Anonymous__2311) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__2310,Vvar__1___24Anonymous__2312)
=> ( Vvar__1___24Anonymous__2311 = Vvar__1___24Anonymous__2312
& Vvar__0___24Anonymous__2309 = Vvar__0___24Anonymous__2310 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__2016,Vvar__0__X__2017,Vvar__1__lt__2018,Vvar__1__lt__2019,Vvar__2__eq__2020,Vvar__2__eq__2021,Vvar__3__x__2022,Vvar__3__x__2023,Vvar__4__y__2024,Vvar__4__y__2025,Vvar__5___24Anonymous__2026,Vvar__5___24Anonymous__2027] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__2016,Vvar__1__lt__2018,Vvar__2__eq__2020,Vvar__3__x__2022,Vvar__4__y__2024) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__2017,Vvar__1__lt__2019,Vvar__2__eq__2021,Vvar__3__x__2023,Vvar__4__y__2025)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__2024 = Vvar__4__y__2025
& Vvar__3__x__2022 = Vvar__3__x__2023
& Vvar__2__eq__2020 = Vvar__2__eq__2021
& Vvar__1__lt__2018 = Vvar__1__lt__2019
& Vvar__0__X__2016 = Vvar__0__X__2017 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__2028,Vvar__0__X__2029,Vvar__1__lt__2030,Vvar__1__lt__2031,Vvar__2__eq__2032,Vvar__2__eq__2033,Vvar__3__x__2034,Vvar__3__x__2035,Vvar__4__y__2036,Vvar__4__y__2037,Vvar__5___24Anonymous__2038,Vvar__5___24Anonymous__2039] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__2028,Vvar__1__lt__2030,Vvar__2__eq__2032,Vvar__3__x__2034,Vvar__4__y__2036) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__2029,Vvar__1__lt__2031,Vvar__2__eq__2033,Vvar__3__x__2035,Vvar__4__y__2037)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__2036 = Vvar__4__y__2037
& Vvar__3__x__2034 = Vvar__3__x__2035
& Vvar__2__eq__2032 = Vvar__2__eq__2033
& Vvar__1__lt__2030 = Vvar__1__lt__2031
& Vvar__0__X__2028 = Vvar__0__X__2029 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__2004,Vvar__0__X__2005,Vvar__1__lt__2006,Vvar__1__lt__2007,Vvar__2__eq__2008,Vvar__2__eq__2009,Vvar__3__x__2010,Vvar__3__x__2011,Vvar__4__y__2012,Vvar__4__y__2013,Vvar__5___24Anonymous__2014,Vvar__5___24Anonymous__2015] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__2004,Vvar__1__lt__2006,Vvar__2__eq__2008,Vvar__3__x__2010,Vvar__4__y__2012) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__2005,Vvar__1__lt__2007,Vvar__2__eq__2009,Vvar__3__x__2011,Vvar__4__y__2013)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__2012 = Vvar__4__y__2013
& Vvar__3__x__2010 = Vvar__3__x__2011
& Vvar__2__eq__2008 = Vvar__2__eq__2009
& Vvar__1__lt__2006 = Vvar__1__lt__2007
& Vvar__0__X__2004 = Vvar__0__X__2005 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__22515,Vvar__0__n__22516] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__22515) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__22516)
=> Vvar__0__n__22515 = Vvar__0__n__22516 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__22517,Vvar__0__n__22518,Vvar__1___24Anonymous__22519,Vvar__1___24Anonymous__22520] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__22517,Vvar__1___24Anonymous__22519) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__22518,Vvar__1___24Anonymous__22520)
=> ( Vvar__1___24Anonymous__22519 = Vvar__1___24Anonymous__22520
& Vvar__0__n__22517 = Vvar__0__n__22518 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__426,Vvar__0__A__427,Vvar__1__h__428,Vvar__1__h__429,Vvar__2__n__430,Vvar__2__n__431,Vvar__3___24Anonymous__432,Vvar__3___24Anonymous__433] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__426,Vvar__1__h__428,Vvar__2__n__430,Vvar__3___24Anonymous__432) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__427,Vvar__1__h__429,Vvar__2__n__431,Vvar__3___24Anonymous__433)
=> ( Vvar__3___24Anonymous__432 = Vvar__3___24Anonymous__433
& Vvar__2__n__430 = Vvar__2__n__431
& Vvar__1__h__428 = Vvar__1__h__429
& Vvar__0__A__426 = Vvar__0__A__427 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__424,Vvar__0__A__425] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__424) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__425)
=> Vvar__0__A__424 = Vvar__0__A__425 ) ).
fof('$_inj_Coq.funind.Recdef.cmt',axiom,
! [Vvar__0__m__8321,Vvar__0__m__8322,Vvar__1__n__8323,Vvar__1__n__8324,Vvar__2__v__8325,Vvar__2__v__8326,Vvar__3___24Anonymous__8327,Vvar__3___24Anonymous__8328,Vvar__4___24Anonymous__8329,Vvar__4___24Anonymous__8330] :
( cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__8321,Vvar__1__n__8323,Vvar__2__v__8325) = cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__8322,Vvar__1__n__8324,Vvar__2__v__8326)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__v__8325 = Vvar__2__v__8326
& Vvar__1__n__8323 = Vvar__1__n__8324
& Vvar__0__m__8321 = Vvar__0__m__8322 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__21279,Vvar__0__C__21280,Vvar__1___24Anonymous__21281,Vvar__1___24Anonymous__21282] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__21279,Vvar__1___24Anonymous__21281) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__21280,Vvar__1___24Anonymous__21282)
=> ( Vvar__1___24Anonymous__21281 = Vvar__1___24Anonymous__21282
& Vvar__0__C__21279 = Vvar__0__C__21280 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__21283,Vvar__0__C__21284,Vvar__1___24Anonymous__21285,Vvar__1___24Anonymous__21286,Vvar__2___24Anonymous__21287,Vvar__2___24Anonymous__21288] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__21283,Vvar__1___24Anonymous__21285,Vvar__2___24Anonymous__21287) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__21284,Vvar__1___24Anonymous__21286,Vvar__2___24Anonymous__21288)
=> ( Vvar__2___24Anonymous__21287 = Vvar__2___24Anonymous__21288
& Vvar__1___24Anonymous__21285 = Vvar__1___24Anonymous__21286
& Vvar__0__C__21283 = Vvar__0__C__21284 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__21275,Vvar__0__C__21276,Vvar__1___24Anonymous__21277,Vvar__1___24Anonymous__21278] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__21275,Vvar__1___24Anonymous__21277) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__21276,Vvar__1___24Anonymous__21278)
=> ( Vvar__1___24Anonymous__21277 = Vvar__1___24Anonymous__21278
& Vvar__0__C__21275 = Vvar__0__C__21276 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__21295,Vvar__0__C__21296,Vvar__1___24Anonymous__21297,Vvar__1___24Anonymous__21298,Vvar__2___24Anonymous__21299,Vvar__2___24Anonymous__21300] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__21295,Vvar__1___24Anonymous__21297,Vvar__2___24Anonymous__21299) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__21296,Vvar__1___24Anonymous__21298,Vvar__2___24Anonymous__21300)
=> ( Vvar__2___24Anonymous__21299 = Vvar__2___24Anonymous__21300
& Vvar__1___24Anonymous__21297 = Vvar__1___24Anonymous__21298
& Vvar__0__C__21295 = Vvar__0__C__21296 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__21301,Vvar__0__C__21302,Vvar__1___24Anonymous__21303,Vvar__1___24Anonymous__21304] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__21301,Vvar__1___24Anonymous__21303) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__21302,Vvar__1___24Anonymous__21304)
=> ( Vvar__1___24Anonymous__21303 = Vvar__1___24Anonymous__21304
& Vvar__0__C__21301 = Vvar__0__C__21302 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__21305,Vvar__0__C__21306,Vvar__1___24Anonymous__21307,Vvar__1___24Anonymous__21308,Vvar__2___24Anonymous__21309,Vvar__2___24Anonymous__21310] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__21305,Vvar__1___24Anonymous__21307,Vvar__2___24Anonymous__21309) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__21306,Vvar__1___24Anonymous__21308,Vvar__2___24Anonymous__21310)
=> ( Vvar__2___24Anonymous__21309 = Vvar__2___24Anonymous__21310
& Vvar__1___24Anonymous__21307 = Vvar__1___24Anonymous__21308
& Vvar__0__C__21305 = Vvar__0__C__21306 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__21289,Vvar__0__C__21290,Vvar__1___24Anonymous__21291,Vvar__1___24Anonymous__21292,Vvar__2___24Anonymous__21293,Vvar__2___24Anonymous__21294] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__21289,Vvar__1___24Anonymous__21291,Vvar__2___24Anonymous__21293) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__21290,Vvar__1___24Anonymous__21292,Vvar__2___24Anonymous__21294)
=> ( Vvar__2___24Anonymous__21293 = Vvar__2___24Anonymous__21294
& Vvar__1___24Anonymous__21291 = Vvar__1___24Anonymous__21292
& Vvar__0__C__21289 = Vvar__0__C__21290 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__21350,Vvar__0__C__21351,Vvar__1___24Anonymous__21352,Vvar__1___24Anonymous__21353,Vvar__2___24Anonymous__21354,Vvar__2___24Anonymous__21355,Vvar__3___24Anonymous__21356,Vvar__3___24Anonymous__21357] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__21350,Vvar__1___24Anonymous__21352,Vvar__2___24Anonymous__21354,Vvar__3___24Anonymous__21356) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__21351,Vvar__1___24Anonymous__21353,Vvar__2___24Anonymous__21355,Vvar__3___24Anonymous__21357)
=> ( Vvar__3___24Anonymous__21356 = Vvar__3___24Anonymous__21357
& Vvar__2___24Anonymous__21354 = Vvar__2___24Anonymous__21355
& Vvar__1___24Anonymous__21352 = Vvar__1___24Anonymous__21353
& Vvar__0__C__21350 = Vvar__0__C__21351 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__21340,Vvar__0__C__21341,Vvar__1___24Anonymous__21342,Vvar__1___24Anonymous__21343] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__21340,Vvar__1___24Anonymous__21342) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__21341,Vvar__1___24Anonymous__21343)
=> ( Vvar__1___24Anonymous__21342 = Vvar__1___24Anonymous__21343
& Vvar__0__C__21340 = Vvar__0__C__21341 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__21344,Vvar__0__C__21345,Vvar__1___24Anonymous__21346,Vvar__1___24Anonymous__21347,Vvar__2___24Anonymous__21348,Vvar__2___24Anonymous__21349] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__21344,Vvar__1___24Anonymous__21346,Vvar__2___24Anonymous__21348) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__21345,Vvar__1___24Anonymous__21347,Vvar__2___24Anonymous__21349)
=> ( Vvar__2___24Anonymous__21348 = Vvar__2___24Anonymous__21349
& Vvar__1___24Anonymous__21346 = Vvar__1___24Anonymous__21347
& Vvar__0__C__21344 = Vvar__0__C__21345 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__21378,Vvar__0___24Anonymous__21379,Vvar__1___24Anonymous__21380,Vvar__1___24Anonymous__21381] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__21378,Vvar__1___24Anonymous__21380) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__21379,Vvar__1___24Anonymous__21381)
=> ( Vvar__1___24Anonymous__21380 = Vvar__1___24Anonymous__21381
& Vvar__0___24Anonymous__21378 = Vvar__0___24Anonymous__21379 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__21374,Vvar__0___24Anonymous__21375,Vvar__1___24Anonymous__21376,Vvar__1___24Anonymous__21377] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__21374,Vvar__1___24Anonymous__21376) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__21375,Vvar__1___24Anonymous__21377)
=> ( Vvar__1___24Anonymous__21376 = Vvar__1___24Anonymous__21377
& Vvar__0___24Anonymous__21374 = Vvar__0___24Anonymous__21375 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__24036,Vvar__0__r__24037] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__24036) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__24037)
=> Vvar__0__r__24036 = Vvar__0__r__24037 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__24024,Vvar__0__r1__24025,Vvar__1__r2__24026,Vvar__1__r2__24027] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__24024,Vvar__1__r2__24026) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__24025,Vvar__1__r2__24027)
=> ( Vvar__1__r2__24026 = Vvar__1__r2__24027
& Vvar__0__r1__24024 = Vvar__0__r1__24025 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__24028,Vvar__0__r1__24029,Vvar__1__r2__24030,Vvar__1__r2__24031] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__24028,Vvar__1__r2__24030) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__24029,Vvar__1__r2__24031)
=> ( Vvar__1__r2__24030 = Vvar__1__r2__24031
& Vvar__0__r1__24028 = Vvar__0__r1__24029 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__24038,Vvar__0__r__24039] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__24038) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__24039)
=> Vvar__0__r__24038 = Vvar__0__r__24039 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__24020,Vvar__0__r1__24021,Vvar__1__r2__24022,Vvar__1__r2__24023] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__24020,Vvar__1__r2__24022) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__24021,Vvar__1__r2__24023)
=> ( Vvar__1__r2__24022 = Vvar__1__r2__24023
& Vvar__0__r1__24020 = Vvar__0__r1__24021 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__24032,Vvar__0__r1__24033,Vvar__1__z__24034,Vvar__1__z__24035] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__24032,Vvar__1__z__24034) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__24033,Vvar__1__z__24035)
=> ( Vvar__1__z__24034 = Vvar__1__z__24035
& Vvar__0__r1__24032 = Vvar__0__r1__24033 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__24016,Vvar__0__r__24017] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__24016) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__24017)
=> Vvar__0__r__24016 = Vvar__0__r__24017 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__24018,Vvar__0__r__24019] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__24018) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__24019)
=> Vvar__0__r__24018 = Vvar__0__r__24019 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__30123,Vvar__0__T__30124,Vvar__1__Flhs__30125,Vvar__1__Flhs__30126,Vvar__2__Fop__30127,Vvar__2__Fop__30128,Vvar__3__Frhs__30129,Vvar__3__Frhs__30130] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__30123,Vvar__1__Flhs__30125,Vvar__2__Fop__30127,Vvar__3__Frhs__30129) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__30124,Vvar__1__Flhs__30126,Vvar__2__Fop__30128,Vvar__3__Frhs__30130)
=> ( Vvar__3__Frhs__30129 = Vvar__3__Frhs__30130
& Vvar__2__Fop__30127 = Vvar__2__Fop__30128
& Vvar__1__Flhs__30125 = Vvar__1__Flhs__30126
& Vvar__0__T__30123 = Vvar__0__T__30124 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__30098,Vvar__0__C__30099,Vvar__1___24Anonymous__30100,Vvar__1___24Anonymous__30101,Vvar__2___24Anonymous__30102,Vvar__2___24Anonymous__30103] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__30098,Vvar__1___24Anonymous__30100,Vvar__2___24Anonymous__30102) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__30099,Vvar__1___24Anonymous__30101,Vvar__2___24Anonymous__30103)
=> ( Vvar__2___24Anonymous__30102 = Vvar__2___24Anonymous__30103
& Vvar__1___24Anonymous__30100 = Vvar__1___24Anonymous__30101
& Vvar__0__C__30098 = Vvar__0__C__30099 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__30104,Vvar__0__C__30105,Vvar__1___24Anonymous__30106,Vvar__1___24Anonymous__30107] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__30104,Vvar__1___24Anonymous__30106) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__30105,Vvar__1___24Anonymous__30107)
=> ( Vvar__1___24Anonymous__30106 = Vvar__1___24Anonymous__30107
& Vvar__0__C__30104 = Vvar__0__C__30105 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__30078,Vvar__0__C__30079,Vvar__1___24Anonymous__30080,Vvar__1___24Anonymous__30081] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__30078,Vvar__1___24Anonymous__30080) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__30079,Vvar__1___24Anonymous__30081)
=> ( Vvar__1___24Anonymous__30080 = Vvar__1___24Anonymous__30081
& Vvar__0__C__30078 = Vvar__0__C__30079 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__30086,Vvar__0__C__30087,Vvar__1___24Anonymous__30088,Vvar__1___24Anonymous__30089,Vvar__2___24Anonymous__30090,Vvar__2___24Anonymous__30091] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__30086,Vvar__1___24Anonymous__30088,Vvar__2___24Anonymous__30090) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__30087,Vvar__1___24Anonymous__30089,Vvar__2___24Anonymous__30091)
=> ( Vvar__2___24Anonymous__30090 = Vvar__2___24Anonymous__30091
& Vvar__1___24Anonymous__30088 = Vvar__1___24Anonymous__30089
& Vvar__0__C__30086 = Vvar__0__C__30087 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__30092,Vvar__0__C__30093,Vvar__1___24Anonymous__30094,Vvar__1___24Anonymous__30095,Vvar__2___24Anonymous__30096,Vvar__2___24Anonymous__30097] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__30092,Vvar__1___24Anonymous__30094,Vvar__2___24Anonymous__30096) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__30093,Vvar__1___24Anonymous__30095,Vvar__2___24Anonymous__30097)
=> ( Vvar__2___24Anonymous__30096 = Vvar__2___24Anonymous__30097
& Vvar__1___24Anonymous__30094 = Vvar__1___24Anonymous__30095
& Vvar__0__C__30092 = Vvar__0__C__30093 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__30082,Vvar__0__C__30083,Vvar__1___24Anonymous__30084,Vvar__1___24Anonymous__30085] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__30082,Vvar__1___24Anonymous__30084) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__30083,Vvar__1___24Anonymous__30085)
=> ( Vvar__1___24Anonymous__30084 = Vvar__1___24Anonymous__30085
& Vvar__0__C__30082 = Vvar__0__C__30083 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__30108,Vvar__0__C__30109] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__30108) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__30109)
=> Vvar__0__C__30108 = Vvar__0__C__30109 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__35525,Vvar__0__TA__35526,Vvar__1__TX__35527,Vvar__1__TX__35528,Vvar__2__AA__35529,Vvar__2__AA__35530,Vvar__3__AF__35531,Vvar__3__AF__35532,Vvar__4___24Anonymous__35533,Vvar__4___24Anonymous__35534,Vvar__5___24Anonymous__35535,Vvar__5___24Anonymous__35536] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__35525,Vvar__1__TX__35527,Vvar__2__AA__35529,Vvar__3__AF__35531,Vvar__4___24Anonymous__35533,Vvar__5___24Anonymous__35535) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__35526,Vvar__1__TX__35528,Vvar__2__AA__35530,Vvar__3__AF__35532,Vvar__4___24Anonymous__35534,Vvar__5___24Anonymous__35536)
=> ( Vvar__5___24Anonymous__35535 = Vvar__5___24Anonymous__35536
& Vvar__4___24Anonymous__35533 = Vvar__4___24Anonymous__35534
& Vvar__3__AF__35531 = Vvar__3__AF__35532
& Vvar__2__AA__35529 = Vvar__2__AA__35530
& Vvar__1__TX__35527 = Vvar__1__TX__35528
& Vvar__0__TA__35525 = Vvar__0__TA__35526 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__35537,Vvar__0__TA__35538,Vvar__1__TX__35539,Vvar__1__TX__35540,Vvar__2__AA__35541,Vvar__2__AA__35542,Vvar__3__AF__35543,Vvar__3__AF__35544,Vvar__4___24Anonymous__35545,Vvar__4___24Anonymous__35546,Vvar__5___24Anonymous__35547,Vvar__5___24Anonymous__35548] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__35537,Vvar__1__TX__35539,Vvar__2__AA__35541,Vvar__3__AF__35543,Vvar__4___24Anonymous__35545,Vvar__5___24Anonymous__35547) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__35538,Vvar__1__TX__35540,Vvar__2__AA__35542,Vvar__3__AF__35544,Vvar__4___24Anonymous__35546,Vvar__5___24Anonymous__35548)
=> ( Vvar__5___24Anonymous__35547 = Vvar__5___24Anonymous__35548
& Vvar__4___24Anonymous__35545 = Vvar__4___24Anonymous__35546
& Vvar__3__AF__35543 = Vvar__3__AF__35544
& Vvar__2__AA__35541 = Vvar__2__AA__35542
& Vvar__1__TX__35539 = Vvar__1__TX__35540
& Vvar__0__TA__35537 = Vvar__0__TA__35538 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__35549,Vvar__0__TA__35550,Vvar__1__TX__35551,Vvar__1__TX__35552,Vvar__2__AA__35553,Vvar__2__AA__35554,Vvar__3__AF__35555,Vvar__3__AF__35556,Vvar__4___24Anonymous__35557,Vvar__4___24Anonymous__35558,Vvar__5___24Anonymous__35559,Vvar__5___24Anonymous__35560] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__35549,Vvar__1__TX__35551,Vvar__2__AA__35553,Vvar__3__AF__35555,Vvar__4___24Anonymous__35557,Vvar__5___24Anonymous__35559) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__35550,Vvar__1__TX__35552,Vvar__2__AA__35554,Vvar__3__AF__35556,Vvar__4___24Anonymous__35558,Vvar__5___24Anonymous__35560)
=> ( Vvar__5___24Anonymous__35559 = Vvar__5___24Anonymous__35560
& Vvar__4___24Anonymous__35557 = Vvar__4___24Anonymous__35558
& Vvar__3__AF__35555 = Vvar__3__AF__35556
& Vvar__2__AA__35553 = Vvar__2__AA__35554
& Vvar__1__TX__35551 = Vvar__1__TX__35552
& Vvar__0__TA__35549 = Vvar__0__TA__35550 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__35507,Vvar__0__TA__35508,Vvar__1__TX__35509,Vvar__1__TX__35510,Vvar__2__AA__35511,Vvar__2__AA__35512,Vvar__3__AF__35513,Vvar__3__AF__35514] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__35507,Vvar__1__TX__35509,Vvar__2__AA__35511,Vvar__3__AF__35513) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__35508,Vvar__1__TX__35510,Vvar__2__AA__35512,Vvar__3__AF__35514)
=> ( Vvar__3__AF__35513 = Vvar__3__AF__35514
& Vvar__2__AA__35511 = Vvar__2__AA__35512
& Vvar__1__TX__35509 = Vvar__1__TX__35510
& Vvar__0__TA__35507 = Vvar__0__TA__35508 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__35571,Vvar__0__TA__35572,Vvar__1__TX__35573,Vvar__1__TX__35574,Vvar__2__AA__35575,Vvar__2__AA__35576,Vvar__3__AF__35577,Vvar__3__AF__35578,Vvar__4___24Anonymous__35579,Vvar__4___24Anonymous__35580,Vvar__5___24Anonymous__35581,Vvar__5___24Anonymous__35582,Vvar__6___24Anonymous__35583,Vvar__6___24Anonymous__35584] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__35571,Vvar__1__TX__35573,Vvar__2__AA__35575,Vvar__3__AF__35577,Vvar__4___24Anonymous__35579,Vvar__5___24Anonymous__35581,Vvar__6___24Anonymous__35583) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__35572,Vvar__1__TX__35574,Vvar__2__AA__35576,Vvar__3__AF__35578,Vvar__4___24Anonymous__35580,Vvar__5___24Anonymous__35582,Vvar__6___24Anonymous__35584)
=> ( Vvar__6___24Anonymous__35583 = Vvar__6___24Anonymous__35584
& Vvar__5___24Anonymous__35581 = Vvar__5___24Anonymous__35582
& Vvar__4___24Anonymous__35579 = Vvar__4___24Anonymous__35580
& Vvar__3__AF__35577 = Vvar__3__AF__35578
& Vvar__2__AA__35575 = Vvar__2__AA__35576
& Vvar__1__TX__35573 = Vvar__1__TX__35574
& Vvar__0__TA__35571 = Vvar__0__TA__35572 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__35561,Vvar__0__TA__35562,Vvar__1__TX__35563,Vvar__1__TX__35564,Vvar__2__AA__35565,Vvar__2__AA__35566,Vvar__3__AF__35567,Vvar__3__AF__35568,Vvar__4___24Anonymous__35569,Vvar__4___24Anonymous__35570] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__35561,Vvar__1__TX__35563,Vvar__2__AA__35565,Vvar__3__AF__35567,Vvar__4___24Anonymous__35569) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__35562,Vvar__1__TX__35564,Vvar__2__AA__35566,Vvar__3__AF__35568,Vvar__4___24Anonymous__35570)
=> ( Vvar__4___24Anonymous__35569 = Vvar__4___24Anonymous__35570
& Vvar__3__AF__35567 = Vvar__3__AF__35568
& Vvar__2__AA__35565 = Vvar__2__AA__35566
& Vvar__1__TX__35563 = Vvar__1__TX__35564
& Vvar__0__TA__35561 = Vvar__0__TA__35562 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__35499,Vvar__0__TA__35500,Vvar__1__TX__35501,Vvar__1__TX__35502,Vvar__2__AA__35503,Vvar__2__AA__35504,Vvar__3__AF__35505,Vvar__3__AF__35506] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__35499,Vvar__1__TX__35501,Vvar__2__AA__35503,Vvar__3__AF__35505) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__35500,Vvar__1__TX__35502,Vvar__2__AA__35504,Vvar__3__AF__35506)
=> ( Vvar__3__AF__35505 = Vvar__3__AF__35506
& Vvar__2__AA__35503 = Vvar__2__AA__35504
& Vvar__1__TX__35501 = Vvar__1__TX__35502
& Vvar__0__TA__35499 = Vvar__0__TA__35500 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__35515,Vvar__0__TA__35516,Vvar__1__TX__35517,Vvar__1__TX__35518,Vvar__2__AA__35519,Vvar__2__AA__35520,Vvar__3__AF__35521,Vvar__3__AF__35522,Vvar__4___24Anonymous__35523,Vvar__4___24Anonymous__35524] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__35515,Vvar__1__TX__35517,Vvar__2__AA__35519,Vvar__3__AF__35521,Vvar__4___24Anonymous__35523) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__35516,Vvar__1__TX__35518,Vvar__2__AA__35520,Vvar__3__AF__35522,Vvar__4___24Anonymous__35524)
=> ( Vvar__4___24Anonymous__35523 = Vvar__4___24Anonymous__35524
& Vvar__3__AF__35521 = Vvar__3__AF__35522
& Vvar__2__AA__35519 = Vvar__2__AA__35520
& Vvar__1__TX__35517 = Vvar__1__TX__35518
& Vvar__0__TA__35515 = Vvar__0__TA__35516 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__35621,Vvar__0___24Anonymous__35622,Vvar__1___24Anonymous__35623,Vvar__1___24Anonymous__35624] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35621,Vvar__1___24Anonymous__35623) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35622,Vvar__1___24Anonymous__35624)
=> ( Vvar__1___24Anonymous__35623 = Vvar__1___24Anonymous__35624
& Vvar__0___24Anonymous__35621 = Vvar__0___24Anonymous__35622 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__35625,Vvar__0___24Anonymous__35626,Vvar__1___24Anonymous__35627,Vvar__1___24Anonymous__35628,Vvar__2___24Anonymous__35629,Vvar__2___24Anonymous__35630] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35625,Vvar__1___24Anonymous__35627,Vvar__2___24Anonymous__35629) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35626,Vvar__1___24Anonymous__35628,Vvar__2___24Anonymous__35630)
=> ( Vvar__2___24Anonymous__35629 = Vvar__2___24Anonymous__35630
& Vvar__1___24Anonymous__35627 = Vvar__1___24Anonymous__35628
& Vvar__0___24Anonymous__35625 = Vvar__0___24Anonymous__35626 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__35617,Vvar__0___24Anonymous__35618,Vvar__1___24Anonymous__35619,Vvar__1___24Anonymous__35620] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35617,Vvar__1___24Anonymous__35619) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35618,Vvar__1___24Anonymous__35620)
=> ( Vvar__1___24Anonymous__35619 = Vvar__1___24Anonymous__35620
& Vvar__0___24Anonymous__35617 = Vvar__0___24Anonymous__35618 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__22397,Vvar__0__C__22398] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__22397) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__22398)
=> Vvar__0__C__22397 = Vvar__0__C__22398 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__22395,Vvar__0__C__22396] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__22395) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__22396)
=> Vvar__0__C__22395 = Vvar__0__C__22396 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__22403,Vvar__0__C__22404,Vvar__1___24Anonymous__22405,Vvar__1___24Anonymous__22406] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__22403,Vvar__1___24Anonymous__22405) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__22404,Vvar__1___24Anonymous__22406)
=> ( Vvar__1___24Anonymous__22405 = Vvar__1___24Anonymous__22406
& Vvar__0__C__22403 = Vvar__0__C__22404 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__22407,Vvar__0__C__22408,Vvar__1___24Anonymous__22409,Vvar__1___24Anonymous__22410,Vvar__2___24Anonymous__22411,Vvar__2___24Anonymous__22412] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__22407,Vvar__1___24Anonymous__22409,Vvar__2___24Anonymous__22411) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__22408,Vvar__1___24Anonymous__22410,Vvar__2___24Anonymous__22412)
=> ( Vvar__2___24Anonymous__22411 = Vvar__2___24Anonymous__22412
& Vvar__1___24Anonymous__22409 = Vvar__1___24Anonymous__22410
& Vvar__0__C__22407 = Vvar__0__C__22408 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__22399,Vvar__0__C__22400,Vvar__1___24Anonymous__22401,Vvar__1___24Anonymous__22402] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__22399,Vvar__1___24Anonymous__22401) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__22400,Vvar__1___24Anonymous__22402)
=> ( Vvar__1___24Anonymous__22401 = Vvar__1___24Anonymous__22402
& Vvar__0__C__22399 = Vvar__0__C__22400 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__22433,Vvar__0__C__22434,Vvar__1___24Anonymous__22435,Vvar__1___24Anonymous__22436,Vvar__2___24Anonymous__22437,Vvar__2___24Anonymous__22438] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__22433,Vvar__1___24Anonymous__22435,Vvar__2___24Anonymous__22437) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__22434,Vvar__1___24Anonymous__22436,Vvar__2___24Anonymous__22438)
=> ( Vvar__2___24Anonymous__22437 = Vvar__2___24Anonymous__22438
& Vvar__1___24Anonymous__22435 = Vvar__1___24Anonymous__22436
& Vvar__0__C__22433 = Vvar__0__C__22434 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__22429,Vvar__0__C__22430,Vvar__1___24Anonymous__22431,Vvar__1___24Anonymous__22432] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__22429,Vvar__1___24Anonymous__22431) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__22430,Vvar__1___24Anonymous__22432)
=> ( Vvar__1___24Anonymous__22431 = Vvar__1___24Anonymous__22432
& Vvar__0__C__22429 = Vvar__0__C__22430 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__22419,Vvar__0__C__22420,Vvar__1___24Anonymous__22421,Vvar__1___24Anonymous__22422,Vvar__2___24Anonymous__22423,Vvar__2___24Anonymous__22424] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__22419,Vvar__1___24Anonymous__22421,Vvar__2___24Anonymous__22423) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__22420,Vvar__1___24Anonymous__22422,Vvar__2___24Anonymous__22424)
=> ( Vvar__2___24Anonymous__22423 = Vvar__2___24Anonymous__22424
& Vvar__1___24Anonymous__22421 = Vvar__1___24Anonymous__22422
& Vvar__0__C__22419 = Vvar__0__C__22420 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__22425,Vvar__0__C__22426,Vvar__1___24Anonymous__22427,Vvar__1___24Anonymous__22428] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__22425,Vvar__1___24Anonymous__22427) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__22426,Vvar__1___24Anonymous__22428)
=> ( Vvar__1___24Anonymous__22427 = Vvar__1___24Anonymous__22428
& Vvar__0__C__22425 = Vvar__0__C__22426 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__22439,Vvar__0__C__22440,Vvar__1___24Anonymous__22441,Vvar__1___24Anonymous__22442,Vvar__2___24Anonymous__22443,Vvar__2___24Anonymous__22444] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__22439,Vvar__1___24Anonymous__22441,Vvar__2___24Anonymous__22443) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__22440,Vvar__1___24Anonymous__22442,Vvar__2___24Anonymous__22444)
=> ( Vvar__2___24Anonymous__22443 = Vvar__2___24Anonymous__22444
& Vvar__1___24Anonymous__22441 = Vvar__1___24Anonymous__22442
& Vvar__0__C__22439 = Vvar__0__C__22440 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__22413,Vvar__0__C__22414,Vvar__1___24Anonymous__22415,Vvar__1___24Anonymous__22416,Vvar__2___24Anonymous__22417,Vvar__2___24Anonymous__22418] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__22413,Vvar__1___24Anonymous__22415,Vvar__2___24Anonymous__22417) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__22414,Vvar__1___24Anonymous__22416,Vvar__2___24Anonymous__22418)
=> ( Vvar__2___24Anonymous__22417 = Vvar__2___24Anonymous__22418
& Vvar__1___24Anonymous__22415 = Vvar__1___24Anonymous__22416
& Vvar__0__C__22413 = Vvar__0__C__22414 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__22454,Vvar__0__C__22455,Vvar__1__num__22456,Vvar__1__num__22457,Vvar__2__denum__22458,Vvar__2__denum__22459,Vvar__3__condition__22460,Vvar__3__condition__22461] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__22454,Vvar__1__num__22456,Vvar__2__denum__22458,Vvar__3__condition__22460) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__22455,Vvar__1__num__22457,Vvar__2__denum__22459,Vvar__3__condition__22461)
=> ( Vvar__3__condition__22460 = Vvar__3__condition__22461
& Vvar__2__denum__22458 = Vvar__2__denum__22459
& Vvar__1__num__22456 = Vvar__1__num__22457
& Vvar__0__C__22454 = Vvar__0__C__22455 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__22476,Vvar__0__C__22477,Vvar__1__rsplit__left__22478,Vvar__1__rsplit__left__22479,Vvar__2__rsplit__common__22480,Vvar__2__rsplit__common__22481,Vvar__3__rsplit__right__22482,Vvar__3__rsplit__right__22483] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__22476,Vvar__1__rsplit__left__22478,Vvar__2__rsplit__common__22480,Vvar__3__rsplit__right__22482) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__22477,Vvar__1__rsplit__left__22479,Vvar__2__rsplit__common__22481,Vvar__3__rsplit__right__22483)
=> ( Vvar__3__rsplit__right__22482 = Vvar__3__rsplit__right__22483
& Vvar__2__rsplit__common__22480 = Vvar__2__rsplit__common__22481
& Vvar__1__rsplit__left__22478 = Vvar__1__rsplit__left__22479
& Vvar__0__C__22476 = Vvar__0__C__22477 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__8752,Vvar__0__C__8753] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__8752) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__8753)
=> Vvar__0__C__8752 = Vvar__0__C__8753 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__8750,Vvar__0__C__8751] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__8750) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__8751)
=> Vvar__0__C__8750 = Vvar__0__C__8751 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__8758,Vvar__0__C__8759,Vvar__1___24Anonymous__8760,Vvar__1___24Anonymous__8761] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__8758,Vvar__1___24Anonymous__8760) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__8759,Vvar__1___24Anonymous__8761)
=> ( Vvar__1___24Anonymous__8760 = Vvar__1___24Anonymous__8761
& Vvar__0__C__8758 = Vvar__0__C__8759 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__8762,Vvar__0__C__8763,Vvar__1___24Anonymous__8764,Vvar__1___24Anonymous__8765,Vvar__2___24Anonymous__8766,Vvar__2___24Anonymous__8767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__8762,Vvar__1___24Anonymous__8764,Vvar__2___24Anonymous__8766) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__8763,Vvar__1___24Anonymous__8765,Vvar__2___24Anonymous__8767)
=> ( Vvar__2___24Anonymous__8766 = Vvar__2___24Anonymous__8767
& Vvar__1___24Anonymous__8764 = Vvar__1___24Anonymous__8765
& Vvar__0__C__8762 = Vvar__0__C__8763 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__8754,Vvar__0__C__8755,Vvar__1___24Anonymous__8756,Vvar__1___24Anonymous__8757] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__8754,Vvar__1___24Anonymous__8756) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__8755,Vvar__1___24Anonymous__8757)
=> ( Vvar__1___24Anonymous__8756 = Vvar__1___24Anonymous__8757
& Vvar__0__C__8754 = Vvar__0__C__8755 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__8774,Vvar__0__C__8775,Vvar__1___24Anonymous__8776,Vvar__1___24Anonymous__8777,Vvar__2___24Anonymous__8778,Vvar__2___24Anonymous__8779] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__8774,Vvar__1___24Anonymous__8776,Vvar__2___24Anonymous__8778) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__8775,Vvar__1___24Anonymous__8777,Vvar__2___24Anonymous__8779)
=> ( Vvar__2___24Anonymous__8778 = Vvar__2___24Anonymous__8779
& Vvar__1___24Anonymous__8776 = Vvar__1___24Anonymous__8777
& Vvar__0__C__8774 = Vvar__0__C__8775 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__8780,Vvar__0__C__8781,Vvar__1___24Anonymous__8782,Vvar__1___24Anonymous__8783] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__8780,Vvar__1___24Anonymous__8782) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__8781,Vvar__1___24Anonymous__8783)
=> ( Vvar__1___24Anonymous__8782 = Vvar__1___24Anonymous__8783
& Vvar__0__C__8780 = Vvar__0__C__8781 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__8784,Vvar__0__C__8785,Vvar__1___24Anonymous__8786,Vvar__1___24Anonymous__8787,Vvar__2___24Anonymous__8788,Vvar__2___24Anonymous__8789] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__8784,Vvar__1___24Anonymous__8786,Vvar__2___24Anonymous__8788) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__8785,Vvar__1___24Anonymous__8787,Vvar__2___24Anonymous__8789)
=> ( Vvar__2___24Anonymous__8788 = Vvar__2___24Anonymous__8789
& Vvar__1___24Anonymous__8786 = Vvar__1___24Anonymous__8787
& Vvar__0__C__8784 = Vvar__0__C__8785 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__8768,Vvar__0__C__8769,Vvar__1___24Anonymous__8770,Vvar__1___24Anonymous__8771,Vvar__2___24Anonymous__8772,Vvar__2___24Anonymous__8773] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__8768,Vvar__1___24Anonymous__8770,Vvar__2___24Anonymous__8772) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__8769,Vvar__1___24Anonymous__8771,Vvar__2___24Anonymous__8773)
=> ( Vvar__2___24Anonymous__8772 = Vvar__2___24Anonymous__8773
& Vvar__1___24Anonymous__8770 = Vvar__1___24Anonymous__8771
& Vvar__0__C__8768 = Vvar__0__C__8769 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__8405,Vvar__0__C__8406,Vvar__1___24Anonymous__8407,Vvar__1___24Anonymous__8408,Vvar__2___24Anonymous__8409,Vvar__2___24Anonymous__8410,Vvar__3___24Anonymous__8411,Vvar__3___24Anonymous__8412] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__8405,Vvar__1___24Anonymous__8407,Vvar__2___24Anonymous__8409,Vvar__3___24Anonymous__8411) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__8406,Vvar__1___24Anonymous__8408,Vvar__2___24Anonymous__8410,Vvar__3___24Anonymous__8412)
=> ( Vvar__3___24Anonymous__8411 = Vvar__3___24Anonymous__8412
& Vvar__2___24Anonymous__8409 = Vvar__2___24Anonymous__8410
& Vvar__1___24Anonymous__8407 = Vvar__1___24Anonymous__8408
& Vvar__0__C__8405 = Vvar__0__C__8406 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__8395,Vvar__0__C__8396,Vvar__1___24Anonymous__8397,Vvar__1___24Anonymous__8398] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__8395,Vvar__1___24Anonymous__8397) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__8396,Vvar__1___24Anonymous__8398)
=> ( Vvar__1___24Anonymous__8397 = Vvar__1___24Anonymous__8398
& Vvar__0__C__8395 = Vvar__0__C__8396 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__8399,Vvar__0__C__8400,Vvar__1___24Anonymous__8401,Vvar__1___24Anonymous__8402,Vvar__2___24Anonymous__8403,Vvar__2___24Anonymous__8404] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__8399,Vvar__1___24Anonymous__8401,Vvar__2___24Anonymous__8403) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__8400,Vvar__1___24Anonymous__8402,Vvar__2___24Anonymous__8404)
=> ( Vvar__2___24Anonymous__8403 = Vvar__2___24Anonymous__8404
& Vvar__1___24Anonymous__8401 = Vvar__1___24Anonymous__8402
& Vvar__0__C__8399 = Vvar__0__C__8400 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__8564,Vvar__0___24Anonymous__8565,Vvar__1___24Anonymous__8566,Vvar__1___24Anonymous__8567] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__8564,Vvar__1___24Anonymous__8566) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__8565,Vvar__1___24Anonymous__8567)
=> ( Vvar__1___24Anonymous__8566 = Vvar__1___24Anonymous__8567
& Vvar__0___24Anonymous__8564 = Vvar__0___24Anonymous__8565 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__8560,Vvar__0___24Anonymous__8561,Vvar__1___24Anonymous__8562,Vvar__1___24Anonymous__8563] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__8560,Vvar__1___24Anonymous__8562) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__8561,Vvar__1___24Anonymous__8563)
=> ( Vvar__1___24Anonymous__8562 = Vvar__1___24Anonymous__8563
& Vvar__0___24Anonymous__8560 = Vvar__0___24Anonymous__8561 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_ceil_log2_S_0',axiom,
! [Vvar__0__n__60051,Vvar__0__n__60052,Vvar__1___24Anonymous__60053,Vvar__1___24Anonymous__60054] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__60051) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__60052)
=> ( c_24Proof = c_24Proof
& Vvar__0__n__60051 = Vvar__0__n__60052 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_ceil_log2_S_1',axiom,
! [Vvar__0__n__60055,Vvar__0__n__60056,Vvar__1____x__60057,Vvar__1____x__60058,Vvar__2___24Anonymous__60059,Vvar__2___24Anonymous__60060,Vvar__3____res__60061,Vvar__3____res__60062,Vvar__4___24Anonymous__60063,Vvar__4___24Anonymous__60064] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__60055,Vvar__1____x__60057,Vvar__3____res__60061,Vvar__4___24Anonymous__60063) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__60056,Vvar__1____x__60058,Vvar__3____res__60062,Vvar__4___24Anonymous__60064)
=> ( Vvar__4___24Anonymous__60063 = Vvar__4___24Anonymous__60064
& Vvar__3____res__60061 = Vvar__3____res__60062
& c_24Proof = c_24Proof
& Vvar__1____x__60057 = Vvar__1____x__60058
& Vvar__0__n__60055 = Vvar__0__n__60056 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_floor_log2_S_0',axiom,
! [Vvar__0__n__60083,Vvar__0__n__60084,Vvar__1___24Anonymous__60085,Vvar__1___24Anonymous__60086] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__60083) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__60084)
=> ( c_24Proof = c_24Proof
& Vvar__0__n__60083 = Vvar__0__n__60084 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_floor_log2_S_1',axiom,
! [Vvar__0__n__60087,Vvar__0__n__60088,Vvar__1__n_27__60089,Vvar__1__n_27__60090,Vvar__2___24Anonymous__60091,Vvar__2___24Anonymous__60092,Vvar__3____res__60093,Vvar__3____res__60094,Vvar__4___24Anonymous__60095,Vvar__4___24Anonymous__60096] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__60087,Vvar__1__n_27__60089,Vvar__3____res__60093,Vvar__4___24Anonymous__60095) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__60088,Vvar__1__n_27__60090,Vvar__3____res__60094,Vvar__4___24Anonymous__60096)
=> ( Vvar__4___24Anonymous__60095 = Vvar__4___24Anonymous__60096
& Vvar__3____res__60093 = Vvar__3____res__60094
& c_24Proof = c_24Proof
& Vvar__1__n_27__60089 = Vvar__1__n_27__60090
& Vvar__0__n__60087 = Vvar__0__n__60088 ) ) ).
fof('$_inj_QuicksortComplexity.nat_below.mkNatBelow',axiom,
! [Vvar__0__v__160,Vvar__0__v__161,Vvar__1__p__162,Vvar__1__p__163] :
( cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__160,Vvar__1__p__162) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__161,Vvar__1__p__163)
=> ( Vvar__1__p__162 = Vvar__1__p__163
& Vvar__0__v__160 = Vvar__0__v__161 ) ) ).
fof('$_inj_QuicksortComplexity.sort_order.Build_E',axiom,
! [Vvar__0__Ec__510,Vvar__0__Ec__511,Vvar__1__Ecmp__512,Vvar__1__Ecmp__513,Vvar__2__Ecmp__sym__514,Vvar__2__Ecmp__sym__515,Vvar__3__Ecmp__trans__516,Vvar__3__Ecmp__trans__517,Vvar__4__Ecmp__eq__trans__l__518,Vvar__4__Ecmp__eq__trans__l__519] :
( cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__510,Vvar__1__Ecmp__512) = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__511,Vvar__1__Ecmp__513)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__Ecmp__512 = Vvar__1__Ecmp__513
& Vvar__0__Ec__510 = Vvar__0__Ec__511 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__59534,Vvar__1__Q__59536,Vvar__2__init__59539,Vvar__3___24Anonymous__59540,Vvar__4___24Anonymous__59541] :
( c_24__type__59567___24t(Vvar__0__P__59534,Vvar__1__Q__59536,Vvar__2__init__59539,Vvar__3___24Anonymous__59540,Vvar__4___24Anonymous__59541,Vvar__0__P__59534)
=> ( c_24__type__59575___24t(Vvar__0__P__59534,Vvar__1__Q__59536,Vvar__2__init__59539,Vvar__3___24Anonymous__59540,Vvar__4___24Anonymous__59541,Vvar__1__Q__59536)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__59539)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__59540)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__59541)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__59534,Vvar__1__Q__59536,Vvar__2__init__59539,Vvar__3___24Anonymous__59540,Vvar__4___24Anonymous__59541)
=> ( ( Vvar__4___24Anonymous__59541 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__59540 = Vvar__2__init__59539 )
| ? [Vvar__3__k__59555] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__59555)
& ? [Vvar__4__l__59556] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__59556)
& ? [Vvar__5__n__59557] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__59557)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__59534,Vvar__1__Q__59536,Vvar__2__init__59539,Vvar__3__k__59555,Vvar__5__n__59557)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__59534,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__59555),Vvar__4__l__59556)
& p(happ(Vvar__1__Q__59536,Vvar__4__l__59556))
& Vvar__4___24Anonymous__59541 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__59557)
& Vvar__3___24Anonymous__59540 = Vvar__4__l__59556 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__59515,Vvar__1__k__59517,Vvar__2___24Anonymous__59518] :
( c_24__type__59532___24t(Vvar__0__P__59515,Vvar__1__k__59517,Vvar__2___24Anonymous__59518,Vvar__0__P__59515)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__59517)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__59518)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__59515,Vvar__1__k__59517,Vvar__2___24Anonymous__59518)
=> ( Vvar__2___24Anonymous__59518 = Vvar__1__k__59517
| ? [Vvar__2__l__59526] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__59526)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__59515,Vvar__1__k__59517,Vvar__2__l__59526)
& p(happ(Vvar__0__P__59515,Vvar__2__l__59526))
& Vvar__2___24Anonymous__59518 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__59526) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__37408,Vvar__1__k__37410,Vvar__2___24Anonymous__37411] :
( c_24__type__37427___24t(Vvar__0__Q__37408,Vvar__1__k__37410,Vvar__2___24Anonymous__37411,Vvar__0__Q__37408)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__37410)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__37411)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__37408,Vvar__1__k__37410,Vvar__2___24Anonymous__37411)
=> ( ? [Vvar__2__l__37416] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__37416)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__37408,Vvar__1__k__37410,Vvar__2__l__37416)
& Vvar__2___24Anonymous__37411 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__37416) )
| ? [Vvar__2__l__37421] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__37421)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__37410,Vvar__2__l__37421))
& p(happ(Vvar__0__Q__37408,Vvar__2__l__37421))
& Vvar__2___24Anonymous__37411 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__37421) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__59730] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59730)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__59730)
=> ( Vvar__0___24Anonymous__59730 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__59732] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__59732)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__59732)
& Vvar__0___24Anonymous__59730 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__59732) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__59734] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__59734)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__59734)
=> ? [Vvar__0__n__59736] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__59736)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__59736)
& Vvar__0___24Anonymous__59734 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__59736) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__21080,Vvar__1___24Anonymous__21081,VX21082] :
( cProp___24t(Vvar__0__P__21080)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__21081)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__21080,Vvar__1___24Anonymous__21081,VX21082)
=> ( ( p(Vvar__0__P__21080)
& Vvar__1___24Anonymous__21081 = cCoq_2eInit_2eDatatypes_2etrue
& VX21082 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__21080) )
| ( ~ p(Vvar__0__P__21080)
& Vvar__1___24Anonymous__21081 = cCoq_2eInit_2eDatatypes_2efalse
& VX21082 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__21080) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX20276] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX20276)
=> ( VX20276 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__20277] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__20277)
& ? [Vvar__1___24Anonymous__20278] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__20278)
& ? [Vvar__2___24Anonymous__20279] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__20279)
& VX20276 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__20277,Vvar__1___24Anonymous__20278,Vvar__2___24Anonymous__20279) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX21102] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX21102)
=> ( VX21102 = cCoq_2eInit_2eByte_2ex00
| VX21102 = cCoq_2eInit_2eByte_2ex01
| VX21102 = cCoq_2eInit_2eByte_2ex02
| VX21102 = cCoq_2eInit_2eByte_2ex03
| VX21102 = cCoq_2eInit_2eByte_2ex04
| VX21102 = cCoq_2eInit_2eByte_2ex05
| VX21102 = cCoq_2eInit_2eByte_2ex06
| VX21102 = cCoq_2eInit_2eByte_2ex07
| VX21102 = cCoq_2eInit_2eByte_2ex08
| VX21102 = cCoq_2eInit_2eByte_2ex09
| VX21102 = cCoq_2eInit_2eByte_2ex0a
| VX21102 = cCoq_2eInit_2eByte_2ex0b
| VX21102 = cCoq_2eInit_2eByte_2ex0c
| VX21102 = cCoq_2eInit_2eByte_2ex0d
| VX21102 = cCoq_2eInit_2eByte_2ex0e
| VX21102 = cCoq_2eInit_2eByte_2ex0f
| VX21102 = cCoq_2eInit_2eByte_2ex10
| VX21102 = cCoq_2eInit_2eByte_2ex11
| VX21102 = cCoq_2eInit_2eByte_2ex12
| VX21102 = cCoq_2eInit_2eByte_2ex13
| VX21102 = cCoq_2eInit_2eByte_2ex14
| VX21102 = cCoq_2eInit_2eByte_2ex15
| VX21102 = cCoq_2eInit_2eByte_2ex16
| VX21102 = cCoq_2eInit_2eByte_2ex17
| VX21102 = cCoq_2eInit_2eByte_2ex18
| VX21102 = cCoq_2eInit_2eByte_2ex19
| VX21102 = cCoq_2eInit_2eByte_2ex1a
| VX21102 = cCoq_2eInit_2eByte_2ex1b
| VX21102 = cCoq_2eInit_2eByte_2ex1c
| VX21102 = cCoq_2eInit_2eByte_2ex1d
| VX21102 = cCoq_2eInit_2eByte_2ex1e
| VX21102 = cCoq_2eInit_2eByte_2ex1f
| VX21102 = cCoq_2eInit_2eByte_2ex20
| VX21102 = cCoq_2eInit_2eByte_2ex21
| VX21102 = cCoq_2eInit_2eByte_2ex22
| VX21102 = cCoq_2eInit_2eByte_2ex23
| VX21102 = cCoq_2eInit_2eByte_2ex24
| VX21102 = cCoq_2eInit_2eByte_2ex25
| VX21102 = cCoq_2eInit_2eByte_2ex26
| VX21102 = cCoq_2eInit_2eByte_2ex27
| VX21102 = cCoq_2eInit_2eByte_2ex28
| VX21102 = cCoq_2eInit_2eByte_2ex29
| VX21102 = cCoq_2eInit_2eByte_2ex2a
| VX21102 = cCoq_2eInit_2eByte_2ex2b
| VX21102 = cCoq_2eInit_2eByte_2ex2c
| VX21102 = cCoq_2eInit_2eByte_2ex2d
| VX21102 = cCoq_2eInit_2eByte_2ex2e
| VX21102 = cCoq_2eInit_2eByte_2ex2f
| VX21102 = cCoq_2eInit_2eByte_2ex30
| VX21102 = cCoq_2eInit_2eByte_2ex31
| VX21102 = cCoq_2eInit_2eByte_2ex32
| VX21102 = cCoq_2eInit_2eByte_2ex33
| VX21102 = cCoq_2eInit_2eByte_2ex34
| VX21102 = cCoq_2eInit_2eByte_2ex35
| VX21102 = cCoq_2eInit_2eByte_2ex36
| VX21102 = cCoq_2eInit_2eByte_2ex37
| VX21102 = cCoq_2eInit_2eByte_2ex38
| VX21102 = cCoq_2eInit_2eByte_2ex39
| VX21102 = cCoq_2eInit_2eByte_2ex3a
| VX21102 = cCoq_2eInit_2eByte_2ex3b
| VX21102 = cCoq_2eInit_2eByte_2ex3c
| VX21102 = cCoq_2eInit_2eByte_2ex3d
| VX21102 = cCoq_2eInit_2eByte_2ex3e
| VX21102 = cCoq_2eInit_2eByte_2ex3f
| VX21102 = cCoq_2eInit_2eByte_2ex40
| VX21102 = cCoq_2eInit_2eByte_2ex41
| VX21102 = cCoq_2eInit_2eByte_2ex42
| VX21102 = cCoq_2eInit_2eByte_2ex43
| VX21102 = cCoq_2eInit_2eByte_2ex44
| VX21102 = cCoq_2eInit_2eByte_2ex45
| VX21102 = cCoq_2eInit_2eByte_2ex46
| VX21102 = cCoq_2eInit_2eByte_2ex47
| VX21102 = cCoq_2eInit_2eByte_2ex48
| VX21102 = cCoq_2eInit_2eByte_2ex49
| VX21102 = cCoq_2eInit_2eByte_2ex4a
| VX21102 = cCoq_2eInit_2eByte_2ex4b
| VX21102 = cCoq_2eInit_2eByte_2ex4c
| VX21102 = cCoq_2eInit_2eByte_2ex4d
| VX21102 = cCoq_2eInit_2eByte_2ex4e
| VX21102 = cCoq_2eInit_2eByte_2ex4f
| VX21102 = cCoq_2eInit_2eByte_2ex50
| VX21102 = cCoq_2eInit_2eByte_2ex51
| VX21102 = cCoq_2eInit_2eByte_2ex52
| VX21102 = cCoq_2eInit_2eByte_2ex53
| VX21102 = cCoq_2eInit_2eByte_2ex54
| VX21102 = cCoq_2eInit_2eByte_2ex55
| VX21102 = cCoq_2eInit_2eByte_2ex56
| VX21102 = cCoq_2eInit_2eByte_2ex57
| VX21102 = cCoq_2eInit_2eByte_2ex58
| VX21102 = cCoq_2eInit_2eByte_2ex59
| VX21102 = cCoq_2eInit_2eByte_2ex5a
| VX21102 = cCoq_2eInit_2eByte_2ex5b
| VX21102 = cCoq_2eInit_2eByte_2ex5c
| VX21102 = cCoq_2eInit_2eByte_2ex5d
| VX21102 = cCoq_2eInit_2eByte_2ex5e
| VX21102 = cCoq_2eInit_2eByte_2ex5f
| VX21102 = cCoq_2eInit_2eByte_2ex60
| VX21102 = cCoq_2eInit_2eByte_2ex61
| VX21102 = cCoq_2eInit_2eByte_2ex62
| VX21102 = cCoq_2eInit_2eByte_2ex63
| VX21102 = cCoq_2eInit_2eByte_2ex64
| VX21102 = cCoq_2eInit_2eByte_2ex65
| VX21102 = cCoq_2eInit_2eByte_2ex66
| VX21102 = cCoq_2eInit_2eByte_2ex67
| VX21102 = cCoq_2eInit_2eByte_2ex68
| VX21102 = cCoq_2eInit_2eByte_2ex69
| VX21102 = cCoq_2eInit_2eByte_2ex6a
| VX21102 = cCoq_2eInit_2eByte_2ex6b
| VX21102 = cCoq_2eInit_2eByte_2ex6c
| VX21102 = cCoq_2eInit_2eByte_2ex6d
| VX21102 = cCoq_2eInit_2eByte_2ex6e
| VX21102 = cCoq_2eInit_2eByte_2ex6f
| VX21102 = cCoq_2eInit_2eByte_2ex70
| VX21102 = cCoq_2eInit_2eByte_2ex71
| VX21102 = cCoq_2eInit_2eByte_2ex72
| VX21102 = cCoq_2eInit_2eByte_2ex73
| VX21102 = cCoq_2eInit_2eByte_2ex74
| VX21102 = cCoq_2eInit_2eByte_2ex75
| VX21102 = cCoq_2eInit_2eByte_2ex76
| VX21102 = cCoq_2eInit_2eByte_2ex77
| VX21102 = cCoq_2eInit_2eByte_2ex78
| VX21102 = cCoq_2eInit_2eByte_2ex79
| VX21102 = cCoq_2eInit_2eByte_2ex7a
| VX21102 = cCoq_2eInit_2eByte_2ex7b
| VX21102 = cCoq_2eInit_2eByte_2ex7c
| VX21102 = cCoq_2eInit_2eByte_2ex7d
| VX21102 = cCoq_2eInit_2eByte_2ex7e
| VX21102 = cCoq_2eInit_2eByte_2ex7f
| VX21102 = cCoq_2eInit_2eByte_2ex80
| VX21102 = cCoq_2eInit_2eByte_2ex81
| VX21102 = cCoq_2eInit_2eByte_2ex82
| VX21102 = cCoq_2eInit_2eByte_2ex83
| VX21102 = cCoq_2eInit_2eByte_2ex84
| VX21102 = cCoq_2eInit_2eByte_2ex85
| VX21102 = cCoq_2eInit_2eByte_2ex86
| VX21102 = cCoq_2eInit_2eByte_2ex87
| VX21102 = cCoq_2eInit_2eByte_2ex88
| VX21102 = cCoq_2eInit_2eByte_2ex89
| VX21102 = cCoq_2eInit_2eByte_2ex8a
| VX21102 = cCoq_2eInit_2eByte_2ex8b
| VX21102 = cCoq_2eInit_2eByte_2ex8c
| VX21102 = cCoq_2eInit_2eByte_2ex8d
| VX21102 = cCoq_2eInit_2eByte_2ex8e
| VX21102 = cCoq_2eInit_2eByte_2ex8f
| VX21102 = cCoq_2eInit_2eByte_2ex90
| VX21102 = cCoq_2eInit_2eByte_2ex91
| VX21102 = cCoq_2eInit_2eByte_2ex92
| VX21102 = cCoq_2eInit_2eByte_2ex93
| VX21102 = cCoq_2eInit_2eByte_2ex94
| VX21102 = cCoq_2eInit_2eByte_2ex95
| VX21102 = cCoq_2eInit_2eByte_2ex96
| VX21102 = cCoq_2eInit_2eByte_2ex97
| VX21102 = cCoq_2eInit_2eByte_2ex98
| VX21102 = cCoq_2eInit_2eByte_2ex99
| VX21102 = cCoq_2eInit_2eByte_2ex9a
| VX21102 = cCoq_2eInit_2eByte_2ex9b
| VX21102 = cCoq_2eInit_2eByte_2ex9c
| VX21102 = cCoq_2eInit_2eByte_2ex9d
| VX21102 = cCoq_2eInit_2eByte_2ex9e
| VX21102 = cCoq_2eInit_2eByte_2ex9f
| VX21102 = cCoq_2eInit_2eByte_2exa0
| VX21102 = cCoq_2eInit_2eByte_2exa1
| VX21102 = cCoq_2eInit_2eByte_2exa2
| VX21102 = cCoq_2eInit_2eByte_2exa3
| VX21102 = cCoq_2eInit_2eByte_2exa4
| VX21102 = cCoq_2eInit_2eByte_2exa5
| VX21102 = cCoq_2eInit_2eByte_2exa6
| VX21102 = cCoq_2eInit_2eByte_2exa7
| VX21102 = cCoq_2eInit_2eByte_2exa8
| VX21102 = cCoq_2eInit_2eByte_2exa9
| VX21102 = cCoq_2eInit_2eByte_2exaa
| VX21102 = cCoq_2eInit_2eByte_2exab
| VX21102 = cCoq_2eInit_2eByte_2exac
| VX21102 = cCoq_2eInit_2eByte_2exad
| VX21102 = cCoq_2eInit_2eByte_2exae
| VX21102 = cCoq_2eInit_2eByte_2exaf
| VX21102 = cCoq_2eInit_2eByte_2exb0
| VX21102 = cCoq_2eInit_2eByte_2exb1
| VX21102 = cCoq_2eInit_2eByte_2exb2
| VX21102 = cCoq_2eInit_2eByte_2exb3
| VX21102 = cCoq_2eInit_2eByte_2exb4
| VX21102 = cCoq_2eInit_2eByte_2exb5
| VX21102 = cCoq_2eInit_2eByte_2exb6
| VX21102 = cCoq_2eInit_2eByte_2exb7
| VX21102 = cCoq_2eInit_2eByte_2exb8
| VX21102 = cCoq_2eInit_2eByte_2exb9
| VX21102 = cCoq_2eInit_2eByte_2exba
| VX21102 = cCoq_2eInit_2eByte_2exbb
| VX21102 = cCoq_2eInit_2eByte_2exbc
| VX21102 = cCoq_2eInit_2eByte_2exbd
| VX21102 = cCoq_2eInit_2eByte_2exbe
| VX21102 = cCoq_2eInit_2eByte_2exbf
| VX21102 = cCoq_2eInit_2eByte_2exc0
| VX21102 = cCoq_2eInit_2eByte_2exc1
| VX21102 = cCoq_2eInit_2eByte_2exc2
| VX21102 = cCoq_2eInit_2eByte_2exc3
| VX21102 = cCoq_2eInit_2eByte_2exc4
| VX21102 = cCoq_2eInit_2eByte_2exc5
| VX21102 = cCoq_2eInit_2eByte_2exc6
| VX21102 = cCoq_2eInit_2eByte_2exc7
| VX21102 = cCoq_2eInit_2eByte_2exc8
| VX21102 = cCoq_2eInit_2eByte_2exc9
| VX21102 = cCoq_2eInit_2eByte_2exca
| VX21102 = cCoq_2eInit_2eByte_2excb
| VX21102 = cCoq_2eInit_2eByte_2excc
| VX21102 = cCoq_2eInit_2eByte_2excd
| VX21102 = cCoq_2eInit_2eByte_2exce
| VX21102 = cCoq_2eInit_2eByte_2excf
| VX21102 = cCoq_2eInit_2eByte_2exd0
| VX21102 = cCoq_2eInit_2eByte_2exd1
| VX21102 = cCoq_2eInit_2eByte_2exd2
| VX21102 = cCoq_2eInit_2eByte_2exd3
| VX21102 = cCoq_2eInit_2eByte_2exd4
| VX21102 = cCoq_2eInit_2eByte_2exd5
| VX21102 = cCoq_2eInit_2eByte_2exd6
| VX21102 = cCoq_2eInit_2eByte_2exd7
| VX21102 = cCoq_2eInit_2eByte_2exd8
| VX21102 = cCoq_2eInit_2eByte_2exd9
| VX21102 = cCoq_2eInit_2eByte_2exda
| VX21102 = cCoq_2eInit_2eByte_2exdb
| VX21102 = cCoq_2eInit_2eByte_2exdc
| VX21102 = cCoq_2eInit_2eByte_2exdd
| VX21102 = cCoq_2eInit_2eByte_2exde
| VX21102 = cCoq_2eInit_2eByte_2exdf
| VX21102 = cCoq_2eInit_2eByte_2exe0
| VX21102 = cCoq_2eInit_2eByte_2exe1
| VX21102 = cCoq_2eInit_2eByte_2exe2
| VX21102 = cCoq_2eInit_2eByte_2exe3
| VX21102 = cCoq_2eInit_2eByte_2exe4
| VX21102 = cCoq_2eInit_2eByte_2exe5
| VX21102 = cCoq_2eInit_2eByte_2exe6
| VX21102 = cCoq_2eInit_2eByte_2exe7
| VX21102 = cCoq_2eInit_2eByte_2exe8
| VX21102 = cCoq_2eInit_2eByte_2exe9
| VX21102 = cCoq_2eInit_2eByte_2exea
| VX21102 = cCoq_2eInit_2eByte_2exeb
| VX21102 = cCoq_2eInit_2eByte_2exec
| VX21102 = cCoq_2eInit_2eByte_2exed
| VX21102 = cCoq_2eInit_2eByte_2exee
| VX21102 = cCoq_2eInit_2eByte_2exef
| VX21102 = cCoq_2eInit_2eByte_2exf0
| VX21102 = cCoq_2eInit_2eByte_2exf1
| VX21102 = cCoq_2eInit_2eByte_2exf2
| VX21102 = cCoq_2eInit_2eByte_2exf3
| VX21102 = cCoq_2eInit_2eByte_2exf4
| VX21102 = cCoq_2eInit_2eByte_2exf5
| VX21102 = cCoq_2eInit_2eByte_2exf6
| VX21102 = cCoq_2eInit_2eByte_2exf7
| VX21102 = cCoq_2eInit_2eByte_2exf8
| VX21102 = cCoq_2eInit_2eByte_2exf9
| VX21102 = cCoq_2eInit_2eByte_2exfa
| VX21102 = cCoq_2eInit_2eByte_2exfb
| VX21102 = cCoq_2eInit_2eByte_2exfc
| VX21102 = cCoq_2eInit_2eByte_2exfd
| VX21102 = cCoq_2eInit_2eByte_2exfe
| VX21102 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__21104,Vvar__1__Q__21105,Vvar__2___24Anonymous__21106] :
( cProp___24t(Vvar__0__P__21104)
=> ( cProp___24t(Vvar__1__Q__21105)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__21106)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__21104,Vvar__1__Q__21105,Vvar__2___24Anonymous__21106)
=> ( ( p(Vvar__0__P__21104)
& Vvar__2___24Anonymous__21106 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__21105)
& Vvar__2___24Anonymous__21106 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__1359,Vvar__1__Plt__1360,Vvar__2__Pgt__1361,Vvar__3___24Anonymous__1362] :
( cProp___24t(Vvar__0__Peq__1359)
=> ( cProp___24t(Vvar__1__Plt__1360)
=> ( cProp___24t(Vvar__2__Pgt__1361)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__1362)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__1359,Vvar__1__Plt__1360,Vvar__2__Pgt__1361,Vvar__3___24Anonymous__1362)
=> ( ( p(Vvar__0__Peq__1359)
& Vvar__3___24Anonymous__1362 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__1360)
& Vvar__3___24Anonymous__1362 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__1361)
& Vvar__3___24Anonymous__1362 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1339] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1339)
=> ( VX1339 = cCoq_2eInit_2eDatatypes_2etrue
| VX1339 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX44] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX44)
=> ( VX44 = cCoq_2eInit_2eDatatypes_2eEq
| VX44 = cCoq_2eInit_2eDatatypes_2eLt
| VX44 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__14,VX15] :
( cType___24t(Vvar__0__A__14)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14,VX15)
=> ( VX15 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__14)
| ? [Vvar__1___24Anonymous__18] :
( t(Vvar__1___24Anonymous__18,Vvar__0__A__14)
& ? [Vvar__2___24Anonymous__19] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__14,Vvar__2___24Anonymous__19)
& VX15 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__14,Vvar__1___24Anonymous__18,Vvar__2___24Anonymous__19) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX3)
=> ( VX3 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4)
& VX3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__7269,VX7270] :
( cType___24t(Vvar__0__A__7269)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__7269,VX7270)
=> ( ? [Vvar__1___24Anonymous__7272] :
( t(Vvar__1___24Anonymous__7272,Vvar__0__A__7269)
& VX7270 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7269,Vvar__1___24Anonymous__7272) )
| VX7270 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7269) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__7288,Vvar__1__B__7289,VX7290] :
( cType___24t(Vvar__0__A__7288)
=> ( cType___24t(Vvar__1__B__7289)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__7288,Vvar__1__B__7289,VX7290)
=> ? [Vvar__2___24Anonymous__7293] :
( t(Vvar__2___24Anonymous__7293,Vvar__0__A__7288)
& ? [Vvar__3___24Anonymous__7294] :
( t(Vvar__3___24Anonymous__7294,Vvar__1__B__7289)
& VX7290 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7288,Vvar__1__B__7289,Vvar__2___24Anonymous__7293,Vvar__3___24Anonymous__7294) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__21114,Vvar__1__B__21115,VX21116] :
( cType___24t(Vvar__0__A__21114)
=> ( cType___24t(Vvar__1__B__21115)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__21114,Vvar__1__B__21115,VX21116)
=> ( ? [Vvar__2___24Anonymous__21119] :
( t(Vvar__2___24Anonymous__21119,Vvar__0__A__21114)
& VX21116 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21114,Vvar__1__B__21115,Vvar__2___24Anonymous__21119) )
| ? [Vvar__2___24Anonymous__21122] :
( t(Vvar__2___24Anonymous__21122,Vvar__1__B__21115)
& VX21116 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21114,Vvar__1__B__21115,Vvar__2___24Anonymous__21122) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX7264] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX7264)
=> VX7264 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX59709] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX59709)
=> ( ? [Vvar__0__d__59710] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__59710)
& VX59709 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__59710) )
| ? [Vvar__0__d__59711] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__59711)
& VX59709 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__59711) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX59578] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX59578)
=> ( VX59578 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__59579] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59579)
& VX59578 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__59579) )
| ? [Vvar__0___24Anonymous__59580] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59580)
& VX59578 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__59580) )
| ? [Vvar__0___24Anonymous__59581] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59581)
& VX59578 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__59581) )
| ? [Vvar__0___24Anonymous__59582] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59582)
& VX59578 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__59582) )
| ? [Vvar__0___24Anonymous__59583] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59583)
& VX59578 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__59583) )
| ? [Vvar__0___24Anonymous__59584] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59584)
& VX59578 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__59584) )
| ? [Vvar__0___24Anonymous__59585] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59585)
& VX59578 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__59585) )
| ? [Vvar__0___24Anonymous__59586] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59586)
& VX59578 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__59586) )
| ? [Vvar__0___24Anonymous__59587] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59587)
& VX59578 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__59587) )
| ? [Vvar__0___24Anonymous__59588] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__59588)
& VX59578 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__59588) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__293,Vvar__1___24Anonymous__294] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__293)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__294)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__293,Vvar__1___24Anonymous__294))
=> ( Vvar__1___24Anonymous__294 = Vvar__0__n__293
| ? [Vvar__1__m__298] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__298)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__293,Vvar__1__m__298))
& Vvar__1___24Anonymous__294 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__298) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__2160,Vvar__1__P__2161,VX2164] :
( cType___24t(Vvar__0__A__2160)
=> ( c_24__type__2174___24t(Vvar__0__A__2160,Vvar__1__P__2161,Vvar__1__P__2161)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__2160,Vvar__1__P__2161,VX2164)
=> ? [Vvar__2__x__2169] :
( t(Vvar__2__x__2169,Vvar__0__A__2160)
& p(happ(Vvar__1__P__2161,Vvar__2__x__2169))
& VX2164 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__2160,Vvar__1__P__2161,Vvar__2__x__2169) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__35053,Vvar__1__P__35054,VX35057] :
( cType___24t(Vvar__0__A__35053)
=> ( c_24__type__35067___24t(Vvar__0__A__35053,Vvar__1__P__35054,Vvar__1__P__35054)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__35053,Vvar__1__P__35054,VX35057)
=> ? [Vvar__2__x__35062] :
( t(Vvar__2__x__35062,Vvar__0__A__35053)
& ? [Vvar__3___24Anonymous__35063] :
( t(Vvar__3___24Anonymous__35063,happ(Vvar__1__P__35054,Vvar__2__x__35062))
& VX35057 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__35053,Vvar__1__P__35054,Vvar__2__x__35062,Vvar__3___24Anonymous__35063) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__2224,Vvar__1__B__2225,VX2226] :
( cProp___24t(Vvar__0__A__2224)
=> ( cProp___24t(Vvar__1__B__2225)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__2224,Vvar__1__B__2225,VX2226)
=> ( ( p(Vvar__0__A__2224)
& VX2226 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2224,Vvar__1__B__2225) )
| ( p(Vvar__1__B__2225)
& VX2226 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2224,Vvar__1__B__2225) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__2264,Vvar__1__B__2265,VX2266] :
( cType___24t(Vvar__0__A__2264)
=> ( cProp___24t(Vvar__1__B__2265)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__2264,Vvar__1__B__2265,VX2266)
=> ( ? [Vvar__2___24Anonymous__2269] :
( t(Vvar__2___24Anonymous__2269,Vvar__0__A__2264)
& VX2266 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__2264,Vvar__1__B__2265,Vvar__2___24Anonymous__2269) )
| ( p(Vvar__1__B__2265)
& VX2266 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__2264,Vvar__1__B__2265) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__9421,Vvar__1__R__9422,Vvar__2__x__9427] :
( cType___24t(Vvar__0__A__9421)
=> ( c_24__type__9456___24t(Vvar__0__A__9421,Vvar__1__R__9422,Vvar__2__x__9427,Vvar__1__R__9422)
=> ( t(Vvar__2__x__9427,Vvar__0__A__9421)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__9421,Vvar__1__R__9422,Vvar__2__x__9427)
=> ( ! [Vvar__var__var__var__var__3__y__9437__9439__9441__9443__9445] :
( t(Vvar__var__var__var__var__3__y__9437__9439__9441__9443__9445,Vvar__0__A__9421)
=> ( p(happ(happ(Vvar__1__R__9422,Vvar__var__var__var__var__3__y__9437__9439__9441__9443__9445),Vvar__2__x__9427))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__9421,Vvar__1__R__9422,Vvar__var__var__var__var__3__y__9437__9439__9441__9443__9445) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__8093,Vvar__1__a__8094,Vvar__2___24Anonymous__8095,Vvar__3___24Anonymous__8096] :
( cType___24t(Vvar__0__A__8093)
=> ( t(Vvar__1__a__8094,Vvar__0__A__8093)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8093,Vvar__2___24Anonymous__8095)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8093,Vvar__3___24Anonymous__8096)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8093,Vvar__1__a__8094,Vvar__2___24Anonymous__8095,Vvar__3___24Anonymous__8096)
=> ( ? [Vvar__2__l__8100] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8093,Vvar__2__l__8100)
& Vvar__3___24Anonymous__8096 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8093,Vvar__1__a__8094,Vvar__2__l__8100)
& Vvar__2___24Anonymous__8095 = Vvar__2__l__8100 )
| ? [Vvar__2__x__8103] :
( t(Vvar__2__x__8103,Vvar__0__A__8093)
& ? [Vvar__3__l__8104] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8093,Vvar__3__l__8104)
& ? [Vvar__4__l_27__8105] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8093,Vvar__4__l_27__8105)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8093,Vvar__1__a__8094,Vvar__3__l__8104,Vvar__4__l_27__8105)
& Vvar__3___24Anonymous__8096 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8093,Vvar__2__x__8103,Vvar__4__l_27__8105)
& Vvar__2___24Anonymous__8095 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8093,Vvar__2__x__8103,Vvar__3__l__8104) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__22670,Vvar__1__P__22671,Vvar__2___24Anonymous__22674] :
( cType___24t(Vvar__0__A__22670)
=> ( c_24__type__22694___24t(Vvar__0__A__22670,Vvar__1__P__22671,Vvar__2___24Anonymous__22674,Vvar__1__P__22671)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22670,Vvar__2___24Anonymous__22674)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__22670,Vvar__1__P__22671,Vvar__2___24Anonymous__22674)
=> ( ? [Vvar__2__x__22680] :
( t(Vvar__2__x__22680,Vvar__0__A__22670)
& ? [Vvar__3__l__22681] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22670,Vvar__3__l__22681)
& p(happ(Vvar__1__P__22671,Vvar__2__x__22680))
& Vvar__2___24Anonymous__22674 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22670,Vvar__2__x__22680,Vvar__3__l__22681) ) )
| ? [Vvar__2__x__22687] :
( t(Vvar__2__x__22687,Vvar__0__A__22670)
& ? [Vvar__3__l__22688] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22670,Vvar__3__l__22688)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__22670,Vvar__1__P__22671,Vvar__3__l__22688)
& Vvar__2___24Anonymous__22674 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22670,Vvar__2__x__22687,Vvar__3__l__22688) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__22696,Vvar__1__P__22697,Vvar__2___24Anonymous__22700] :
( cType___24t(Vvar__0__A__22696)
=> ( c_24__type__22718___24t(Vvar__0__A__22696,Vvar__1__P__22697,Vvar__2___24Anonymous__22700,Vvar__1__P__22697)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22696,Vvar__2___24Anonymous__22700)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__22696,Vvar__1__P__22697,Vvar__2___24Anonymous__22700)
=> ( Vvar__2___24Anonymous__22700 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22696)
| ? [Vvar__2__x__22710] :
( t(Vvar__2__x__22710,Vvar__0__A__22696)
& ? [Vvar__3__l__22711] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22696,Vvar__3__l__22711)
& p(happ(Vvar__1__P__22697,Vvar__2__x__22710))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__22696,Vvar__1__P__22697,Vvar__3__l__22711)
& Vvar__2___24Anonymous__22700 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22696,Vvar__2__x__22710,Vvar__3__l__22711) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__22720,Vvar__1__B__22721,Vvar__2__R__22722,Vvar__3___24Anonymous__22727,Vvar__4___24Anonymous__22728] :
( cType___24t(Vvar__0__A__22720)
=> ( cType___24t(Vvar__1__B__22721)
=> ( c_24__type__22765___24t(Vvar__0__A__22720,Vvar__1__B__22721,Vvar__2__R__22722,Vvar__3___24Anonymous__22727,Vvar__4___24Anonymous__22728,Vvar__2__R__22722)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22720,Vvar__3___24Anonymous__22727)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__22721,Vvar__4___24Anonymous__22728)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__22720,Vvar__1__B__22721,Vvar__2__R__22722,Vvar__3___24Anonymous__22727,Vvar__4___24Anonymous__22728)
=> ( ( Vvar__4___24Anonymous__22728 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__22721)
& Vvar__3___24Anonymous__22727 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22720) )
| ? [Vvar__3__x__22744] :
( t(Vvar__3__x__22744,Vvar__0__A__22720)
& ? [Vvar__4__y__22745] :
( t(Vvar__4__y__22745,Vvar__1__B__22721)
& ? [Vvar__5__l__22746] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22720,Vvar__5__l__22746)
& ? [Vvar__6__l_27__22747] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__22721,Vvar__6__l_27__22747)
& p(happ(happ(Vvar__2__R__22722,Vvar__3__x__22744),Vvar__4__y__22745))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__22720,Vvar__1__B__22721,Vvar__2__R__22722,Vvar__5__l__22746,Vvar__6__l_27__22747)
& Vvar__4___24Anonymous__22728 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__22721,Vvar__4__y__22745,Vvar__6__l_27__22747)
& Vvar__3___24Anonymous__22727 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22720,Vvar__3__x__22744,Vvar__5__l__22746) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__22767,Vvar__1__R__22768,Vvar__2___24Anonymous__22773] :
( cType___24t(Vvar__0__A__22767)
=> ( c_24__type__22800___24t(Vvar__0__A__22767,Vvar__1__R__22768,Vvar__2___24Anonymous__22773,Vvar__1__R__22768)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22767,Vvar__2___24Anonymous__22773)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__22767,Vvar__1__R__22768,Vvar__2___24Anonymous__22773)
=> ( Vvar__2___24Anonymous__22773 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22767)
| ? [Vvar__2__a__22787] :
( t(Vvar__2__a__22787,Vvar__0__A__22767)
& ? [Vvar__3__l__22788] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22767,Vvar__3__l__22788)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__22767,happ(Vvar__1__R__22768,Vvar__2__a__22787),Vvar__3__l__22788)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__22767,Vvar__1__R__22768,Vvar__3__l__22788)
& Vvar__2___24Anonymous__22773 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22767,Vvar__2__a__22787,Vvar__3__l__22788) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__8118,Vvar__1___24Anonymous__8119] :
( cType___24t(Vvar__0__A__8118)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8118,Vvar__1___24Anonymous__8119)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8118,Vvar__1___24Anonymous__8119)
=> ( Vvar__1___24Anonymous__8119 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8118)
| ? [Vvar__1__x__8123] :
( t(Vvar__1__x__8123,Vvar__0__A__8118)
& ? [Vvar__2__l__8124] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8118,Vvar__2__l__8124)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__8118,Vvar__1__x__8123,Vvar__2__l__8124)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8118,Vvar__2__l__8124)
& Vvar__1___24Anonymous__8119 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8118,Vvar__1__x__8123,Vvar__2__l__8124) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__9202,Vvar__1__eqA__9203,Vvar__2__x__9208,Vvar__3___24Anonymous__9209] :
( cType___24t(Vvar__0__A__9202)
=> ( c_24__type__9242___24t(Vvar__0__A__9202,Vvar__1__eqA__9203,Vvar__2__x__9208,Vvar__3___24Anonymous__9209,Vvar__1__eqA__9203)
=> ( t(Vvar__2__x__9208,Vvar__0__A__9202)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9202,Vvar__3___24Anonymous__9209)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__9202,Vvar__1__eqA__9203,Vvar__2__x__9208,Vvar__3___24Anonymous__9209)
=> ( ? [Vvar__3__y__9218] :
( t(Vvar__3__y__9218,Vvar__0__A__9202)
& ? [Vvar__4__l__9219] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9202,Vvar__4__l__9219)
& p(happ(happ(Vvar__1__eqA__9203,Vvar__2__x__9208),Vvar__3__y__9218))
& Vvar__3___24Anonymous__9209 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9202,Vvar__3__y__9218,Vvar__4__l__9219) ) )
| ? [Vvar__3__y__9228] :
( t(Vvar__3__y__9228,Vvar__0__A__9202)
& ? [Vvar__4__l__9229] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9202,Vvar__4__l__9229)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__9202,Vvar__1__eqA__9203,Vvar__2__x__9208,Vvar__4__l__9229)
& Vvar__3___24Anonymous__9209 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9202,Vvar__3__y__9228,Vvar__4__l__9229) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__9244,Vvar__1__eqA__9245,Vvar__2___24Anonymous__9250] :
( cType___24t(Vvar__0__A__9244)
=> ( c_24__type__9277___24t(Vvar__0__A__9244,Vvar__1__eqA__9245,Vvar__2___24Anonymous__9250,Vvar__1__eqA__9245)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9244,Vvar__2___24Anonymous__9250)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__9244,Vvar__1__eqA__9245,Vvar__2___24Anonymous__9250)
=> ( Vvar__2___24Anonymous__9250 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9244)
| ? [Vvar__2__x__9264] :
( t(Vvar__2__x__9264,Vvar__0__A__9244)
& ? [Vvar__3__l__9265] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9244,Vvar__3__l__9265)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__9244,Vvar__1__eqA__9245,Vvar__2__x__9264,Vvar__3__l__9265)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__9244,Vvar__1__eqA__9245,Vvar__3__l__9265)
& Vvar__2___24Anonymous__9250 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9244,Vvar__2__x__9264,Vvar__3__l__9265) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__9279,Vvar__1__eqA__9280,Vvar__2___24Anonymous__9285,Vvar__3___24Anonymous__9286] :
( cType___24t(Vvar__0__A__9279)
=> ( c_24__type__9317___24t(Vvar__0__A__9279,Vvar__1__eqA__9280,Vvar__2___24Anonymous__9285,Vvar__3___24Anonymous__9286,Vvar__1__eqA__9280)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9279,Vvar__2___24Anonymous__9285)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9279,Vvar__3___24Anonymous__9286)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__9279,Vvar__1__eqA__9280,Vvar__2___24Anonymous__9285,Vvar__3___24Anonymous__9286)
=> ( ( Vvar__3___24Anonymous__9286 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9279)
& Vvar__2___24Anonymous__9285 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9279) )
| ? [Vvar__2__x__9300] :
( t(Vvar__2__x__9300,Vvar__0__A__9279)
& ? [Vvar__3__x_27__9301] :
( t(Vvar__3__x_27__9301,Vvar__0__A__9279)
& ? [Vvar__4__l__9302] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9279,Vvar__4__l__9302)
& ? [Vvar__5__l_27__9303] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9279,Vvar__5__l_27__9303)
& p(happ(happ(Vvar__1__eqA__9280,Vvar__2__x__9300),Vvar__3__x_27__9301))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__9279,Vvar__1__eqA__9280,Vvar__4__l__9302,Vvar__5__l_27__9303)
& Vvar__3___24Anonymous__9286 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9279,Vvar__3__x_27__9301,Vvar__5__l_27__9303)
& Vvar__2___24Anonymous__9285 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9279,Vvar__2__x__9300,Vvar__4__l__9302) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1323] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1323)
=> ( VX1323 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1324] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1324)
& VX1323 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1324) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1328] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1328)
=> ( VX1328 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1329)
& VX1328 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1329) )
| ? [Vvar__0___24Anonymous__1330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1330)
& VX1328 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1330) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1312)
=> ( ? [Vvar__0___24Anonymous__1313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1313)
& VX1312 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1313) )
| ? [Vvar__0___24Anonymous__1314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1314)
& VX1312 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1314) )
| VX1312 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX8246] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX8246)
=> ? [Vvar__0__Qnum__8247] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__8247)
& ? [Vvar__1__Qden__8248] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__8248)
& VX8246 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__8247,Vvar__1__Qden__8248) ) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__59756,Vvar__1___24Anonymous__59757,VX59758] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__59756)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__59757)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__59756,Vvar__1___24Anonymous__59757,VX59758)
=> ( ( Vvar__0__x__59756 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__59757 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX59758 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__59756) )
| ? [Vvar__1__n__59762] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__59762)
& Vvar__0__x__59756 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__59762)
& Vvar__1___24Anonymous__59757 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2459782___24a3(Vvar__0__x__59756,Vvar__1___24Anonymous__59757,Vvar__1__n__59762)
& VX59758 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__59756,Vvar__1__n__59762) )
| ? [Vvar__1__n__59767] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__59767)
& Vvar__0__x__59756 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__59767))
& Vvar__1___24Anonymous__59757 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799___24a3(Vvar__0__x__59756,Vvar__1___24Anonymous__59757,Vvar__1__n__59767)
& VX59758 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__59756,Vvar__1__n__59767) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__401,Vvar__1__R__402] :
( cType___24t(Vvar__0__A__401)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__401,Vvar__1__R__402)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__401,Vvar__1__R__402)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__401,Vvar__1__R__402)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__401,Vvar__1__R__402)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__24151,Vvar__1__leA__24152,Vvar__2___24Anonymous__24157] :
( cType___24t(Vvar__0__A__24151)
=> ( c_24__type__24247___24t(Vvar__0__A__24151,Vvar__1__leA__24152,Vvar__2___24Anonymous__24157,Vvar__1__leA__24152)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24151,Vvar__2___24Anonymous__24157)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__24151,Vvar__1__leA__24152,Vvar__2___24Anonymous__24157)
=> ( Vvar__2___24Anonymous__24157 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24151)
| ? [Vvar__2__x__24171] :
( t(Vvar__2__x__24171,Vvar__0__A__24151)
& Vvar__2___24Anonymous__24157 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24151,Vvar__2__x__24171,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24151)) )
| ? [Vvar__2__x__24178] :
( t(Vvar__2__x__24178,Vvar__0__A__24151)
& ? [Vvar__3__y__24179] :
( t(Vvar__3__y__24179,Vvar__0__A__24151)
& ? [Vvar__4__l__24180] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24151,Vvar__4__l__24180)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__24151,Vvar__1__leA__24152,Vvar__2__x__24178,Vvar__3__y__24179)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__24151,Vvar__1__leA__24152,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__24151,Vvar__4__l__24180,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24151,Vvar__3__y__24179,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24151))))
& Vvar__2___24Anonymous__24157 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2424445___24a6(Vvar__0__A__24151,Vvar__1__leA__24152,Vvar__2___24Anonymous__24157,Vvar__2__x__24178,Vvar__3__y__24179,Vvar__4__l__24180) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__24100,Vvar__1__leA__24101,Vvar__2___24Anonymous__24106,Vvar__3___24Anonymous__24107] :
( cType___24t(Vvar__0__A__24100)
=> ( c_24__type__24149___24t(Vvar__0__A__24100,Vvar__1__leA__24101,Vvar__2___24Anonymous__24106,Vvar__3___24Anonymous__24107,Vvar__1__leA__24101)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__2___24Anonymous__24106)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__3___24Anonymous__24107)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__24100,Vvar__1__leA__24101,Vvar__2___24Anonymous__24106,Vvar__3___24Anonymous__24107)
=> ( ? [Vvar__2__a__24115] :
( t(Vvar__2__a__24115,Vvar__0__A__24100)
& ? [Vvar__3__x__24116] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__3__x__24116)
& Vvar__3___24Anonymous__24107 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24100,Vvar__2__a__24115,Vvar__3__x__24116)
& Vvar__2___24Anonymous__24106 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24100) ) )
| ? [Vvar__2__a__24123] :
( t(Vvar__2__a__24123,Vvar__0__A__24100)
& ? [Vvar__3__b__24124] :
( t(Vvar__3__b__24124,Vvar__0__A__24100)
& p(happ(happ(Vvar__1__leA__24101,Vvar__2__a__24123),Vvar__3__b__24124))
& ? [Vvar__5__x__24126] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__5__x__24126)
& ? [Vvar__6__y__24127] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__6__y__24127)
& Vvar__3___24Anonymous__24107 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24100,Vvar__3__b__24124,Vvar__6__y__24127)
& Vvar__2___24Anonymous__24106 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24100,Vvar__2__a__24123,Vvar__5__x__24126) ) ) ) )
| ? [Vvar__2__a__24134] :
( t(Vvar__2__a__24134,Vvar__0__A__24100)
& ? [Vvar__3__x__24135] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__3__x__24135)
& ? [Vvar__4__y__24136] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24100,Vvar__4__y__24136)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__24100,Vvar__1__leA__24101,Vvar__3__x__24135,Vvar__4__y__24136)
& Vvar__3___24Anonymous__24107 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24100,Vvar__2__a__24134,Vvar__4__y__24136)
& Vvar__2___24Anonymous__24106 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24100,Vvar__2__a__24134,Vvar__3__x__24135) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__2136,Vvar__1___24Anonymous__2137,Vvar__2___24Anonymous__2138] :
( cType___24t(Vvar__0__A__2136)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__1___24Anonymous__2137)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__2___24Anonymous__2138)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2136,Vvar__1___24Anonymous__2137,Vvar__2___24Anonymous__2138)
=> ( ( Vvar__2___24Anonymous__2138 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2136)
& Vvar__1___24Anonymous__2137 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2136) )
| ? [Vvar__1__x__2142] :
( t(Vvar__1__x__2142,Vvar__0__A__2136)
& ? [Vvar__2__l__2143] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__2__l__2143)
& ? [Vvar__3__l_27__2144] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__3__l_27__2144)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2136,Vvar__2__l__2143,Vvar__3__l_27__2144)
& Vvar__2___24Anonymous__2138 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__1__x__2142,Vvar__3__l_27__2144)
& Vvar__1___24Anonymous__2137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__1__x__2142,Vvar__2__l__2143) ) ) )
| ? [Vvar__1__x__2147] :
( t(Vvar__1__x__2147,Vvar__0__A__2136)
& ? [Vvar__2__y__2148] :
( t(Vvar__2__y__2148,Vvar__0__A__2136)
& ? [Vvar__3__l__2149] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__3__l__2149)
& Vvar__2___24Anonymous__2138 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__1__x__2147,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__2__y__2148,Vvar__3__l__2149))
& Vvar__1___24Anonymous__2137 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__2__y__2148,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2136,Vvar__1__x__2147,Vvar__3__l__2149)) ) ) )
| ? [Vvar__1__l__2151] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__1__l__2151)
& ? [Vvar__2__l_27__2152] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__2__l_27__2152)
& ? [Vvar__3__l_27_27__2153] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2136,Vvar__3__l_27_27__2153)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2136,Vvar__1__l__2151,Vvar__2__l_27__2152)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__2136,Vvar__2__l_27__2152,Vvar__3__l_27_27__2153)
& Vvar__2___24Anonymous__2138 = Vvar__3__l_27_27__2153
& Vvar__1___24Anonymous__2137 = Vvar__1__l__2151 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__34944,Vvar__1__R__34945,Vvar__2__a__34950,Vvar__3___24Anonymous__34951] :
( cType___24t(Vvar__0__A__34944)
=> ( c_24__type__34981___24t(Vvar__0__A__34944,Vvar__1__R__34945,Vvar__2__a__34950,Vvar__3___24Anonymous__34951,Vvar__1__R__34945)
=> ( t(Vvar__2__a__34950,Vvar__0__A__34944)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34944,Vvar__3___24Anonymous__34951)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__34944,Vvar__1__R__34945,Vvar__2__a__34950,Vvar__3___24Anonymous__34951)
=> ( Vvar__3___24Anonymous__34951 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34944)
| ? [Vvar__3__b__34967] :
( t(Vvar__3__b__34967,Vvar__0__A__34944)
& ? [Vvar__4__l__34968] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34944,Vvar__4__l__34968)
& p(happ(happ(Vvar__1__R__34945,Vvar__2__a__34950),Vvar__3__b__34967))
& Vvar__3___24Anonymous__34951 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34944,Vvar__3__b__34967,Vvar__4__l__34968) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__34901,Vvar__1__R__34902,Vvar__2___24Anonymous__34907] :
( cType___24t(Vvar__0__A__34901)
=> ( c_24__type__34942___24t(Vvar__0__A__34901,Vvar__1__R__34902,Vvar__2___24Anonymous__34907,Vvar__1__R__34902)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34901,Vvar__2___24Anonymous__34907)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__34901,Vvar__1__R__34902,Vvar__2___24Anonymous__34907)
=> ( Vvar__2___24Anonymous__34907 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34901)
| ? [Vvar__2__a__34921] :
( t(Vvar__2__a__34921,Vvar__0__A__34901)
& Vvar__2___24Anonymous__34907 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34901,Vvar__2__a__34921,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34901)) )
| ? [Vvar__2__a__34928] :
( t(Vvar__2__a__34928,Vvar__0__A__34901)
& ? [Vvar__3__b__34929] :
( t(Vvar__3__b__34929,Vvar__0__A__34901)
& ? [Vvar__4__l__34930] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34901,Vvar__4__l__34930)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__34901,Vvar__1__R__34902,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34901,Vvar__3__b__34929,Vvar__4__l__34930))
& p(happ(happ(Vvar__1__R__34902,Vvar__2__a__34928),Vvar__3__b__34929))
& Vvar__2___24Anonymous__34907 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34901,Vvar__2__a__34928,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34901,Vvar__3__b__34929,Vvar__4__l__34930)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__34983,Vvar__1__R__34984,Vvar__2___24Anonymous__34989] :
( cType___24t(Vvar__0__A__34983)
=> ( c_24__type__35016___24t(Vvar__0__A__34983,Vvar__1__R__34984,Vvar__2___24Anonymous__34989,Vvar__1__R__34984)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34983,Vvar__2___24Anonymous__34989)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__34983,Vvar__1__R__34984,Vvar__2___24Anonymous__34989)
=> ( Vvar__2___24Anonymous__34989 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34983)
| ? [Vvar__2__a__35003] :
( t(Vvar__2__a__35003,Vvar__0__A__34983)
& ? [Vvar__3__l__35004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34983,Vvar__3__l__35004)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__34983,Vvar__1__R__34984,Vvar__3__l__35004)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__34983,Vvar__1__R__34984,Vvar__2__a__35003,Vvar__3__l__35004)
& Vvar__2___24Anonymous__34989 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34983,Vvar__2__a__35003,Vvar__3__l__35004) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__35018,Vvar__1__R__35019,Vvar__2___24Anonymous__35024] :
( cType___24t(Vvar__0__A__35018)
=> ( c_24__type__35051___24t(Vvar__0__A__35018,Vvar__1__R__35019,Vvar__2___24Anonymous__35024,Vvar__1__R__35019)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35018,Vvar__2___24Anonymous__35024)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__35018,Vvar__1__R__35019,Vvar__2___24Anonymous__35024)
=> ( Vvar__2___24Anonymous__35024 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35018)
| ? [Vvar__2__a__35038] :
( t(Vvar__2__a__35038,Vvar__0__A__35018)
& ? [Vvar__3__l__35039] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35018,Vvar__3__l__35039)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__35018,Vvar__1__R__35019,Vvar__3__l__35039)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__35018,happ(Vvar__1__R__35019,Vvar__2__a__35038),Vvar__3__l__35039)
& Vvar__2___24Anonymous__35024 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35018,Vvar__2__a__35038,Vvar__3__l__35039) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX1282] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX1282)
=> ? [Vvar__0___24Anonymous__1283] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__1283)
& ? [Vvar__1___24Anonymous__1284] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__1284)
& ? [Vvar__2___24Anonymous__1285] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__1285)
& ? [Vvar__3___24Anonymous__1286] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__1286)
& ? [Vvar__4___24Anonymous__1287] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__1287)
& ? [Vvar__5___24Anonymous__1288] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__1288)
& ? [Vvar__6___24Anonymous__1289] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__1289)
& ? [Vvar__7___24Anonymous__1290] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__1290)
& VX1282 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__1283,Vvar__1___24Anonymous__1284,Vvar__2___24Anonymous__1285,Vvar__3___24Anonymous__1286,Vvar__4___24Anonymous__1287,Vvar__5___24Anonymous__1288,Vvar__6___24Anonymous__1289,Vvar__7___24Anonymous__1290) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX2304] :
( cCoq_2eStrings_2eString_2estring___24t(VX2304)
=> ( VX2304 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__2305] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__2305)
& ? [Vvar__1___24Anonymous__2306] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__2306)
& VX2304 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__2305,Vvar__1___24Anonymous__2306) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860,VX1861] :
( cType___24t(Vvar__0__X__1848)
=> ( c_24__type__1921___24t(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860,Vvar__1__lt__1849)
=> ( c_24__type__1940___24t(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860,Vvar__2__eq__1854)
=> ( t(Vvar__3__x__1859,Vvar__0__X__1848)
=> ( t(Vvar__4__y__1860,Vvar__0__X__1848)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860,VX1861)
=> ( ( p(happ(happ(Vvar__1__lt__1849,Vvar__3__x__1859),Vvar__4__y__1860))
& VX1861 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860) )
| ( p(happ(happ(Vvar__2__eq__1854,Vvar__3__x__1859),Vvar__4__y__1860))
& VX1861 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860) )
| ( p(happ(happ(Vvar__1__lt__1849,Vvar__4__y__1860),Vvar__3__x__1859))
& VX1861 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__1848,Vvar__1__lt__1849,Vvar__2__eq__1854,Vvar__3__x__1859,Vvar__4__y__1860) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX8212] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX8212)
=> ( VX8212 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX8212 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX8212 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__22507,VX22508] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22507)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__22507,VX22508)
=> ( ? [Vvar__0__n__22509] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__22509)
& Vvar__0___24Anonymous__22507 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__22509)
& VX22508 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__22509) )
| ? [Vvar__0__n__22510] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__22510)
& ? [Vvar__1___24Anonymous__22511] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__22510,Vvar__1___24Anonymous__22511)
& Vvar__0___24Anonymous__22507 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__22510)
& VX22508 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__22510,Vvar__1___24Anonymous__22511) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
! [Vvar__0__A__59872,Vvar__1__P__59873,Vvar__2__n__59876,Vvar__3___24Anonymous__59877] :
( cType___24t(Vvar__0__A__59872)
=> ( c_24__type__59900___24t(Vvar__0__A__59872,Vvar__1__P__59873,Vvar__2__n__59876,Vvar__3___24Anonymous__59877,Vvar__1__P__59873)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__59876)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59872,Vvar__2__n__59876,Vvar__3___24Anonymous__59877)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__59872,Vvar__1__P__59873,Vvar__2__n__59876,Vvar__3___24Anonymous__59877)
=> ( ? [Vvar__2__m__59883] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__59883)
& ? [Vvar__3__x__59884] :
( t(Vvar__3__x__59884,Vvar__0__A__59872)
& ? [Vvar__4__v__59885] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59872,Vvar__2__m__59883,Vvar__4__v__59885)
& p(happ(Vvar__1__P__59873,Vvar__3__x__59884))
& Vvar__3___24Anonymous__59877 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59872,Vvar__3__x__59884,Vvar__2__m__59883,Vvar__4__v__59885)
& Vvar__2__n__59876 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__59883) ) ) )
| ? [Vvar__2__m__59891] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__59891)
& ? [Vvar__3__x__59892] :
( t(Vvar__3__x__59892,Vvar__0__A__59872)
& ? [Vvar__4__v__59893] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59872,Vvar__2__m__59891,Vvar__4__v__59893)
& cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__59872,Vvar__1__P__59873,Vvar__2__m__59891,Vvar__4__v__59893)
& Vvar__3___24Anonymous__59877 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59872,Vvar__3__x__59892,Vvar__2__m__59891,Vvar__4__v__59893)
& Vvar__2__n__59876 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__59891) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
! [Vvar__0__A__59968,Vvar__1__B__59969,Vvar__2__P__59970,Vvar__3__n__59975,Vvar__4___24Anonymous__59976,Vvar__5___24Anonymous__59977] :
( cType___24t(Vvar__0__A__59968)
=> ( cType___24t(Vvar__1__B__59969)
=> ( c_24__type__60022___24t(Vvar__0__A__59968,Vvar__1__B__59969,Vvar__2__P__59970,Vvar__3__n__59975,Vvar__4___24Anonymous__59976,Vvar__5___24Anonymous__59977,Vvar__2__P__59970)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__59975)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59968,Vvar__3__n__59975,Vvar__4___24Anonymous__59976)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__59969,Vvar__3__n__59975,Vvar__5___24Anonymous__59977)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__59968,Vvar__1__B__59969,Vvar__2__P__59970,Vvar__3__n__59975,Vvar__4___24Anonymous__59976,Vvar__5___24Anonymous__59977)
=> ( ? [Vvar__3__m__59986] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__59986)
& ? [Vvar__4__x1__59987] :
( t(Vvar__4__x1__59987,Vvar__0__A__59968)
& ? [Vvar__5__x2__59988] :
( t(Vvar__5__x2__59988,Vvar__1__B__59969)
& ? [Vvar__6__v1__59989] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59968,Vvar__3__m__59986,Vvar__6__v1__59989)
& ? [Vvar__7__v2__59990] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__59969,Vvar__3__m__59986,Vvar__7__v2__59990)
& p(happ(happ(Vvar__2__P__59970,Vvar__4__x1__59987),Vvar__5__x2__59988))
& Vvar__5___24Anonymous__59977 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__59969,Vvar__5__x2__59988,Vvar__3__m__59986,Vvar__7__v2__59990)
& Vvar__4___24Anonymous__59976 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59968,Vvar__4__x1__59987,Vvar__3__m__59986,Vvar__6__v1__59989)
& Vvar__3__n__59975 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__59986) ) ) ) ) )
| ? [Vvar__3__m__59999] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__59999)
& ? [Vvar__4__x1__60000] :
( t(Vvar__4__x1__60000,Vvar__0__A__59968)
& ? [Vvar__5__x2__60001] :
( t(Vvar__5__x2__60001,Vvar__1__B__59969)
& ? [Vvar__6__v1__60002] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59968,Vvar__3__m__59999,Vvar__6__v1__60002)
& ? [Vvar__7__v2__60003] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__59969,Vvar__3__m__59999,Vvar__7__v2__60003)
& cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__59968,Vvar__1__B__59969,Vvar__2__P__59970,Vvar__3__m__59999,Vvar__6__v1__60002,Vvar__7__v2__60003)
& Vvar__5___24Anonymous__59977 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__59969,Vvar__5__x2__60001,Vvar__3__m__59999,Vvar__7__v2__60003)
& Vvar__4___24Anonymous__59976 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59968,Vvar__4__x1__60000,Vvar__3__m__59999,Vvar__6__v1__60002)
& Vvar__3__n__59975 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__59999) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
! [Vvar__0__A__59845,Vvar__1__P__59846,Vvar__2__n__59849,Vvar__3__v__59850] :
( cType___24t(Vvar__0__A__59845)
=> ( c_24__type__59870___24t(Vvar__0__A__59845,Vvar__1__P__59846,Vvar__2__n__59849,Vvar__3__v__59850,Vvar__1__P__59846)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__59849)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59845,Vvar__2__n__59849,Vvar__3__v__59850)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__59845,Vvar__1__P__59846,Vvar__2__n__59849,Vvar__3__v__59850)
=> ( ( Vvar__3__v__59850 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__59845)
& Vvar__2__n__59849 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__n__59860] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__59860)
& ? [Vvar__3__x__59861] :
( t(Vvar__3__x__59861,Vvar__0__A__59845)
& ? [Vvar__4__v__59862] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59845,Vvar__2__n__59860,Vvar__4__v__59862)
& p(happ(Vvar__1__P__59846,Vvar__3__x__59861))
& cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__59845,Vvar__1__P__59846,Vvar__2__n__59860,Vvar__4__v__59862)
& Vvar__3__v__59850 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59845,Vvar__3__x__59861,Vvar__2__n__59860,Vvar__4__v__59862)
& Vvar__2__n__59849 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__59860) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
! [Vvar__0__A__59917,Vvar__1__B__59918,Vvar__2__P__59919,Vvar__3__n__59924,Vvar__4___24Anonymous__59925,Vvar__5___24Anonymous__59926] :
( cType___24t(Vvar__0__A__59917)
=> ( cType___24t(Vvar__1__B__59918)
=> ( c_24__type__59966___24t(Vvar__0__A__59917,Vvar__1__B__59918,Vvar__2__P__59919,Vvar__3__n__59924,Vvar__4___24Anonymous__59925,Vvar__5___24Anonymous__59926,Vvar__2__P__59919)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__59924)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59917,Vvar__3__n__59924,Vvar__4___24Anonymous__59925)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__59918,Vvar__3__n__59924,Vvar__5___24Anonymous__59926)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__59917,Vvar__1__B__59918,Vvar__2__P__59919,Vvar__3__n__59924,Vvar__4___24Anonymous__59925,Vvar__5___24Anonymous__59926)
=> ( ( Vvar__5___24Anonymous__59926 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__59918)
& Vvar__4___24Anonymous__59925 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__59917)
& Vvar__3__n__59924 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__3__m__59942] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__59942)
& ? [Vvar__4__x1__59943] :
( t(Vvar__4__x1__59943,Vvar__0__A__59917)
& ? [Vvar__5__x2__59944] :
( t(Vvar__5__x2__59944,Vvar__1__B__59918)
& ? [Vvar__6__v1__59945] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59917,Vvar__3__m__59942,Vvar__6__v1__59945)
& ? [Vvar__7__v2__59946] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__59918,Vvar__3__m__59942,Vvar__7__v2__59946)
& p(happ(happ(Vvar__2__P__59919,Vvar__4__x1__59943),Vvar__5__x2__59944))
& cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__59917,Vvar__1__B__59918,Vvar__2__P__59919,Vvar__3__m__59942,Vvar__6__v1__59945,Vvar__7__v2__59946)
& Vvar__5___24Anonymous__59926 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__59918,Vvar__5__x2__59944,Vvar__3__m__59942,Vvar__7__v2__59946)
& Vvar__4___24Anonymous__59925 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59917,Vvar__4__x1__59943,Vvar__3__m__59942,Vvar__6__v1__59945)
& Vvar__3__n__59924 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__59942) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
! [Vvar__0__A__59902,Vvar__1__a__59903,Vvar__2__n__59904,Vvar__3___24Anonymous__59905] :
( cType___24t(Vvar__0__A__59902)
=> ( t(Vvar__1__a__59903,Vvar__0__A__59902)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__59904)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59902,Vvar__2__n__59904,Vvar__3___24Anonymous__59905)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__59902,Vvar__1__a__59903,Vvar__2__n__59904,Vvar__3___24Anonymous__59905)
=> ( ? [Vvar__2__m__59909] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__59909)
& ? [Vvar__3__v__59910] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59902,Vvar__2__m__59909,Vvar__3__v__59910)
& Vvar__3___24Anonymous__59905 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59902,Vvar__1__a__59903,Vvar__2__m__59909,Vvar__3__v__59910)
& Vvar__2__n__59904 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__59909) ) )
| ? [Vvar__2__m__59913] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__59913)
& ? [Vvar__3__x__59914] :
( t(Vvar__3__x__59914,Vvar__0__A__59902)
& ? [Vvar__4__v__59915] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__59902,Vvar__2__m__59913,Vvar__4__v__59915)
& cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__59902,Vvar__1__a__59903,Vvar__2__m__59913,Vvar__4__v__59915)
& Vvar__3___24Anonymous__59905 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__59902,Vvar__3__x__59914,Vvar__2__m__59913,Vvar__4__v__59915)
& Vvar__2__n__59904 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__59913) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__408,Vvar__1___24Anonymous__409,VX410] :
( cType___24t(Vvar__0__A__408)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__409)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__408,Vvar__1___24Anonymous__409,VX410)
=> ( ( Vvar__1___24Anonymous__409 = cCoq_2eInit_2eDatatypes_2eO
& VX410 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__408) )
| ? [Vvar__1__h__413] :
( t(Vvar__1__h__413,Vvar__0__A__408)
& ? [Vvar__2__n__414] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__414)
& ? [Vvar__3___24Anonymous__415] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__408,Vvar__2__n__414,Vvar__3___24Anonymous__415)
& Vvar__1___24Anonymous__409 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__414)
& VX410 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__408,Vvar__1__h__413,Vvar__2__n__414,Vvar__3___24Anonymous__415) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.funind.Recdef.max_type',axiom,
! [Vvar__0__m__8310,Vvar__1__n__8311,VX8312] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__m__8310)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__8311)
=> ( cCoq_2efunind_2eRecdef_2emax__type___24t(Vvar__0__m__8310,Vvar__1__n__8311,VX8312)
=> ? [Vvar__2__v__8315] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__v__8315)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__m__8310,Vvar__2__v__8315))
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__n__8311,Vvar__2__v__8315))
& VX8312 = cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__8310,Vvar__1__n__8311,Vvar__2__v__8315) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__59718,Vvar__1__F__59719] :
( cType___24t(Vvar__0__T__59718)
=> ( t(Vvar__1__F__59719,Vvar__0__T__59718)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__59718,Vvar__1__F__59719)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX21361] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX21361)
=> ( VX21361 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__21362] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21362)
& ? [Vvar__1___24Anonymous__21363] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__21363)
& VX21361 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__21362,Vvar__1___24Anonymous__21363) ) )
| ? [Vvar__0___24Anonymous__21364] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21364)
& ? [Vvar__1___24Anonymous__21365] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__21365)
& VX21361 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__21364,Vvar__1___24Anonymous__21365) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__21147,VX21148] :
( cType___24t(Vvar__0__C__21147)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,VX21148)
=> ( ? [Vvar__1___24Anonymous__21150] :
( t(Vvar__1___24Anonymous__21150,Vvar__0__C__21147)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__21147,Vvar__1___24Anonymous__21150) )
| ? [Vvar__1___24Anonymous__21152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__21152)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__21147,Vvar__1___24Anonymous__21152) )
| ? [Vvar__1___24Anonymous__21154] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__1___24Anonymous__21154)
& ? [Vvar__2___24Anonymous__21155] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__2___24Anonymous__21155)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__21147,Vvar__1___24Anonymous__21154,Vvar__2___24Anonymous__21155) ) )
| ? [Vvar__1___24Anonymous__21157] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__1___24Anonymous__21157)
& ? [Vvar__2___24Anonymous__21158] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__2___24Anonymous__21158)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__21147,Vvar__1___24Anonymous__21157,Vvar__2___24Anonymous__21158) ) )
| ? [Vvar__1___24Anonymous__21160] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__1___24Anonymous__21160)
& ? [Vvar__2___24Anonymous__21161] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__2___24Anonymous__21161)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__21147,Vvar__1___24Anonymous__21160,Vvar__2___24Anonymous__21161) ) )
| ? [Vvar__1___24Anonymous__21163] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__1___24Anonymous__21163)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__21147,Vvar__1___24Anonymous__21163) )
| ? [Vvar__1___24Anonymous__21165] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__21147,Vvar__1___24Anonymous__21165)
& ? [Vvar__2___24Anonymous__21166] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__21166)
& VX21148 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__21147,Vvar__1___24Anonymous__21165,Vvar__2___24Anonymous__21166) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__21311,VX21312] :
( cType___24t(Vvar__0__C__21311)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__21311,VX21312)
=> ( ? [Vvar__1___24Anonymous__21314] :
( t(Vvar__1___24Anonymous__21314,Vvar__0__C__21311)
& VX21312 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__21311,Vvar__1___24Anonymous__21314) )
| ? [Vvar__1___24Anonymous__21316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__21316)
& ? [Vvar__2___24Anonymous__21317] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__21311,Vvar__2___24Anonymous__21317)
& VX21312 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__21311,Vvar__1___24Anonymous__21316,Vvar__2___24Anonymous__21317) ) )
| ? [Vvar__1___24Anonymous__21319] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__21311,Vvar__1___24Anonymous__21319)
& ? [Vvar__2___24Anonymous__21320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__21320)
& ? [Vvar__3___24Anonymous__21321] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__21311,Vvar__3___24Anonymous__21321)
& VX21312 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__21311,Vvar__1___24Anonymous__21319,Vvar__2___24Anonymous__21320,Vvar__3___24Anonymous__21321) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848] :
( cType___24t(Vvar__0__R__22817)
=> ( t(Vvar__1__rO__22818,Vvar__0__R__22817)
=> ( t(Vvar__2__rI__22819,Vvar__0__R__22817)
=> ( c_24__type__23249___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__3__rplus__22820)
=> ( c_24__type__23350___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__4__rtimes__22825)
=> ( c_24__type__23451___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__5__rminus__22830)
=> ( c_24__type__23541___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__6__ropp__22835)
=> ( c_24__type__23642___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__7__req__22838)
=> ( c_24__type__23743___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__8__rle__22843)
=> ( c_24__type__23844___24t(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848,Vvar__9__rlt__22848)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838,Vvar__8__rle__22843,Vvar__9__rlt__22848)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__22817,Vvar__7__req__22838)
& ! [Vvar__var__var__var__var__11__x1__22892__22898__23003__23009__23015] :
( t(Vvar__var__var__var__var__11__x1__22892__22898__23003__23009__23015,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__12__x2__22893__22899__23004__23010__23016] :
( t(Vvar__var__var__var__var__12__x2__22893__22899__23004__23010__23016,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__11__x1__22892__22898__23003__23009__23015),Vvar__var__var__var__var__12__x2__22893__22899__23004__23010__23016))
=> ! [Vvar__var__var__var__var__14__y1__22894__22900__23005__23011__23017] :
( t(Vvar__var__var__var__var__14__y1__22894__22900__23005__23011__23017,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__15__y2__22895__22901__23006__23012__23018] :
( t(Vvar__var__var__var__var__15__y2__22895__22901__23006__23012__23018,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__14__y1__22894__22900__23005__23011__23017),Vvar__var__var__var__var__15__y2__22895__22901__23006__23012__23018))
=> p(happ(happ(Vvar__7__req__22838,happ(happ(Vvar__3__rplus__22820,Vvar__var__var__var__var__11__x1__22892__22898__23003__23009__23015),Vvar__var__var__var__var__14__y1__22894__22900__23005__23011__23017)),happ(happ(Vvar__3__rplus__22820,Vvar__var__var__var__var__12__x2__22893__22899__23004__23010__23016),Vvar__var__var__var__var__15__y2__22895__22901__23006__23012__23018))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__22905__22911__23021__23027__23033] :
( t(Vvar__var__var__var__var__12__x1__22905__22911__23021__23027__23033,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__13__x2__22906__22912__23022__23028__23034] :
( t(Vvar__var__var__var__var__13__x2__22906__22912__23022__23028__23034,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__12__x1__22905__22911__23021__23027__23033),Vvar__var__var__var__var__13__x2__22906__22912__23022__23028__23034))
=> ! [Vvar__var__var__var__var__15__y1__22907__22913__23023__23029__23035] :
( t(Vvar__var__var__var__var__15__y1__22907__22913__23023__23029__23035,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__16__y2__22908__22914__23024__23030__23036] :
( t(Vvar__var__var__var__var__16__y2__22908__22914__23024__23030__23036,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__15__y1__22907__22913__23023__23029__23035),Vvar__var__var__var__var__16__y2__22908__22914__23024__23030__23036))
=> p(happ(happ(Vvar__7__req__22838,happ(happ(Vvar__4__rtimes__22825,Vvar__var__var__var__var__12__x1__22905__22911__23021__23027__23033),Vvar__var__var__var__var__15__y1__22907__22913__23023__23029__23035)),happ(happ(Vvar__4__rtimes__22825,Vvar__var__var__var__var__13__x2__22906__22912__23022__23028__23034),Vvar__var__var__var__var__16__y2__22908__22914__23024__23030__23036))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__22918__22921__23039__23042__23045] :
( t(Vvar__var__var__var__var__13__x1__22918__22921__23039__23042__23045,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__14__x2__22919__22922__23040__23043__23046] :
( t(Vvar__var__var__var__var__14__x2__22919__22922__23040__23043__23046,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__13__x1__22918__22921__23039__23042__23045),Vvar__var__var__var__var__14__x2__22919__22922__23040__23043__23046))
=> p(happ(happ(Vvar__7__req__22838,happ(Vvar__6__ropp__22835,Vvar__var__var__var__var__13__x1__22918__22921__23039__23042__23045)),happ(Vvar__6__ropp__22835,Vvar__var__var__var__var__14__x2__22919__22922__23040__23043__23046))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__22925__22931__23048__23054__23060] :
( t(Vvar__var__var__var__var__14__x1__22925__22931__23048__23054__23060,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__15__x2__22926__22932__23049__23055__23061] :
( t(Vvar__var__var__var__var__15__x2__22926__22932__23049__23055__23061,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__14__x1__22925__22931__23048__23054__23060),Vvar__var__var__var__var__15__x2__22926__22932__23049__23055__23061))
=> ! [Vvar__var__var__var__var__17__y1__22927__22933__23050__23056__23062] :
( t(Vvar__var__var__var__var__17__y1__22927__22933__23050__23056__23062,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__18__y2__22928__22934__23051__23057__23063] :
( t(Vvar__var__var__var__var__18__y2__22928__22934__23051__23057__23063,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__17__y1__22927__22933__23050__23056__23062),Vvar__var__var__var__var__18__y2__22928__22934__23051__23057__23063))
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__14__x1__22925__22931__23048__23054__23060),Vvar__var__var__var__var__17__y1__22927__22933__23050__23056__23062))
<=> p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__15__x2__22926__22932__23049__23055__23061),Vvar__var__var__var__var__18__y2__22928__22934__23051__23057__23063)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__22938__22944__23066__23072__23078] :
( t(Vvar__var__var__var__var__15__x1__22938__22944__23066__23072__23078,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__16__x2__22939__22945__23067__23073__23079] :
( t(Vvar__var__var__var__var__16__x2__22939__22945__23067__23073__23079,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__15__x1__22938__22944__23066__23072__23078),Vvar__var__var__var__var__16__x2__22939__22945__23067__23073__23079))
=> ! [Vvar__var__var__var__var__18__y1__22940__22946__23068__23074__23080] :
( t(Vvar__var__var__var__var__18__y1__22940__22946__23068__23074__23080,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__19__y2__22941__22947__23069__23075__23081] :
( t(Vvar__var__var__var__var__19__y2__22941__22947__23069__23075__23081,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__18__y1__22940__22946__23068__23074__23080),Vvar__var__var__var__var__19__y2__22941__22947__23069__23075__23081))
=> ( p(happ(happ(Vvar__9__rlt__22848,Vvar__var__var__var__var__15__x1__22938__22944__23066__23072__23078),Vvar__var__var__var__var__18__y1__22940__22946__23068__23074__23080))
<=> p(happ(happ(Vvar__9__rlt__22848,Vvar__var__var__var__var__16__x2__22939__22945__23067__23073__23079),Vvar__var__var__var__var__19__y2__22941__22947__23069__23075__23081)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__22817,Vvar__1__rO__22818,Vvar__2__rI__22819,Vvar__3__rplus__22820,Vvar__4__rtimes__22825,Vvar__5__rminus__22830,Vvar__6__ropp__22835,Vvar__7__req__22838)
& ! [Vvar__var__var__var__17__n__22952__22953__23084__23085] :
( t(Vvar__var__var__var__17__n__22952__22953__23084__23085,Vvar__0__R__22817)
=> p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__17__n__22952__22953__23084__23085),Vvar__var__var__var__17__n__22952__22953__23084__23085)) )
& ! [Vvar__var__var__var__var__18__n__22955__22959__23086__23090__23094] :
( t(Vvar__var__var__var__var__18__n__22955__22959__23086__23090__23094,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__19__m__22956__22960__23087__23091__23095] :
( t(Vvar__var__var__var__var__19__m__22956__22960__23087__23091__23095,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__18__n__22955__22959__23086__23090__23094),Vvar__var__var__var__var__19__m__22956__22960__23087__23091__23095))
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__19__m__22956__22960__23087__23091__23095),Vvar__var__var__var__var__18__n__22955__22959__23086__23090__23094))
=> p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__18__n__22955__22959__23086__23090__23094),Vvar__var__var__var__var__19__m__22956__22960__23087__23091__23095)) ) ) ) )
& ! [Vvar__var__var__var__19__n__22964__22969__23098__23103] :
( t(Vvar__var__var__var__19__n__22964__22969__23098__23103,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__20__m__22965__22970__23099__23104] :
( t(Vvar__var__var__var__20__m__22965__22970__23099__23104,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__21__p__22966__22971__23100__23105] :
( t(Vvar__var__var__var__21__p__22966__22971__23100__23105,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__19__n__22964__22969__23098__23103),Vvar__var__var__var__20__m__22965__22970__23099__23104))
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__20__m__22965__22970__23099__23104),Vvar__var__var__var__21__p__22966__22971__23100__23105))
=> p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__19__n__22964__22969__23098__23103),Vvar__var__var__var__21__p__22966__22971__23100__23105)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__22975__22977__23108__23110__23112__23114] :
( t(Vvar__var__var__var__var__var__20__n__22975__22977__23108__23110__23112__23114,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__var__21__m__22976__22978__23109__23111__23113__23115] :
( t(Vvar__var__var__var__var__var__21__m__22976__22978__23109__23111__23113__23115,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__9__rlt__22848,Vvar__var__var__var__var__var__20__n__22975__22977__23108__23110__23112__23114),Vvar__var__var__var__var__var__21__m__22976__22978__23109__23111__23113__23115))
<=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__var__20__n__22975__22977__23108__23110__23112__23114),Vvar__var__var__var__var__var__21__m__22976__22978__23109__23111__23113__23115))
& ~ p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__var__20__n__22975__22977__23108__23110__23112__23114),Vvar__var__var__var__var__var__21__m__22976__22978__23109__23111__23113__23115)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__22980__22982__23116__23118__23120] :
( t(Vvar__var__var__var__var__21__n__22980__22982__23116__23118__23120,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__22__m__22981__22983__23117__23119__23121] :
( t(Vvar__var__var__var__var__22__m__22981__22983__23117__23119__23121,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__9__rlt__22848,Vvar__var__var__var__var__21__n__22980__22982__23116__23118__23120),Vvar__var__var__var__var__22__m__22981__22983__23117__23119__23121))
| p(happ(happ(Vvar__7__req__22838,Vvar__var__var__var__var__21__n__22980__22982__23116__23118__23120),Vvar__var__var__var__var__22__m__22981__22983__23117__23119__23121))
| p(happ(happ(Vvar__9__rlt__22848,Vvar__var__var__var__var__22__m__22981__22983__23117__23119__23121),Vvar__var__var__var__var__21__n__22980__22982__23116__23118__23120)) ) ) )
& ! [Vvar__var__var__var__var__22__n__22985__22989__23122__23126__23130] :
( t(Vvar__var__var__var__var__22__n__22985__22989__23122__23126__23130,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__23__m__22986__22990__23123__23127__23131] :
( t(Vvar__var__var__var__var__23__m__22986__22990__23123__23127__23131,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__24__p__22987__22991__23124__23128__23132] :
( t(Vvar__var__var__var__var__24__p__22987__22991__23124__23128__23132,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__8__rle__22843,Vvar__var__var__var__var__22__n__22985__22989__23122__23126__23130),Vvar__var__var__var__var__23__m__22986__22990__23123__23127__23131))
=> p(happ(happ(Vvar__8__rle__22843,happ(happ(Vvar__3__rplus__22820,Vvar__var__var__var__var__24__p__22987__22991__23124__23128__23132),Vvar__var__var__var__var__22__n__22985__22989__23122__23126__23130)),happ(happ(Vvar__3__rplus__22820,Vvar__var__var__var__var__24__p__22987__22991__23124__23128__23132),Vvar__var__var__var__var__23__m__22986__22990__23123__23127__23131))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__22994__22998__23134__23138__23142__23146] :
( t(Vvar__var__var__var__var__var__23__n__22994__22998__23134__23138__23142__23146,Vvar__0__R__22817)
=> ! [Vvar__var__var__var__var__var__24__m__22995__22999__23135__23139__23143__23147] :
( t(Vvar__var__var__var__var__var__24__m__22995__22999__23135__23139__23143__23147,Vvar__0__R__22817)
=> ( p(happ(happ(Vvar__9__rlt__22848,Vvar__1__rO__22818),Vvar__var__var__var__var__var__23__n__22994__22998__23134__23138__23142__23146))
=> ( p(happ(happ(Vvar__9__rlt__22848,Vvar__1__rO__22818),Vvar__var__var__var__var__var__24__m__22995__22999__23135__23139__23143__23147))
=> p(happ(happ(Vvar__9__rlt__22848,Vvar__1__rO__22818),happ(happ(Vvar__4__rtimes__22825,Vvar__var__var__var__var__var__23__n__22994__22998__23134__23138__23142__23146),Vvar__var__var__var__var__var__24__m__22995__22999__23135__23139__23143__23147))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__22838,Vvar__1__rO__22818),Vvar__2__rI__22819))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX23895] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX23895)
=> ( VX23895 = cCoq_2emicromega_2eRMicromega_2eC0
| VX23895 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__23896] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__23896)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__23896) )
| ? [Vvar__0__r__23897] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__23897)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__23897) )
| ? [Vvar__0__r1__23898] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__23898)
& ? [Vvar__1__r2__23899] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__23899)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__23898,Vvar__1__r2__23899) ) )
| ? [Vvar__0__r1__23900] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__23900)
& ? [Vvar__1__r2__23901] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__23901)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__23900,Vvar__1__r2__23901) ) )
| ? [Vvar__0__r1__23902] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__23902)
& ? [Vvar__1__r2__23903] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__23903)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__23902,Vvar__1__r2__23903) ) )
| ? [Vvar__0__r1__23904] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__23904)
& ? [Vvar__1__z__23905] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__23905)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__23904,Vvar__1__z__23905) ) )
| ? [Vvar__0__r__23906] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__23906)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__23906) )
| ? [Vvar__0__r__23907] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__23907)
& VX23895 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__23907) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__30117,VX30118] :
( cType___24t(Vvar__0__T__30117)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__30117,VX30118)
=> ? [Vvar__1__Flhs__30120] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__30117,Vvar__1__Flhs__30120)
& ? [Vvar__2__Fop__30121] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__30121)
& ? [Vvar__3__Frhs__30122] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__30117,Vvar__3__Frhs__30122)
& VX30118 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__30117,Vvar__1__Flhs__30120,Vvar__2__Fop__30121,Vvar__3__Frhs__30122) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX29963] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX29963)
=> ( VX29963 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX29963 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX29963 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX29963 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__29964,VX29965] :
( cType___24t(Vvar__0__C__29964)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,VX29965)
=> ( ? [Vvar__1___24Anonymous__29967] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__29967)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__29964,Vvar__1___24Anonymous__29967) )
| ? [Vvar__1___24Anonymous__29969] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__29964,Vvar__1___24Anonymous__29969)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__29964,Vvar__1___24Anonymous__29969) )
| ? [Vvar__1___24Anonymous__29971] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__29964,Vvar__1___24Anonymous__29971)
& ? [Vvar__2___24Anonymous__29972] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,Vvar__2___24Anonymous__29972)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__29964,Vvar__1___24Anonymous__29971,Vvar__2___24Anonymous__29972) ) )
| ? [Vvar__1___24Anonymous__29974] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,Vvar__1___24Anonymous__29974)
& ? [Vvar__2___24Anonymous__29975] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,Vvar__2___24Anonymous__29975)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__29964,Vvar__1___24Anonymous__29974,Vvar__2___24Anonymous__29975) ) )
| ? [Vvar__1___24Anonymous__29977] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,Vvar__1___24Anonymous__29977)
& ? [Vvar__2___24Anonymous__29978] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29964,Vvar__2___24Anonymous__29978)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__29964,Vvar__1___24Anonymous__29977,Vvar__2___24Anonymous__29978) ) )
| ? [Vvar__1___24Anonymous__29980] :
( t(Vvar__1___24Anonymous__29980,Vvar__0__C__29964)
& VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__29964,Vvar__1___24Anonymous__29980) )
| VX29965 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__29964) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739] :
( cType___24t(Vvar__0__R__24670)
=> ( t(Vvar__1__rO__24671,Vvar__0__R__24670)
=> ( t(Vvar__2__rI__24672,Vvar__0__R__24670)
=> ( c_24__type__25203___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__3__rplus__24673)
=> ( c_24__type__25549___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__4__rtimes__24678)
=> ( c_24__type__25895___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__5__rminus__24683)
=> ( c_24__type__26218___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__6__ropp__24688)
=> ( c_24__type__26564___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__7__req__24691)
=> ( c_24__type__26910___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__8__rle__24696)
=> ( cType___24t(Vvar__9__C__24701)
=> ( t(Vvar__10__cO__24702,Vvar__9__C__24701)
=> ( t(Vvar__11__cI__24703,Vvar__9__C__24701)
=> ( c_24__type__27256___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__12__cplus__24704)
=> ( c_24__type__27602___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__13__ctimes__24709)
=> ( c_24__type__27948___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__14__cminus__24714)
=> ( c_24__type__28271___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__15__copp__24719)
=> ( c_24__type__28617___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__16__ceqb__24722)
=> ( c_24__type__28963___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__17__cleb__24727)
=> ( c_24__type__29286___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__18__phi__24732)
=> ( cType___24t(Vvar__19__E__24735)
=> ( c_24__type__29609___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__20__pow__phi__24736)
=> ( c_24__type__29955___24t(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739,Vvar__21__rpow__24739)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__8__rle__24696,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__17__cleb__24727,Vvar__18__phi__24732,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__24670,Vvar__1__rO__24671,Vvar__2__rI__24672,Vvar__3__rplus__24673,Vvar__4__rtimes__24678,Vvar__5__rminus__24683,Vvar__6__ropp__24688,Vvar__7__req__24691,Vvar__9__C__24701,Vvar__10__cO__24702,Vvar__11__cI__24703,Vvar__12__cplus__24704,Vvar__13__ctimes__24709,Vvar__14__cminus__24714,Vvar__15__copp__24719,Vvar__16__ceqb__24722,Vvar__18__phi__24732)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__24670,Vvar__2__rI__24672,Vvar__4__rtimes__24678,Vvar__7__req__24691,Vvar__19__E__24735,Vvar__20__pow__phi__24736,Vvar__21__rpow__24739)
& ! [Vvar__var__var__var__var__var__24__x__24822__24825__24835__24838__24841__24844] :
( t(Vvar__var__var__var__var__var__24__x__24822__24825__24835__24838__24841__24844,Vvar__9__C__24701)
=> ! [Vvar__var__var__var__var__var__25__y__24823__24826__24836__24839__24842__24845] :
( t(Vvar__var__var__var__var__var__25__y__24823__24826__24836__24839__24842__24845,Vvar__9__C__24701)
=> ( happ(happ(Vvar__16__ceqb__24722,Vvar__var__var__var__var__var__24__x__24822__24825__24835__24838__24841__24844),Vvar__var__var__var__var__var__25__y__24823__24826__24836__24839__24842__24845) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__24691,happ(Vvar__18__phi__24732,Vvar__var__var__var__var__var__24__x__24822__24825__24835__24838__24841__24844)),happ(Vvar__18__phi__24732,Vvar__var__var__var__var__var__25__y__24823__24826__24836__24839__24842__24845))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__24829__24832__24847__24850__24853__24856] :
( t(Vvar__var__var__var__var__var__25__x__24829__24832__24847__24850__24853__24856,Vvar__9__C__24701)
=> ! [Vvar__var__var__var__var__var__26__y__24830__24833__24848__24851__24854__24857] :
( t(Vvar__var__var__var__var__var__26__y__24830__24833__24848__24851__24854__24857,Vvar__9__C__24701)
=> ( happ(happ(Vvar__17__cleb__24727,Vvar__var__var__var__var__var__25__x__24829__24832__24847__24850__24853__24856),Vvar__var__var__var__var__var__26__y__24830__24833__24848__24851__24854__24857) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__24696,happ(Vvar__18__phi__24732,Vvar__var__var__var__var__var__25__x__24829__24832__24847__24850__24853__24856)),happ(Vvar__18__phi__24732,Vvar__var__var__var__var__var__26__y__24830__24833__24848__24851__24854__24857))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,VX35146] :
( cType___24t(Vvar__0__TA__35142)
=> ( cType___24t(Vvar__1__TX__35143)
=> ( cType___24t(Vvar__2__AA__35144)
=> ( cType___24t(Vvar__3__AF__35145)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,VX35146)
=> ( VX35146 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145)
| VX35146 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145)
| ? [Vvar__4___24Anonymous__35159] :
( t(Vvar__4___24Anonymous__35159,Vvar__1__TX__35143)
& VX35146 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35159) )
| ? [Vvar__4___24Anonymous__35164] :
( t(Vvar__4___24Anonymous__35164,Vvar__0__TA__35142)
& ? [Vvar__5___24Anonymous__35165] :
( t(Vvar__5___24Anonymous__35165,Vvar__2__AA__35144)
& VX35146 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35164,Vvar__5___24Anonymous__35165) ) )
| ? [Vvar__4___24Anonymous__35170] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35170)
& ? [Vvar__5___24Anonymous__35171] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__5___24Anonymous__35171)
& VX35146 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35170,Vvar__5___24Anonymous__35171) ) )
| ? [Vvar__4___24Anonymous__35176] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35176)
& ? [Vvar__5___24Anonymous__35177] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__5___24Anonymous__35177)
& VX35146 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35176,Vvar__5___24Anonymous__35177) ) )
| ? [Vvar__4___24Anonymous__35182] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35182)
& VX35146 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35182) )
| ? [Vvar__4___24Anonymous__35187] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35187)
& ? [Vvar__5___24Anonymous__35188] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__35145,Vvar__5___24Anonymous__35188)
& ? [Vvar__6___24Anonymous__35189] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__6___24Anonymous__35189)
& VX35146 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__35142,Vvar__1__TX__35143,Vvar__2__AA__35144,Vvar__3__AF__35145,Vvar__4___24Anonymous__35187,Vvar__5___24Anonymous__35188,Vvar__6___24Anonymous__35189) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX35588] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX35588)
=> ( VX35588 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__35589] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35589)
& ? [Vvar__1___24Anonymous__35590] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__35590)
& VX35588 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__35589,Vvar__1___24Anonymous__35590) ) )
| ? [Vvar__0___24Anonymous__35591] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35591)
& ? [Vvar__1___24Anonymous__35592] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__35592)
& VX35588 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__35591,Vvar__1___24Anonymous__35592) ) )
| ? [Vvar__0___24Anonymous__35593] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__35593)
& ? [Vvar__1___24Anonymous__35594] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__35594)
& ? [Vvar__2___24Anonymous__35595] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__35595)
& VX35588 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__35593,Vvar__1___24Anonymous__35594,Vvar__2___24Anonymous__35595) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__22118,VX22119] :
( cType___24t(Vvar__0__C__22118)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,VX22119)
=> ( VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__22118)
| VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__22118)
| ? [Vvar__1___24Anonymous__22123] :
( t(Vvar__1___24Anonymous__22123,Vvar__0__C__22118)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__22118,Vvar__1___24Anonymous__22123) )
| ? [Vvar__1___24Anonymous__22125] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__22125)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__22118,Vvar__1___24Anonymous__22125) )
| ? [Vvar__1___24Anonymous__22127] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22127)
& ? [Vvar__2___24Anonymous__22128] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__2___24Anonymous__22128)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__22118,Vvar__1___24Anonymous__22127,Vvar__2___24Anonymous__22128) ) )
| ? [Vvar__1___24Anonymous__22130] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22130)
& ? [Vvar__2___24Anonymous__22131] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__2___24Anonymous__22131)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__22118,Vvar__1___24Anonymous__22130,Vvar__2___24Anonymous__22131) ) )
| ? [Vvar__1___24Anonymous__22133] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22133)
& ? [Vvar__2___24Anonymous__22134] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__2___24Anonymous__22134)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__22118,Vvar__1___24Anonymous__22133,Vvar__2___24Anonymous__22134) ) )
| ? [Vvar__1___24Anonymous__22136] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22136)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__22118,Vvar__1___24Anonymous__22136) )
| ? [Vvar__1___24Anonymous__22138] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22138)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__22118,Vvar__1___24Anonymous__22138) )
| ? [Vvar__1___24Anonymous__22140] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22140)
& ? [Vvar__2___24Anonymous__22141] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__2___24Anonymous__22141)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__22118,Vvar__1___24Anonymous__22140,Vvar__2___24Anonymous__22141) ) )
| ? [Vvar__1___24Anonymous__22143] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__22118,Vvar__1___24Anonymous__22143)
& ? [Vvar__2___24Anonymous__22144] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__22144)
& VX22119 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__22118,Vvar__1___24Anonymous__22143,Vvar__2___24Anonymous__22144) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411] :
( cType___24t(Vvar__0__R__21382)
=> ( t(Vvar__1__rO__21383,Vvar__0__R__21382)
=> ( t(Vvar__2__rI__21384,Vvar__0__R__21382)
=> ( c_24__type__21576___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__3__radd__21385)
=> ( c_24__type__21669___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__4__rmul__21390)
=> ( c_24__type__21762___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__5__rsub__21395)
=> ( c_24__type__21844___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__6__ropp__21400)
=> ( c_24__type__21937___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__7__rdiv__21403)
=> ( c_24__type__22019___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__8__rinv__21408)
=> ( c_24__type__22112___24t(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411,Vvar__9__req__21411)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__7__rdiv__21403,Vvar__8__rinv__21408,Vvar__9__req__21411)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__21382,Vvar__1__rO__21383,Vvar__2__rI__21384,Vvar__3__radd__21385,Vvar__4__rmul__21390,Vvar__5__rsub__21395,Vvar__6__ropp__21400,Vvar__9__req__21411)
& ~ p(happ(happ(Vvar__9__req__21411,Vvar__2__rI__21384),Vvar__1__rO__21383))
& ! [Vvar__var__var__var__var__var__var__12__p__21454__21456__21463__21465__21467__21469__21471] :
( t(Vvar__var__var__var__var__var__var__12__p__21454__21456__21463__21465__21467__21469__21471,Vvar__0__R__21382)
=> ! [Vvar__var__var__var__var__var__var__13__q__21455__21457__21464__21466__21468__21470__21472] :
( t(Vvar__var__var__var__var__var__var__13__q__21455__21457__21464__21466__21468__21470__21472,Vvar__0__R__21382)
=> p(happ(happ(Vvar__9__req__21411,happ(happ(Vvar__7__rdiv__21403,Vvar__var__var__var__var__var__var__12__p__21454__21456__21463__21465__21467__21469__21471),Vvar__var__var__var__var__var__var__13__q__21455__21457__21464__21466__21468__21470__21472)),happ(happ(Vvar__4__rmul__21390,Vvar__var__var__var__var__var__var__12__p__21454__21456__21463__21465__21467__21469__21471),happ(Vvar__8__rinv__21408,Vvar__var__var__var__var__var__var__13__q__21455__21457__21464__21466__21468__21470__21472)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__21459__21461__21473__21475__21477__21479__21481__21483] :
( t(Vvar__var__var__var__var__var__var__var__13__p__21459__21461__21473__21475__21477__21479__21481__21483,Vvar__0__R__21382)
=> ( ~ p(happ(happ(Vvar__9__req__21411,Vvar__var__var__var__var__var__var__var__13__p__21459__21461__21473__21475__21477__21479__21481__21483),Vvar__1__rO__21383))
=> p(happ(happ(Vvar__9__req__21411,happ(happ(Vvar__4__rmul__21390,happ(Vvar__8__rinv__21408,Vvar__var__var__var__var__var__var__var__13__p__21459__21461__21473__21475__21477__21479__21481__21483)),Vvar__var__var__var__var__var__var__var__13__p__21459__21461__21473__21475__21477__21479__21481__21483)),Vvar__2__rI__21384)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__22448,VX22449] :
( cType___24t(Vvar__0__C__22448)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__22448,VX22449)
=> ? [Vvar__1__num__22451] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__22448,Vvar__1__num__22451)
& ? [Vvar__2__denum__22452] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__22448,Vvar__2__denum__22452)
& ? [Vvar__3__condition__22453] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__22448),Vvar__3__condition__22453)
& VX22449 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__22448,Vvar__1__num__22451,Vvar__2__denum__22452,Vvar__3__condition__22453) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__22470,VX22471] :
( cType___24t(Vvar__0__C__22470)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__22470,VX22471)
=> ? [Vvar__1__rsplit__left__22473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__22470,Vvar__1__rsplit__left__22473)
& ? [Vvar__2__rsplit__common__22474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__22470,Vvar__2__rsplit__common__22474)
& ? [Vvar__3__rsplit__right__22475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__22470,Vvar__3__rsplit__right__22475)
& VX22471 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__22470,Vvar__1__rsplit__left__22473,Vvar__2__rsplit__common__22474,Vvar__3__rsplit__right__22475) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX8547] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX8547)
=> ( VX8547 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__8548] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8548)
& ? [Vvar__1___24Anonymous__8549] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__8549)
& VX8547 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__8548,Vvar__1___24Anonymous__8549) ) )
| ? [Vvar__0___24Anonymous__8550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8550)
& ? [Vvar__1___24Anonymous__8551] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__8551)
& VX8547 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__8550,Vvar__1___24Anonymous__8551) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__8568,VX8569] :
( cType___24t(Vvar__0__C__8568)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,VX8569)
=> ( VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__8568)
| VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__8568)
| ? [Vvar__1___24Anonymous__8573] :
( t(Vvar__1___24Anonymous__8573,Vvar__0__C__8568)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__8568,Vvar__1___24Anonymous__8573) )
| ? [Vvar__1___24Anonymous__8575] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8575)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__8568,Vvar__1___24Anonymous__8575) )
| ? [Vvar__1___24Anonymous__8577] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__1___24Anonymous__8577)
& ? [Vvar__2___24Anonymous__8578] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__2___24Anonymous__8578)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__8568,Vvar__1___24Anonymous__8577,Vvar__2___24Anonymous__8578) ) )
| ? [Vvar__1___24Anonymous__8580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__1___24Anonymous__8580)
& ? [Vvar__2___24Anonymous__8581] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__2___24Anonymous__8581)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__8568,Vvar__1___24Anonymous__8580,Vvar__2___24Anonymous__8581) ) )
| ? [Vvar__1___24Anonymous__8583] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__1___24Anonymous__8583)
& ? [Vvar__2___24Anonymous__8584] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__2___24Anonymous__8584)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__8568,Vvar__1___24Anonymous__8583,Vvar__2___24Anonymous__8584) ) )
| ? [Vvar__1___24Anonymous__8586] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__1___24Anonymous__8586)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__8568,Vvar__1___24Anonymous__8586) )
| ? [Vvar__1___24Anonymous__8588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8568,Vvar__1___24Anonymous__8588)
& ? [Vvar__2___24Anonymous__8589] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8589)
& VX8569 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__8568,Vvar__1___24Anonymous__8588,Vvar__2___24Anonymous__8589) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__8366,VX8367] :
( cType___24t(Vvar__0__C__8366)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__8366,VX8367)
=> ( ? [Vvar__1___24Anonymous__8369] :
( t(Vvar__1___24Anonymous__8369,Vvar__0__C__8366)
& VX8367 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__8366,Vvar__1___24Anonymous__8369) )
| ? [Vvar__1___24Anonymous__8371] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8371)
& ? [Vvar__2___24Anonymous__8372] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__8366,Vvar__2___24Anonymous__8372)
& VX8367 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__8366,Vvar__1___24Anonymous__8371,Vvar__2___24Anonymous__8372) ) )
| ? [Vvar__1___24Anonymous__8374] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__8366,Vvar__1___24Anonymous__8374)
& ? [Vvar__2___24Anonymous__8375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__8375)
& ? [Vvar__3___24Anonymous__8376] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__8366,Vvar__3___24Anonymous__8376)
& VX8367 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__8366,Vvar__1___24Anonymous__8374,Vvar__2___24Anonymous__8375,Vvar__3___24Anonymous__8376) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449] :
( cType___24t(Vvar__0__R__30428)
=> ( t(Vvar__1__rO__30429,Vvar__0__R__30428)
=> ( t(Vvar__2__rI__30430,Vvar__0__R__30428)
=> ( c_24__type__30677___24t(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449,Vvar__3__radd__30431)
=> ( c_24__type__30740___24t(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449,Vvar__4__rmul__30436)
=> ( c_24__type__30803___24t(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449,Vvar__5__rsub__30441)
=> ( c_24__type__30857___24t(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449,Vvar__6__ropp__30446)
=> ( c_24__type__30920___24t(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449,Vvar__7__req__30449)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__30428,Vvar__1__rO__30429,Vvar__2__rI__30430,Vvar__3__radd__30431,Vvar__4__rmul__30436,Vvar__5__rsub__30441,Vvar__6__ropp__30446,Vvar__7__req__30449)
=> ( ! [Vvar__var__var__var__var__var__8__x__30482__30483__30536__30537__30538__30539] :
( t(Vvar__var__var__var__var__var__8__x__30482__30483__30536__30537__30538__30539,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__3__radd__30431,Vvar__1__rO__30429),Vvar__var__var__var__var__var__8__x__30482__30483__30536__30537__30538__30539)),Vvar__var__var__var__var__var__8__x__30482__30483__30536__30537__30538__30539)) )
& ! [Vvar__var__var__var__var__9__x__30485__30487__30540__30542__30544] :
( t(Vvar__var__var__var__var__9__x__30485__30487__30540__30542__30544,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__10__y__30486__30488__30541__30543__30545] :
( t(Vvar__var__var__var__var__10__y__30486__30488__30541__30543__30545,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__9__x__30485__30487__30540__30542__30544),Vvar__var__var__var__var__10__y__30486__30488__30541__30543__30545)),happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__10__y__30486__30488__30541__30543__30545),Vvar__var__var__var__var__9__x__30485__30487__30540__30542__30544))) ) )
& ! [Vvar__var__var__var__var__10__x__30490__30493__30546__30549__30552] :
( t(Vvar__var__var__var__var__10__x__30490__30493__30546__30549__30552,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__11__y__30491__30494__30547__30550__30553] :
( t(Vvar__var__var__var__var__11__y__30491__30494__30547__30550__30553,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__12__z__30492__30495__30548__30551__30554] :
( t(Vvar__var__var__var__var__12__z__30492__30495__30548__30551__30554,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__10__x__30490__30493__30546__30549__30552),happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__11__y__30491__30494__30547__30550__30553),Vvar__var__var__var__var__12__z__30492__30495__30548__30551__30554))),happ(happ(Vvar__3__radd__30431,happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__10__x__30490__30493__30546__30549__30552),Vvar__var__var__var__var__11__y__30491__30494__30547__30550__30553)),Vvar__var__var__var__var__12__z__30492__30495__30548__30551__30554))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__30497__30498__30555__30556__30557__30558] :
( t(Vvar__var__var__var__var__var__11__x__30497__30498__30555__30556__30557__30558,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__4__rmul__30436,Vvar__2__rI__30430),Vvar__var__var__var__var__var__11__x__30497__30498__30555__30556__30557__30558)),Vvar__var__var__var__var__var__11__x__30497__30498__30555__30556__30557__30558)) )
& ! [Vvar__var__var__var__var__var__12__x__30500__30501__30559__30560__30561__30562] :
( t(Vvar__var__var__var__var__var__12__x__30500__30501__30559__30560__30561__30562,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__4__rmul__30436,Vvar__1__rO__30429),Vvar__var__var__var__var__var__12__x__30500__30501__30559__30560__30561__30562)),Vvar__1__rO__30429)) )
& ! [Vvar__var__var__var__var__13__x__30503__30505__30563__30565__30567] :
( t(Vvar__var__var__var__var__13__x__30503__30505__30563__30565__30567,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__14__y__30504__30506__30564__30566__30568] :
( t(Vvar__var__var__var__var__14__y__30504__30506__30564__30566__30568,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__13__x__30503__30505__30563__30565__30567),Vvar__var__var__var__var__14__y__30504__30506__30564__30566__30568)),happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__14__y__30504__30506__30564__30566__30568),Vvar__var__var__var__var__13__x__30503__30505__30563__30565__30567))) ) )
& ! [Vvar__var__var__var__var__14__x__30508__30511__30569__30572__30575] :
( t(Vvar__var__var__var__var__14__x__30508__30511__30569__30572__30575,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__15__y__30509__30512__30570__30573__30576] :
( t(Vvar__var__var__var__var__15__y__30509__30512__30570__30573__30576,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__16__z__30510__30513__30571__30574__30577] :
( t(Vvar__var__var__var__var__16__z__30510__30513__30571__30574__30577,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__14__x__30508__30511__30569__30572__30575),happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__15__y__30509__30512__30570__30573__30576),Vvar__var__var__var__var__16__z__30510__30513__30571__30574__30577))),happ(happ(Vvar__4__rmul__30436,happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__14__x__30508__30511__30569__30572__30575),Vvar__var__var__var__var__15__y__30509__30512__30570__30573__30576)),Vvar__var__var__var__var__16__z__30510__30513__30571__30574__30577))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__30515__30518__30578__30581__30584__30587] :
( t(Vvar__var__var__var__var__var__15__x__30515__30518__30578__30581__30584__30587,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__var__16__y__30516__30519__30579__30582__30585__30588] :
( t(Vvar__var__var__var__var__var__16__y__30516__30519__30579__30582__30585__30588,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__var__17__z__30517__30520__30580__30583__30586__30589] :
( t(Vvar__var__var__var__var__var__17__z__30517__30520__30580__30583__30586__30589,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__4__rmul__30436,happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__var__15__x__30515__30518__30578__30581__30584__30587),Vvar__var__var__var__var__var__16__y__30516__30519__30579__30582__30585__30588)),Vvar__var__var__var__var__var__17__z__30517__30520__30580__30583__30586__30589)),happ(happ(Vvar__3__radd__30431,happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__var__15__x__30515__30518__30578__30581__30584__30587),Vvar__var__var__var__var__var__17__z__30517__30520__30580__30583__30586__30589)),happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__var__16__y__30516__30519__30579__30582__30585__30588),Vvar__var__var__var__var__var__17__z__30517__30520__30580__30583__30586__30589)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__30522__30524__30590__30592__30594__30596] :
( t(Vvar__var__var__var__var__var__16__x__30522__30524__30590__30592__30594__30596,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__var__17__y__30523__30525__30591__30593__30595__30597] :
( t(Vvar__var__var__var__var__var__17__y__30523__30525__30591__30593__30595__30597,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(Vvar__6__ropp__30446,happ(happ(Vvar__4__rmul__30436,Vvar__var__var__var__var__var__16__x__30522__30524__30590__30592__30594__30596),Vvar__var__var__var__var__var__17__y__30523__30525__30591__30593__30595__30597))),happ(happ(Vvar__4__rmul__30436,happ(Vvar__6__ropp__30446,Vvar__var__var__var__var__var__16__x__30522__30524__30590__30592__30594__30596)),Vvar__var__var__var__var__var__17__y__30523__30525__30591__30593__30595__30597))) ) )
& ! [Vvar__var__var__var__var__var__17__x__30527__30529__30598__30600__30602__30604] :
( t(Vvar__var__var__var__var__var__17__x__30527__30529__30598__30600__30602__30604,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__var__18__y__30528__30530__30599__30601__30603__30605] :
( t(Vvar__var__var__var__var__var__18__y__30528__30530__30599__30601__30603__30605,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(Vvar__6__ropp__30446,happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__var__17__x__30527__30529__30598__30600__30602__30604),Vvar__var__var__var__var__var__18__y__30528__30530__30599__30601__30603__30605))),happ(happ(Vvar__3__radd__30431,happ(Vvar__6__ropp__30446,Vvar__var__var__var__var__var__17__x__30527__30529__30598__30600__30602__30604)),happ(Vvar__6__ropp__30446,Vvar__var__var__var__var__var__18__y__30528__30530__30599__30601__30603__30605)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__30532__30534__30606__30608__30610__30612__30614] :
( t(Vvar__var__var__var__var__var__var__18__x__30532__30534__30606__30608__30610__30612__30614,Vvar__0__R__30428)
=> ! [Vvar__var__var__var__var__var__var__19__y__30533__30535__30607__30609__30611__30613__30615] :
( t(Vvar__var__var__var__var__var__var__19__y__30533__30535__30607__30609__30611__30613__30615,Vvar__0__R__30428)
=> p(happ(happ(Vvar__7__req__30449,happ(happ(Vvar__5__rsub__30441,Vvar__var__var__var__var__var__var__18__x__30532__30534__30606__30608__30610__30612__30614),Vvar__var__var__var__var__var__var__19__y__30533__30535__30607__30609__30611__30613__30615)),happ(happ(Vvar__3__radd__30431,Vvar__var__var__var__var__var__var__18__x__30532__30534__30606__30608__30610__30612__30614),happ(Vvar__6__ropp__30446,Vvar__var__var__var__var__var__var__19__y__30533__30535__30607__30609__30611__30613__30615)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172] :
( cType___24t(Vvar__0__R__34152)
=> ( c_24__type__34292___24t(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__1__req__34153)
=> ( cType___24t(Vvar__2__C__34158)
=> ( c_24__type__34342___24t(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__3__cadd__34159)
=> ( c_24__type__34392___24t(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__4__cmul__34164)
=> ( c_24__type__34434___24t(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__5__phi__34169)
=> ( c_24__type__34484___24t(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__6__cdiv__34172)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__34204__34209__34214__34219__34224__34229__34234__34239] :
( t(Vvar__var__var__var__var__var__var__var__7__a__34204__34209__34214__34219__34224__34229__34234__34239,Vvar__2__C__34158)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__34205__34210__34215__34220__34225__34230__34235__34240] :
( t(Vvar__var__var__var__var__var__var__var__8__b__34205__34210__34215__34220__34225__34230__34235__34240,Vvar__2__C__34158)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2434547___24a9(Vvar__0__R__34152,Vvar__1__req__34153,Vvar__2__C__34158,Vvar__3__cadd__34159,Vvar__4__cmul__34164,Vvar__5__phi__34169,Vvar__6__cdiv__34172,Vvar__var__var__var__var__var__var__var__7__a__34204__34209__34214__34219__34224__34229__34234__34239,Vvar__var__var__var__var__var__var__var__8__b__34205__34210__34215__34220__34225__34230__34235__34240) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586] :
( cType___24t(Vvar__0__R__34570)
=> ( t(Vvar__1__rI__34571,Vvar__0__R__34570)
=> ( c_24__type__34672___24t(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586,Vvar__2__rmul__34572)
=> ( c_24__type__34716___24t(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586,Vvar__3__req__34577)
=> ( cType___24t(Vvar__4__Cpow__34582)
=> ( c_24__type__34752___24t(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586,Vvar__5__Cp__phi__34583)
=> ( c_24__type__34796___24t(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586,Vvar__6__rpow__34586)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__3__req__34577,Vvar__4__Cpow__34582,Vvar__5__Cp__phi__34583,Vvar__6__rpow__34586)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__34614__34616__34618__34620__34622__34624__34626__34628] :
( t(Vvar__var__var__var__var__var__var__var__7__r__34614__34616__34618__34620__34622__34624__34626__34628,Vvar__0__R__34570)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__34615__34617__34619__34621__34623__34625__34627__34629] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__34615__34617__34619__34621__34623__34625__34627__34629)
=> p(happ(happ(Vvar__3__req__34577,happ(happ(Vvar__6__rpow__34586,Vvar__var__var__var__var__var__var__var__7__r__34614__34616__34618__34620__34622__34624__34626__34628),happ(Vvar__5__Cp__phi__34583,Vvar__var__var__var__var__var__var__var__8__n__34615__34617__34619__34621__34623__34625__34627__34629))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__34570,Vvar__1__rI__34571,Vvar__2__rmul__34572,Vvar__var__var__var__var__var__var__var__7__r__34614__34616__34618__34620__34622__34624__34626__34628,Vvar__var__var__var__var__var__var__var__8__n__34615__34617__34619__34621__34623__34625__34627__34629))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258] :
( cType___24t(Vvar__0__R__31244)
=> ( c_24__type__31349___24t(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258,Vvar__1__radd__31245)
=> ( c_24__type__31379___24t(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258,Vvar__2__rmul__31250)
=> ( c_24__type__31403___24t(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258,Vvar__3__ropp__31255)
=> ( c_24__type__31433___24t(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258,Vvar__4__req__31258)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31463___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31244,c_24__type__31487___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258),Vvar__4__req__31258,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31244,Vvar__0__R__31244,Vvar__4__req__31258,Vvar__4__req__31258)),Vvar__1__radd__31245)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31520___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31244,c_24__type__31544___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258),Vvar__4__req__31258,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31244,Vvar__0__R__31244,Vvar__4__req__31258,Vvar__4__req__31258)),Vvar__2__rmul__31250)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31571___24a5(Vvar__0__R__31244,Vvar__1__radd__31245,Vvar__2__rmul__31250,Vvar__3__ropp__31255,Vvar__4__req__31258),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31244,Vvar__0__R__31244,Vvar__4__req__31258,Vvar__4__req__31258),Vvar__3__ropp__31255)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626] :
( cType___24t(Vvar__0__R__31574)
=> ( t(Vvar__1__rO__31575,Vvar__0__R__31574)
=> ( t(Vvar__2__rI__31576,Vvar__0__R__31574)
=> ( c_24__type__31970___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__3__radd__31577)
=> ( c_24__type__32183___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__4__rmul__31582)
=> ( c_24__type__32396___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__5__rsub__31587)
=> ( c_24__type__32591___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__6__ropp__31592)
=> ( c_24__type__32804___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__7__req__31595)
=> ( cType___24t(Vvar__8__C__31600)
=> ( t(Vvar__9__cO__31601,Vvar__8__C__31600)
=> ( t(Vvar__10__cI__31602,Vvar__8__C__31600)
=> ( c_24__type__33017___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__11__cadd__31603)
=> ( c_24__type__33230___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__12__cmul__31608)
=> ( c_24__type__33443___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__13__csub__31613)
=> ( c_24__type__33638___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__14__copp__31618)
=> ( c_24__type__33851___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__15__ceqb__31621)
=> ( c_24__type__34046___24t(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626,Vvar__16__phi__31626)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__31574,Vvar__1__rO__31575,Vvar__2__rI__31576,Vvar__3__radd__31577,Vvar__4__rmul__31582,Vvar__5__rsub__31587,Vvar__6__ropp__31592,Vvar__7__req__31595,Vvar__8__C__31600,Vvar__9__cO__31601,Vvar__10__cI__31602,Vvar__11__cadd__31603,Vvar__12__cmul__31608,Vvar__13__csub__31613,Vvar__14__copp__31618,Vvar__15__ceqb__31621,Vvar__16__phi__31626)
=> ( p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,Vvar__9__cO__31601)),Vvar__1__rO__31575))
& p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,Vvar__10__cI__31602)),Vvar__2__rI__31576))
& ! [Vvar__var__var__var__var__var__var__19__x__31688__31690__31712__31714__31716__31718__31720] :
( t(Vvar__var__var__var__var__var__var__19__x__31688__31690__31712__31714__31716__31718__31720,Vvar__8__C__31600)
=> ! [Vvar__var__var__var__var__var__var__20__y__31689__31691__31713__31715__31717__31719__31721] :
( t(Vvar__var__var__var__var__var__var__20__y__31689__31691__31713__31715__31717__31719__31721,Vvar__8__C__31600)
=> p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,happ(happ(Vvar__11__cadd__31603,Vvar__var__var__var__var__var__var__19__x__31688__31690__31712__31714__31716__31718__31720),Vvar__var__var__var__var__var__var__20__y__31689__31691__31713__31715__31717__31719__31721))),happ(happ(Vvar__3__radd__31577,happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__19__x__31688__31690__31712__31714__31716__31718__31720)),happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__20__y__31689__31691__31713__31715__31717__31719__31721)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__31693__31695__31722__31724__31726__31728__31730] :
( t(Vvar__var__var__var__var__var__var__20__x__31693__31695__31722__31724__31726__31728__31730,Vvar__8__C__31600)
=> ! [Vvar__var__var__var__var__var__var__21__y__31694__31696__31723__31725__31727__31729__31731] :
( t(Vvar__var__var__var__var__var__var__21__y__31694__31696__31723__31725__31727__31729__31731,Vvar__8__C__31600)
=> p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,happ(happ(Vvar__13__csub__31613,Vvar__var__var__var__var__var__var__20__x__31693__31695__31722__31724__31726__31728__31730),Vvar__var__var__var__var__var__var__21__y__31694__31696__31723__31725__31727__31729__31731))),happ(happ(Vvar__5__rsub__31587,happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__20__x__31693__31695__31722__31724__31726__31728__31730)),happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__21__y__31694__31696__31723__31725__31727__31729__31731)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__31698__31700__31732__31734__31736__31738__31740] :
( t(Vvar__var__var__var__var__var__var__21__x__31698__31700__31732__31734__31736__31738__31740,Vvar__8__C__31600)
=> ! [Vvar__var__var__var__var__var__var__22__y__31699__31701__31733__31735__31737__31739__31741] :
( t(Vvar__var__var__var__var__var__var__22__y__31699__31701__31733__31735__31737__31739__31741,Vvar__8__C__31600)
=> p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,happ(happ(Vvar__12__cmul__31608,Vvar__var__var__var__var__var__var__21__x__31698__31700__31732__31734__31736__31738__31740),Vvar__var__var__var__var__var__var__22__y__31699__31701__31733__31735__31737__31739__31741))),happ(happ(Vvar__4__rmul__31582,happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__21__x__31698__31700__31732__31734__31736__31738__31740)),happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__22__y__31699__31701__31733__31735__31737__31739__31741)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__31703__31704__31742__31743__31744__31745__31746] :
( t(Vvar__var__var__var__var__var__var__22__x__31703__31704__31742__31743__31744__31745__31746,Vvar__8__C__31600)
=> p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,happ(Vvar__14__copp__31618,Vvar__var__var__var__var__var__var__22__x__31703__31704__31742__31743__31744__31745__31746))),happ(Vvar__6__ropp__31592,happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__var__22__x__31703__31704__31742__31743__31744__31745__31746)))) )
& ! [Vvar__var__var__var__var__var__23__x__31706__31709__31747__31750__31753__31756] :
( t(Vvar__var__var__var__var__var__23__x__31706__31709__31747__31750__31753__31756,Vvar__8__C__31600)
=> ! [Vvar__var__var__var__var__var__24__y__31707__31710__31748__31751__31754__31757] :
( t(Vvar__var__var__var__var__var__24__y__31707__31710__31748__31751__31754__31757,Vvar__8__C__31600)
=> ( happ(happ(Vvar__15__ceqb__31621,Vvar__var__var__var__var__var__23__x__31706__31709__31747__31750__31753__31756),Vvar__var__var__var__var__var__24__y__31707__31710__31748__31751__31754__31757) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__31595,happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__23__x__31706__31709__31747__31750__31753__31756)),happ(Vvar__16__phi__31626,Vvar__var__var__var__var__var__24__y__31707__31710__31748__31751__31754__31757))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__34058,Vvar__1__copp__34059,Vvar__2__ceqb__34062,Vvar__3__get__sign__34067] :
( cType___24t(Vvar__0__C__34058)
=> ( c_24__type__34114___24t(Vvar__0__C__34058,Vvar__1__copp__34059,Vvar__2__ceqb__34062,Vvar__3__get__sign__34067,Vvar__1__copp__34059)
=> ( c_24__type__34133___24t(Vvar__0__C__34058,Vvar__1__copp__34059,Vvar__2__ceqb__34062,Vvar__3__get__sign__34067,Vvar__2__ceqb__34062)
=> ( c_24__type__34147___24t(Vvar__0__C__34058,Vvar__1__copp__34059,Vvar__2__ceqb__34062,Vvar__3__get__sign__34067,Vvar__3__get__sign__34067)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__34058,Vvar__1__copp__34059,Vvar__2__ceqb__34062,Vvar__3__get__sign__34067)
=> ( ! [Vvar__var__var__var__var__var__4__c__34084__34087__34090__34093__34096__34099] :
( t(Vvar__var__var__var__var__var__4__c__34084__34087__34090__34093__34096__34099,Vvar__0__C__34058)
=> ! [Vvar__var__var__var__var__var__5__c_27__34085__34088__34091__34094__34097__34100] :
( t(Vvar__var__var__var__var__var__5__c_27__34085__34088__34091__34094__34097__34100,Vvar__0__C__34058)
=> ( happ(Vvar__3__get__sign__34067,Vvar__var__var__var__var__var__4__c__34084__34087__34090__34093__34096__34099) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__34058,Vvar__var__var__var__var__var__5__c_27__34085__34088__34091__34094__34097__34100)
=> happ(happ(Vvar__2__ceqb__34062,Vvar__var__var__var__var__var__4__c__34084__34087__34090__34093__34096__34099),happ(Vvar__1__copp__34059,Vvar__var__var__var__var__var__5__c_27__34085__34088__34091__34094__34097__34100)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033] :
( cType___24t(Vvar__0__R__31022)
=> ( c_24__type__31108___24t(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033,Vvar__1__radd__31023)
=> ( c_24__type__31131___24t(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033,Vvar__2__rmul__31028)
=> ( c_24__type__31154___24t(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033,Vvar__3__req__31033)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31177___24a4(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31022,c_24__type__31195___24a4(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033),Vvar__3__req__31033,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31022,Vvar__0__R__31022,Vvar__3__req__31033,Vvar__3__req__31033)),Vvar__1__radd__31023)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31221___24a4(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31022,c_24__type__31239___24a4(Vvar__0__R__31022,Vvar__1__radd__31023,Vvar__2__rmul__31028,Vvar__3__req__31033),Vvar__3__req__31033,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__31022,Vvar__0__R__31022,Vvar__3__req__31033,Vvar__3__req__31033)),Vvar__2__rmul__31028)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.arith_lems.R_ceil_log2_S',axiom,
! [Vvar__0__n__60033,Vvar__1___24Anonymous__60034,VX60035] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60033)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__60034)
=> ( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(Vvar__0__n__60033,Vvar__1___24Anonymous__60034,VX60035)
=> ( ? [Vvar__0__n__60036] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60036)
& Vvar__0__n__60036 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__60034 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__0__n__60033 = cCoq_2eInit_2eDatatypes_2eO
& VX60035 = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__60036) )
| ? [Vvar__0__n__60038] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60038)
& ? [Vvar__1____x__60039] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1____x__60039)
& Vvar__0__n__60038 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1____x__60039)
& ? [Vvar__3____res__60041] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3____res__60041)
& ? [Vvar__4___24Anonymous__60042] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0__n__60038),Vvar__3____res__60041,Vvar__4___24Anonymous__60042)
& Vvar__1___24Anonymous__60034 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3____res__60041)
& Vvar__0__n__60033 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1____x__60039)
& VX60035 = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__60038,Vvar__1____x__60039,Vvar__3____res__60041,Vvar__4___24Anonymous__60042) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.arith_lems.R_floor_log2_S',axiom,
! [Vvar__0__n__60065,Vvar__1___24Anonymous__60066,VX60067] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60065)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__60066)
=> ( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(Vvar__0__n__60065,Vvar__1___24Anonymous__60066,VX60067)
=> ( ? [Vvar__0__n__60068] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60068)
& Vvar__0__n__60068 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__60066 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__0__n__60065 = cCoq_2eInit_2eDatatypes_2eO
& VX60067 = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__60068) )
| ? [Vvar__0__n__60070] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__60070)
& ? [Vvar__1__n_27__60071] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n_27__60071)
& Vvar__0__n__60070 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__n_27__60071)
& ? [Vvar__3____res__60073] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3____res__60073)
& ? [Vvar__4___24Anonymous__60074] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__1__n_27__60071),Vvar__3____res__60073,Vvar__4___24Anonymous__60074)
& Vvar__1___24Anonymous__60066 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3____res__60073)
& Vvar__0__n__60065 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__n_27__60071)
& VX60067 = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__60070,Vvar__1__n_27__60071,Vvar__3____res__60073,Vvar__4___24Anonymous__60074) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.InP',axiom,
! [Vvar__0__X__35634,Vvar__1__P__35635,Vvar__2___24Anonymous__35638] :
( cType___24t(Vvar__0__X__35634)
=> ( c_24__type__35658___24t(Vvar__0__X__35634,Vvar__1__P__35635,Vvar__2___24Anonymous__35638,Vvar__1__P__35635)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__35634,Vvar__2___24Anonymous__35638)
=> ( cQuicksortComplexity_2elist__utils_2eInP___24a3(Vvar__0__X__35634,Vvar__1__P__35635,Vvar__2___24Anonymous__35638)
=> ( ? [Vvar__2__x__35644] :
( t(Vvar__2__x__35644,Vvar__0__X__35634)
& ? [Vvar__3__t__35645] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__35634,Vvar__3__t__35645)
& p(happ(Vvar__1__P__35635,Vvar__2__x__35644))
& Vvar__2___24Anonymous__35638 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__X__35634,Vvar__2__x__35644,Vvar__3__t__35645) ) )
| ? [Vvar__2__x__35651] :
( t(Vvar__2__x__35651,Vvar__0__X__35634)
& ? [Vvar__3__t__35652] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__X__35634,Vvar__3__t__35652)
& cQuicksortComplexity_2elist__utils_2eInP___24a3(Vvar__0__X__35634,Vvar__1__P__35635,Vvar__3__t__35652)
& Vvar__2___24Anonymous__35638 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__X__35634,Vvar__2__x__35651,Vvar__3__t__35652) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.NoDupL',axiom,
! [Vvar__0__A__39512,Vvar__1___24Anonymous__39513] :
( cType___24t(Vvar__0__A__39512)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__39512),Vvar__1___24Anonymous__39513)
=> ( cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(Vvar__0__A__39512,Vvar__1___24Anonymous__39513)
=> ( Vvar__1___24Anonymous__39513 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__39512))
| ? [Vvar__1__l__39517] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__39512,Vvar__1__l__39517)
& ? [Vvar__2__ll__39518] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__39512),Vvar__2__ll__39518)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__39512,Vvar__1__l__39517)
& ! [Vvar__var__var__4__x__39521__39523__39526] :
( t(Vvar__var__var__4__x__39521__39523__39526,Vvar__0__A__39512)
=> ( cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__39512,Vvar__var__var__4__x__39521__39523__39526,Vvar__1__l__39517)
=> ~ cQuicksortComplexity_2elist__utils_2eInP___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__39512),cCoq_2eLists_2eList_2eIn___24a2(Vvar__0__A__39512,Vvar__var__var__4__x__39521__39523__39526),Vvar__2__ll__39518) ) )
& cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(Vvar__0__A__39512,Vvar__2__ll__39518)
& Vvar__1___24Anonymous__39513 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__A__39512),Vvar__1__l__39517,Vvar__2__ll__39518) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.elemsR',axiom,
! [Vvar__0__A__15101,Vvar__1__B__15102,Vvar__2__R__15103,Vvar__3___24Anonymous__15108,Vvar__4___24Anonymous__15109] :
( cType___24t(Vvar__0__A__15101)
=> ( cType___24t(Vvar__1__B__15102)
=> ( c_24__type__15146___24t(Vvar__0__A__15101,Vvar__1__B__15102,Vvar__2__R__15103,Vvar__3___24Anonymous__15108,Vvar__4___24Anonymous__15109,Vvar__2__R__15103)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__15101,Vvar__3___24Anonymous__15108)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__15102,Vvar__4___24Anonymous__15109)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__15101,Vvar__1__B__15102,Vvar__2__R__15103,Vvar__3___24Anonymous__15108,Vvar__4___24Anonymous__15109)
=> ( ( Vvar__4___24Anonymous__15109 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__15102)
& Vvar__3___24Anonymous__15108 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__15101) )
| ? [Vvar__3__a__15125] :
( t(Vvar__3__a__15125,Vvar__0__A__15101)
& ? [Vvar__4__b__15126] :
( t(Vvar__4__b__15126,Vvar__1__B__15102)
& p(happ(happ(Vvar__2__R__15103,Vvar__3__a__15125),Vvar__4__b__15126))
& ? [Vvar__6__l__15128] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__15101,Vvar__6__l__15128)
& ? [Vvar__7__l_27__15129] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__15102,Vvar__7__l_27__15129)
& cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__15101,Vvar__1__B__15102,Vvar__2__R__15103,Vvar__6__l__15128,Vvar__7__l_27__15129)
& Vvar__4___24Anonymous__15109 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__15102,Vvar__4__b__15126,Vvar__7__l_27__15129)
& Vvar__3___24Anonymous__15108 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__15101,Vvar__3__a__15125,Vvar__6__l__15128) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.merges_spec',axiom,
! [Vvar__0__T__18609,Vvar__1___24Anonymous__18610,Vvar__2___24Anonymous__18611,Vvar__3___24Anonymous__18612] :
( cType___24t(Vvar__0__T__18609)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__1___24Anonymous__18610)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__2___24Anonymous__18611)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609),Vvar__3___24Anonymous__18612)
=> ( cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__18609,Vvar__1___24Anonymous__18610,Vvar__2___24Anonymous__18611,Vvar__3___24Anonymous__18612)
=> ( ? [Vvar__1__x__18615] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__1__x__18615)
& Vvar__3___24Anonymous__18612 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609),Vvar__1__x__18615,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609)))
& Vvar__2___24Anonymous__18611 = Vvar__1__x__18615
& Vvar__1___24Anonymous__18610 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__18609) )
| ? [Vvar__1__x__18617] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__1__x__18617)
& Vvar__3___24Anonymous__18612 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609),Vvar__1__x__18617,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609)))
& Vvar__2___24Anonymous__18611 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__18609)
& Vvar__1___24Anonymous__18610 = Vvar__1__x__18617 )
| ? [Vvar__1__x__18619] :
( t(Vvar__1__x__18619,Vvar__0__T__18609)
& ? [Vvar__2__y__18620] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__2__y__18620)
& ? [Vvar__3__h__18621] :
( t(Vvar__3__h__18621,Vvar__0__T__18609)
& ? [Vvar__4__t__18622] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__18609,Vvar__4__t__18622)
& ? [Vvar__5__r__18623] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609),Vvar__5__r__18623)
& ? [Vvar__6__r_27__18624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__18609),Vvar__6__r_27__18624)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__18609,Vvar__2__y__18620,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__18609,Vvar__3__h__18621,Vvar__4__t__18622),Vvar__5__r__18623)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__18609,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__18609,Vvar__1__x__18619,Vvar__2__y__18620),Vvar__4__t__18622,Vvar__6__r_27__18624)
& Vvar__3___24Anonymous__18612 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119___24a8(Vvar__0__T__18609,Vvar__1___24Anonymous__18610,Vvar__2___24Anonymous__18611,Vvar__3___24Anonymous__18612,Vvar__1__x__18619,Vvar__3__h__18621,Vvar__5__r__18623,Vvar__6__r_27__18624)
& Vvar__2___24Anonymous__18611 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__18609,Vvar__3__h__18621,Vvar__4__t__18622)
& Vvar__1___24Anonymous__18610 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__18609,Vvar__1__x__18619,Vvar__2__y__18620) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.nat_below.natBelow',axiom,
! [Vvar__0___24Anonymous__87,VX88] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__87)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vvar__0___24Anonymous__87,VX88)
=> ? [Vvar__0__v__89] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__89)
& ? [Vvar__1__p__90] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__90)
& Vvar__0___24Anonymous__87 = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24137___24a3(Vvar__0___24Anonymous__87,Vvar__0__v__89,Vvar__1__p__90))
& VX88 = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__89,Vvar__1__p__90) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.skip_list.SkipList',axiom,
! [Vvar__0__T__35660,Vvar__1___24Anonymous__35661,Vvar__2___24Anonymous__35662] :
( cType___24t(Vvar__0__T__35660)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__1___24Anonymous__35661)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__2___24Anonymous__35662)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(Vvar__0__T__35660,Vvar__1___24Anonymous__35661,Vvar__2___24Anonymous__35662)
=> ( ? [Vvar__1__x__35665] :
( t(Vvar__1__x__35665,Vvar__0__T__35660)
& ? [Vvar__2__l__35666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__2__l__35666)
& ? [Vvar__3__l_27__35667] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__3__l_27__35667)
& cQuicksortComplexity_2eskip__list_2eSkipList___24a3(Vvar__0__T__35660,Vvar__2__l__35666,Vvar__3__l_27__35667)
& Vvar__2___24Anonymous__35662 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__35660,Vvar__1__x__35665,Vvar__3__l_27__35667)
& Vvar__1___24Anonymous__35661 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__35660,Vvar__1__x__35665,Vvar__2__l__35666) ) ) )
| ? [Vvar__1__x__35670] :
( t(Vvar__1__x__35670,Vvar__0__T__35660)
& ? [Vvar__2__l__35671] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__2__l__35671)
& ? [Vvar__3__l_27__35672] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__3__l_27__35672)
& cQuicksortComplexity_2eskip__list_2eSkipList___24a3(Vvar__0__T__35660,Vvar__2__l__35671,Vvar__3__l_27__35672)
& Vvar__2___24Anonymous__35662 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__35660,Vvar__1__x__35670,Vvar__3__l_27__35672)
& Vvar__1___24Anonymous__35661 = Vvar__2__l__35671 ) ) )
| ? [Vvar__1__l__35675] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__35660,Vvar__1__l__35675)
& Vvar__2___24Anonymous__35662 = Vvar__1__l__35675
& Vvar__1___24Anonymous__35661 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__35660) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.sort_order.E',axiom,
! [VX455] :
( cQuicksortComplexity_2esort__order_2eE___24t(VX455)
=> ? [Vvar__0__Ec__456] :
( cType___24t(Vvar__0__Ec__456)
& ? [Vvar__1__Ecmp__457] :
( c_24__type__271___24t(Vvar__0__Ec__456,Vvar__1__Ecmp__457)
& ! [Vvar__var__2__x__463__465] :
( t(Vvar__var__2__x__463__465,Vvar__0__Ec__456)
=> ! [Vvar__var__3__y__464__466] :
( t(Vvar__var__3__y__464__466,Vvar__0__Ec__456)
=> happ(happ(Vvar__1__Ecmp__457,Vvar__var__2__x__463__465),Vvar__var__3__y__464__466) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vvar__1__Ecmp__457,Vvar__var__3__y__464__466),Vvar__var__2__x__463__465)) ) )
& ! [Vvar__var__3__x__468__474] :
( t(Vvar__var__3__x__468__474,Vvar__0__Ec__456)
=> ! [Vvar__var__4__y__469__475] :
( t(Vvar__var__4__y__469__475,Vvar__0__Ec__456)
=> ! [Vvar__var__5__z__471__477] :
( t(Vvar__var__5__z__471__477,Vvar__0__Ec__456)
=> ! [Vvar__var__6__c__470__476] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__6__c__470__476)
=> ( happ(happ(Vvar__1__Ecmp__457,Vvar__var__3__x__468__474),Vvar__var__4__y__469__475) = Vvar__var__6__c__470__476
=> ( happ(happ(Vvar__1__Ecmp__457,Vvar__var__4__y__469__475),Vvar__var__5__z__471__477) = Vvar__var__6__c__470__476
=> happ(happ(Vvar__1__Ecmp__457,Vvar__var__3__x__468__474),Vvar__var__5__z__471__477) = Vvar__var__6__c__470__476 ) ) ) ) ) )
& ! [Vvar__var__4__x__481__487] :
( t(Vvar__var__4__x__481__487,Vvar__0__Ec__456)
=> ! [Vvar__var__5__y__482__488] :
( t(Vvar__var__5__y__482__488,Vvar__0__Ec__456)
=> ! [Vvar__var__6__z__483__489] :
( t(Vvar__var__6__z__483__489,Vvar__0__Ec__456)
=> ! [Vvar__var__7__c__484__490] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__7__c__484__490)
=> ( happ(happ(Vvar__1__Ecmp__457,Vvar__var__4__x__481__487),Vvar__var__5__y__482__488) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vvar__1__Ecmp__457,Vvar__var__5__y__482__488),Vvar__var__6__z__483__489) = Vvar__var__7__c__484__490
=> happ(happ(Vvar__1__Ecmp__457,Vvar__var__4__x__481__487),Vvar__var__6__z__483__489) = Vvar__var__7__c__484__490 ) ) ) ) ) )
& VX455 = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__456,Vvar__1__Ecmp__457) ) ) ) ).
fof('$_inversion_QuicksortComplexity.util.pair_rel',axiom,
! [Vvar__0__A__19982,Vvar__1__B__19983,Vvar__2__Ra__19984,Vvar__3__Rb__19985,Vvar__1___24Anonymous__19986,Vvar__2___24Anonymous__19987] :
( cType___24t(Vvar__0__A__19982)
=> ( cType___24t(Vvar__1__B__19983)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__19982,Vvar__2__Ra__19984)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__1__B__19983,Vvar__3__Rb__19985)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__1___24Anonymous__19986)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__2___24Anonymous__19987)
=> ( cQuicksortComplexity_2eutil_2epair__rel___24a6(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__2__Ra__19984,Vvar__3__Rb__19985,Vvar__1___24Anonymous__19986,Vvar__2___24Anonymous__19987)
=> ( ? [Vvar__4__a__19993] :
( t(Vvar__4__a__19993,Vvar__0__A__19982)
& ? [Vvar__5__a_27__19994] :
( t(Vvar__5__a_27__19994,Vvar__0__A__19982)
& ? [Vvar__6__b__19995] :
( t(Vvar__6__b__19995,Vvar__1__B__19983)
& p(happ(happ(Vvar__2__Ra__19984,Vvar__4__a__19993),Vvar__5__a_27__19994))
& Vvar__2___24Anonymous__19987 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__5__a_27__19994,Vvar__6__b__19995)
& Vvar__1___24Anonymous__19986 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__4__a__19993,Vvar__6__b__19995) ) ) )
| ? [Vvar__4__a__20001] :
( t(Vvar__4__a__20001,Vvar__0__A__19982)
& ? [Vvar__5__b__20002] :
( t(Vvar__5__b__20002,Vvar__1__B__19983)
& ? [Vvar__6__b_27__20003] :
( t(Vvar__6__b_27__20003,Vvar__1__B__19983)
& p(happ(happ(Vvar__3__Rb__19985,Vvar__5__b__20002),Vvar__6__b_27__20003))
& Vvar__2___24Anonymous__19987 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__4__a__20001,Vvar__6__b_27__20003)
& Vvar__1___24Anonymous__19986 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__19982,Vvar__1__B__19983,Vvar__4__a__20001,Vvar__5__b__20002) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.vec.Permutation',axiom,
! [Vvar__0__A__60097,Vvar__1__n__60098,Vvar__2___24Anonymous__60099,Vvar__3___24Anonymous__60100] :
( cType___24t(Vvar__0__A__60097)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__60098)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__1__n__60098,Vvar__2___24Anonymous__60099)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__1__n__60098,Vvar__3___24Anonymous__60100)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(Vvar__0__A__60097,Vvar__1__n__60098,Vvar__2___24Anonymous__60099,Vvar__3___24Anonymous__60100)
=> ( ( Vvar__3___24Anonymous__60100 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__60097)
& Vvar__2___24Anonymous__60099 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__60097)
& Vvar__1__n__60098 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1__x__60104] :
( t(Vvar__1__x__60104,Vvar__0__A__60097)
& ? [Vvar__2__n__60105] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__60105)
& ? [Vvar__3__v__60106] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__2__n__60105,Vvar__3__v__60106)
& ? [Vvar__4__v_27__60107] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__2__n__60105,Vvar__4__v_27__60107)
& cQuicksortComplexity_2evec_2ePermutation___24a4(Vvar__0__A__60097,Vvar__2__n__60105,Vvar__3__v__60106,Vvar__4__v_27__60107)
& Vvar__3___24Anonymous__60100 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__1__x__60104,Vvar__2__n__60105,Vvar__4__v_27__60107)
& Vvar__2___24Anonymous__60099 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__1__x__60104,Vvar__2__n__60105,Vvar__3__v__60106)
& Vvar__1__n__60098 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__60105) ) ) ) )
| ? [Vvar__1__x__60110] :
( t(Vvar__1__x__60110,Vvar__0__A__60097)
& ? [Vvar__2__y__60111] :
( t(Vvar__2__y__60111,Vvar__0__A__60097)
& ? [Vvar__3__n__60112] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__60112)
& ? [Vvar__4__l__60113] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__3__n__60112,Vvar__4__l__60113)
& Vvar__3___24Anonymous__60100 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__1__x__60110,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__n__60112),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__2__y__60111,Vvar__3__n__60112,Vvar__4__l__60113))
& Vvar__2___24Anonymous__60099 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__2__y__60111,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__n__60112),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__60097,Vvar__1__x__60110,Vvar__3__n__60112,Vvar__4__l__60113))
& Vvar__1__n__60098 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__n__60112)) ) ) ) )
| ? [Vvar__1__n__60115] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__60115)
& ? [Vvar__2__l__60116] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__1__n__60115,Vvar__2__l__60116)
& ? [Vvar__3__l_27__60117] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__1__n__60115,Vvar__3__l_27__60117)
& ? [Vvar__4__l_27_27__60118] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__60097,Vvar__1__n__60115,Vvar__4__l_27_27__60118)
& cQuicksortComplexity_2evec_2ePermutation___24a4(Vvar__0__A__60097,Vvar__1__n__60115,Vvar__2__l__60116,Vvar__3__l_27__60117)
& cQuicksortComplexity_2evec_2ePermutation___24a4(Vvar__0__A__60097,Vvar__1__n__60115,Vvar__3__l_27__60117,Vvar__4__l_27_27__60118)
& Vvar__3___24Anonymous__60100 = Vvar__4__l_27_27__60118
& Vvar__2___24Anonymous__60099 = Vvar__2__l__60116
& Vvar__1__n__60098 = Vvar__1__n__60115 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.vec.sorted',axiom,
! [Vvar__0__X__1127,Vvar__1__Xle__1128,Vvar__2__n__1133,Vvar__3___24Anonymous__1134] :
( cType___24t(Vvar__0__X__1127)
=> ( c_24__type__1172___24t(Vvar__0__X__1127,Vvar__1__Xle__1128,Vvar__2__n__1133,Vvar__3___24Anonymous__1134,Vvar__1__Xle__1128)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__1133)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__X__1127,Vvar__2__n__1133,Vvar__3___24Anonymous__1134)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(Vvar__0__X__1127,Vvar__1__Xle__1128,Vvar__2__n__1133,Vvar__3___24Anonymous__1134)
=> ( ( Vvar__3___24Anonymous__1134 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__X__1127)
& Vvar__2__n__1133 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__x__1148] :
( t(Vvar__2__x__1148,Vvar__0__X__1127)
& Vvar__3___24Anonymous__1134 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__1127,Vvar__2__x__1148,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__X__1127))
& Vvar__2__n__1133 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__2__a__1155] :
( t(Vvar__2__a__1155,Vvar__0__X__1127)
& ? [Vvar__3__b__1156] :
( t(Vvar__3__b__1156,Vvar__0__X__1127)
& ? [Vvar__4__n__1157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__n__1157)
& ? [Vvar__5__t__1158] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__X__1127,Vvar__4__n__1157,Vvar__5__t__1158)
& p(happ(happ(Vvar__1__Xle__1128,Vvar__2__a__1155),Vvar__3__b__1156))
& cQuicksortComplexity_2evec_2esorted___24a4(Vvar__0__X__1127,Vvar__1__Xle__1128,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__1157),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__1127,Vvar__3__b__1156,Vvar__4__n__1157,Vvar__5__t__1158))
& Vvar__3___24Anonymous__1134 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__1127,Vvar__2__a__1155,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__1157),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__X__1127,Vvar__3__b__1156,Vvar__4__n__1157,Vvar__5__t__1158))
& Vvar__2__n__1133 = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__4__n__1157)) ) ) ) ) ) ) ) ) ) ) ).
fof('$_lam_1070',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1070___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2evec_2enatBelow0__rect___24a2(Vv__CANONICAL__2,Vv__CANONICAL__0) ).
fof('$_lam_1076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__1076___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2evec_2enatBelow__S__bla___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__5,Vv__CANONICAL__2,cQuicksortComplexity_2evec_2enth___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_1212',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1212___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0) ).
fof('$_lam_1223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1223___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2evec_2einsert__ordered___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__3,cQuicksortComplexity_2evec_2einsertion__sort___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,cQuicksortComplexity_2evec_2etail___24a3(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__4))) ).
fof('$_lam_15194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__15194___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eLists_2eList_2emap___24a4(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2epair___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) ).
fof('$_lam_18584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__18584___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2efst___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2esnd___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2))) ).
fof('$_lam_18601',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__18601___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eProgram_2eBasics_2ecompose___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)),cQuicksortComplexity_2elist__utils_2econcat___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)),cCoq_2eLists_2eList_2emap___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)),cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ).
fof('$_lam_19843',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__19843___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cProp ).
fof('$_lam_19867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__19867___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,cCoq_2eLists_2eList_2efilter___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2efst___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),cCoq_2eInit_2eDatatypes_2esnd___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2))) ).
fof('$_lam_19872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__19872___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,cCoq_2eLists_2eList_2efilter___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2efst___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),cCoq_2eInit_2eDatatypes_2esnd___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2))) ).
fof('$_lam_22813',axiom,
! [Vv__CANONICAL__0] : c_24__lam__22813___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_22814',axiom,
! [Vv__CANONICAL__0] : c_24__lam__22814___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2ediv2 ).
fof('$_lam_3155',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__3155___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cQuicksortComplexity_2esort__order_2eEleb___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_lam_3159',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__3159___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cQuicksortComplexity_2esort__order_2eEgeb___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_lam_35806',axiom,
! [Vv__CANONICAL__0] : c_24__lam__35806___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eFalse__rect___24a2(cCoq_2eVectors_2eFin_2et___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eArith_2ePeanoNat_2eNat_2enlt__0__r___24a1(Vv__CANONICAL__0)) ).
fof('$_lam_35808',axiom,
! [Vv__CANONICAL__0] : c_24__lam__35808___24a1(Vv__CANONICAL__0) = cCoq_2eVectors_2eFin_2eF1___24a1(Vv__CANONICAL__0) ).
fof('$_lam_35811',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__35811___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eVectors_2eFin_2eFS___24a2(Vv__CANONICAL__0,cCoq_2eVectors_2eFin_2eof__nat__lt___24a3(Vv__CANONICAL__1,Vv__CANONICAL__0,cCoq_2eArith_2eLt_2elt__S__n___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0))) ).
fof('$_lam_363',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__363___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eeq__rec__r___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cQuicksortComplexity_2enat__below_2enatBelow,Vv__CANONICAL__2,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),cQuicksortComplexity_2evec_2etrans__plus__n__Sm___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ).
fof('$_lam_38501',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__38501___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_38533',axiom,
! [Vv__CANONICAL__0] : c_24__lam__38533___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_4830',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__4830___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cQuicksortComplexity_2esort__order_2eEcmp___24a3(cT,cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__0),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_4832',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__4832___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cQuicksortComplexity_2esort__order_2eEcmp__sym___24a3(cT,cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__0),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_60122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__60122___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_60164',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__60164___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__60165] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__60165)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__60165)
& c_24__lam__60164___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__60165) ) ) ) ).
fof('$_lam_60171',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__60171___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__60172] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__60172)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__60172)
& c_24__lam__60171___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__60172) ) ) ) ).
fof('$_lam_60175',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__60175___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__60176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__60176)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__60176)
& c_24__lam__60175___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_70419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__70419___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eFalse__ind___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_70695',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__70716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__1)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)
& c_24__lam__70695___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) )
| ? [Vvar__1__h__70700] :
( t(Vvar__1__h__70700,Vv__CANONICAL__0)
& ? [Vvar__2__n__70701] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__70701)
& ? [Vvar__3___24Anonymous__70702] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vvar__2__n__70701,Vvar__3___24Anonymous__70702)
& Vv__CANONICAL__4 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vvar__1__h__70700,Vvar__2__n__70701,Vvar__3___24Anonymous__70702)
& c_24__lam__70695___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__lam__70723___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2__n__70701) ) ) ) ) ) ) ) ).
fof('$_lam_7070',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7070___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2esort__order_2eEcmp__trans___24a4(cT,cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__0),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__1),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_70723',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__70723___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eFalse__ind___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_7074',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7074___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2esort__order_2eEcmp__eq__trans__l___24a4(cT,cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__0),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__1),cindices_2econtents_2esubscript___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_70746',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__70746___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(happ(happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),cCoq_2eVectors_2eVectorDef_2erectS___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_70821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__70821___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__0 ).
fof('$_lam_70833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__70833___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 ).
fof('$_lam_70842',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__70842___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).
fof('$_lam_70844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__70844___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0) ).
fof('$_lam_70855',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__70855___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ).
fof('$_lam_70866',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__70866___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ).
fof('$_lam_70868',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__70868___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0))) ).
fof('$_lam_70879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__70879___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)),Vv__CANONICAL__4) ).
fof('$_lam_719',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__719___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cQuicksortComplexity_2evec_2enatBelow0__rect___24a2(Vv__CANONICAL__1,happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO),Vv__CANONICAL__1)) ).
fof('$_lam_72987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__72987___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__1 = cQuicksortComplexity_2enat__below_2eSnb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ) ).
fof('$_lam_73002',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73002___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_73012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__73012___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2eapp___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,cQuicksortComplexity_2evec_2etail___24a3(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_73107',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__73107___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 ).
fof('$_lam_73122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__73122___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__5,cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vv__CANONICAL__3,Vv__CANONICAL__2)) ).
fof('$_lam_73155',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73155___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__type__73158___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ).
fof('$_lam_73162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__73162___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2evec_2etail___24a2(Vv__CANONICAL__2,Vv__CANONICAL__0) ).
fof('$_lam_73181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__73181___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__5),cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(Vv__CANONICAL__4,cQuicksortComplexity_2evec_2etail___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0,Vv__CANONICAL__5))) ).
fof('$_lam_73233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73233___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eLogic_2eeq__rec__r___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),Vv__CANONICAL__2),cQuicksortComplexity_2enat__below_2enatBelow,Vv__CANONICAL__3,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)),cCoq_2eArith_2ePeanoNat_2eNat_2eadd__assoc___24a3(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)) ).
fof('$_lam_73263',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__73263___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)) ).
fof('$_lam_73293',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__73311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ( c_24__type__73322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4),Vv__CANONICAL__5)
=> ( ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)))
& happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),happ(happ(Vv__CANONICAL__1,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),Vv__CANONICAL__3))
& c_24__lam__73293___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4),Vv__CANONICAL__5) )
| ( p(happ(happ(Vv__CANONICAL__1,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),Vv__CANONICAL__3))
& happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),happ(happ(Vv__CANONICAL__1,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)),Vv__CANONICAL__3))
& c_24__lam__73293___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4),cQuicksortComplexity_2evec_2einsert__ordered___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,cQuicksortComplexity_2evec_2etail___24a3(Vv__CANONICAL__4,Vv__CANONICAL__0,Vv__CANONICAL__5))) ) ) ) ) ) ) ) ) ).
fof('$_lam_73452',axiom,
c_24__lam__73452 = cCoq_2eInit_2eLogic_2eFalse__rect___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_73454',axiom,
! [Vv__CANONICAL__0] : c_24__lam__73454___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eFalse__rect___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_73615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__73615___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eVectors_2eFin_2et___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0)) ).
fof('$_lam_73670',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__73670___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__73712__v__CANONICAL__2___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),Vv__CANONICAL__2) ).
fof('$_lam_73918',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__73918___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eFalse__ind___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_73957',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__73957___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eFalse__ind___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_74025',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__74025___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eLogic_2eFalse__rect___24a1(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_lam_74055',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__74055___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__2),Vv__CANONICAL__4) ).
fof('$_lam_74150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__74150___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2ecase0___24a4(Vv__CANONICAL__1,happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__3,Vv__CANONICAL__5) ).
fof('$_lam_74221',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__74221___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a5(Vv__CANONICAL__1,Vv__CANONICAL__7,Vv__CANONICAL__9,c_24__lam__74234___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8),c_24__lam__74282___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)) ).
fof('$_lam_74234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__74234___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4)),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)),Vv__CANONICAL__6) ).
fof('$_lam_74282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__74282___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = happ(happ(happ(happ(happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__9),cCoq_2eVectors_2eVectorDef_2erect2___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__9)),Vv__CANONICAL__5),Vv__CANONICAL__8) ).
fof('$_lam_74423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__74423___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ).
fof('$_lam_74432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__74432___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_74573',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__74573___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__0 ).
fof('$_lam_74583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__74583___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__2 ).
fof('$_lam_74632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__74632___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a6(Vv__CANONICAL__0,c_24__lam__74642___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),c_24__lam__74661___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__3) ).
fof('$_lam_74642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__74642___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__type__74645___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ).
fof('$_lam_74661',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__74661___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2enth___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) ).
fof('$_lam_74801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__74801___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a5(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,c_24__lam__74804___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3),c_24__lam__74812___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_74804',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__74804___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_74812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__74812___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ).
fof('$_lam_74837',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__74837___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a5(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__5,c_24__lam__74804___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3),c_24__lam__74849___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_74849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__74849___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__2,cCoq_2eVectors_2eVectorDef_2ereplace___24a5(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__5,Vv__CANONICAL__3,Vv__CANONICAL__1)) ).
fof('$_lam_74889',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__74889___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_lam_75009',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__75009___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0) ).
fof('$_lam_75013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__75013___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eFalse__rect___24a2(cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)),cCoq_2eArith_2ePeanoNat_2eNat_2enle__succ__0___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_75020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__75020___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__2,cCoq_2eVectors_2eVectorDef_2etake___24a5(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__2,cCoq_2eArith_2eLe_2ele__S__n___24a2(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__5)) ).
fof('$_lam_75355',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__75355___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_75401',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__75401___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__4,Vv__CANONICAL__7) ).
fof('$_lam_75535',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__75535___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__2 ).
fof('$_lam_75584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__75584___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = happ(happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__7) ).
fof('$_lam_75675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__75675___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2ecase0___24a4(Vv__CANONICAL__2,c_24__lam__75678___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__3,Vv__CANONICAL__5) ).
fof('$_lam_75678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__75678___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__0 ).
fof('$_lam_75728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__75728___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a5(Vv__CANONICAL__2,Vv__CANONICAL__7,Vv__CANONICAL__9,c_24__lam__75733___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__7),c_24__lam__75760___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)) ).
fof('$_lam_75733',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__75733___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__0 ).
fof('$_lam_75760',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9] : c_24__lam__75760___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9) = cCoq_2eVectors_2eVectorDef_2efold__left2___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__8),Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__9) ).
fof('$_lam_76031',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__76031___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__4) ).
fof('$_lam_76838',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__76838___24a1(Vv__CANONICAL__0)
<=> p(c_24False) ) ).
fof('$_lam_76867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__76867___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0) ).
fof('$_lam_76949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__76949___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1,cQuicksortComplexity_2evec_2etake___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,cQuicksortComplexity_2evec_2etail___24a3(c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__3))) ).
fof('$_lam_77034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__77034___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_77078',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__77078___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cQuicksortComplexity_2evec_2edrop___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,cQuicksortComplexity_2evec_2etail___24a3(c_24__fix__75238__v__CANONICAL__3___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__0,Vv__CANONICAL__3)) ).
fof('$_lam_77148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__77148___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_77166',axiom,
! [Vv__CANONICAL__0] : c_24__lam__77166___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2epositive ).
fof('$_lam_77167',axiom,
! [Vv__CANONICAL__0] : c_24__lam__77167___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2exO ).
fof('$_lam_7860',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__7860___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_7895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__7895___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1) ).
fof('$_lam_8048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__8048___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_827',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__827___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,cQuicksortComplexity_2evec_2enatBelow__rect___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_8872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__8872___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__8800___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_9527',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6] : c_24__lam__9527___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__6) ).
fof('$_lam_978',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__978___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__1,Vv__CANONICAL__3) ).
fof('$_lam_992',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__992___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3),happ(Vv__CANONICAL__5,cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vv__CANONICAL__4,Vv__CANONICAL__3))) ).
fof('$_prop_21049',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__21049___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_22802',axiom,
! [V0__A,V1__x,V2__y] :
( p(c_24__prop__22802___24a3(V0__A,V1__x,V2__y))
<=> V1__x = V2__y ) ).
fof('$_prop_3021',axiom,
! [V0__T,V1__n,V2__c,V3__x,V4__y] :
( p(c_24__prop__3021___24a5(V0__T,V1__n,V2__c,V3__x,V4__y))
<=> V3__x = V4__y ) ).
fof('$_prop_4272',axiom,
! [V0__P] :
( p(c_24__prop__4272___24a1(V0__P))
<=> ~ p(V0__P) ) ).
fof('$_prop_46',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__46___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_59577',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__59577___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_72988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__72988___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__1 = cQuicksortComplexity_2enat__below_2enb0___24a1(Vv__CANONICAL__0) ) ).
fof('$_prop_76816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__76816___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_76817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__76817___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_77171',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__77171___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_type_1',axiom,
! [Vvar__2] :
( c_24__type__1___24t(Vvar__2)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10',axiom,
! [Vvar__11] :
( c_24__type__10___24t(Vvar__11)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__11,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1014',axiom,
! [Vvar__1015] :
( c_24__type__1014___24t(Vvar__1015)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1017___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1028___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__1015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1017',axiom,
! [Vvar__1018] :
( c_24__type__1017___24t(Vvar__1018)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1018,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1020',axiom,
! [Vv__CANONICAL__0,Vvar__1021] :
( c_24__type__1020___24t(Vv__CANONICAL__0,Vvar__1021)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__1021,Vv__CANONICAL__1),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1))) ) ) ).
fof('$_type_1028',axiom,
! [Vv__CANONICAL__0,Vvar__1029] :
( c_24__type__1028___24t(Vv__CANONICAL__0,Vvar__1029)
<=> ! [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] :
( t(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)))
=> t(happ(happ(happ(Vvar__1029,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_1044',axiom,
! [Vvar__1045] :
( c_24__type__1044___24t(Vvar__1045)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1047___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cQuicksortComplexity_2enat__below_2enb0___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__1052___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__1045,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_1047',axiom,
! [Vv__CANONICAL__0,Vvar__1048] :
( c_24__type__1047___24t(Vv__CANONICAL__0,Vvar__1048)
<=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__1048,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1053] :
( c_24__type__1052___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1053)
<=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(Vvar__1053,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cQuicksortComplexity_2enat__below_2eSnb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))) ) ) ).
fof('$_type_10686',axiom,
! [Vvar__10687] :
( c_24__type__10686___24t(Vvar__10687)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10689___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__10687,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10689',axiom,
! [Vv__CANONICAL__0,Vvar__10690] :
( c_24__type__10689___24t(Vv__CANONICAL__0,Vvar__10690)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__10690,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1083',axiom,
! [Vvar__1084] :
( c_24__type__1083___24t(Vvar__1084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__1084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_10880',axiom,
! [Vvar__10881] :
( c_24__type__10880___24t(Vvar__10881)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10881,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10892',axiom,
! [Vvar__10893] :
( c_24__type__10892___24t(Vvar__10893)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(happ(Vvar__10893,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10895',axiom,
! [Vvar__10896] :
( c_24__type__10895___24t(Vvar__10896)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__10896,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1100',axiom,
! [Vvar__1101] :
( c_24__type__1100___24t(Vvar__1101)
<=> ! [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] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(happ(Vvar__1101,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1111',axiom,
! [Vvar__1112] :
( c_24__type__1111___24t(Vvar__1112)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__1112,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1116',axiom,
! [Vv__CANONICAL__0,Vvar__1117] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vvar__1117)
<=> ! [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__1117,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1173] :
( c_24__type__1172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1173)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1173,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_1180',axiom,
! [Vv__CANONICAL__0,Vvar__1181] :
( c_24__type__1180___24t(Vv__CANONICAL__0,Vvar__1181)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__1181,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_1206',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1207] :
( c_24__type__1206___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1207)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1207,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1242',axiom,
! [Vvar__1243] :
( c_24__type__1242___24t(Vvar__1243)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__1243,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_12512',axiom,
! [Vvar__12513] :
( c_24__type__12512___24t(Vvar__12513)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__8___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__12513,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1255] :
( c_24__type__1254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1255)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__1255,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_1271',axiom,
! [Vvar__1272] :
( c_24__type__1271___24t(Vvar__1272)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__1272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1274',axiom,
! [Vvar__1275] :
( c_24__type__1274___24t(Vvar__1275)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1275,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1277',axiom,
! [Vvar__1278] :
( c_24__type__1277___24t(Vvar__1278)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1278,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1280',axiom,
! [Vvar__1281] :
( c_24__type__1280___24t(Vvar__1281)
<=> ! [Vv__CANONICAL__0] :
( cindices_2econtents_2eIndex___24t(Vv__CANONICAL__0)
=> cQuicksortComplexity_2esort__order_2eEc___24t(cT,happ(Vvar__1281,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1343',axiom,
! [Vvar__1344] :
( c_24__type__1343___24t(Vvar__1344)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1344,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1355',axiom,
! [Vvar__1356] :
( c_24__type__1355___24t(Vvar__1356)
<=> ! [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__1356,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15059',axiom,
! [Vvar__15060] :
( c_24__type__15059___24t(Vvar__15060)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__15060,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15070',axiom,
! [Vv__CANONICAL__0,Vvar__15071] :
( c_24__type__15070___24t(Vv__CANONICAL__0,Vvar__15071)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7910___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(Vvar__15071,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15075',axiom,
! [Vv__CANONICAL__0,Vvar__15076] :
( c_24__type__15075___24t(Vv__CANONICAL__0,Vvar__15076)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__15076,Vv__CANONICAL__1)) ) ) ).
fof('$_type_15081',axiom,
! [Vvar__15082] :
( c_24__type__15081___24t(Vvar__15082)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__15082,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15099',axiom,
! [Vvar__15100] :
( c_24__type__15099___24t(Vvar__15100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15100,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__15147] :
( c_24__type__15146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__15147)
<=> ! [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__15147,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_15153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15154] :
( c_24__type__15153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15154)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__15154,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_15170',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15171] :
( c_24__type__15170___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15171)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(Vvar__15171,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_15181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15182] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15182)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__15182,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_15187',axiom,
! [Vvar__15188] :
( c_24__type__15187___24t(Vvar__15188)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__15188,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15204] :
( c_24__type__15203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15204)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__15204,Vv__CANONICAL__2)) ) ) ).
fof('$_type_158',axiom,
! [Vvar__159] :
( c_24__type__158___24t(Vvar__159)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__159,Vv__CANONICAL__0)) ) ) ).
fof('$_type_171',axiom,
! [Vvar__172] :
( c_24__type__171___24t(Vvar__172)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__172,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1843',axiom,
! [Vvar__1844] :
( c_24__type__1843___24t(Vvar__1844)
<=> ! [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__1844,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1846',axiom,
! [Vvar__1847] :
( c_24__type__1846___24t(Vvar__1847)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1847,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18559] :
( c_24__type__18558___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18559)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__18559,Vv__CANONICAL__2)) ) ) ).
fof('$_type_18586',axiom,
! [Vvar__18587] :
( c_24__type__18586___24t(Vvar__18587)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)),happ(happ(Vvar__18587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_18598',axiom,
! [Vvar__18599] :
( c_24__type__18598___24t(Vvar__18599)
<=> ! [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(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__18599,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18603',axiom,
! [Vvar__18604] :
( c_24__type__18603___24t(Vvar__18604)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(Vvar__18604,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1922] :
( c_24__type__1921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1922)
<=> ! [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__1922,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_1940',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1941] :
( c_24__type__1940___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1941)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1941,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_19443',axiom,
! [Vvar__19444] :
( c_24__type__19443___24t(Vvar__19444)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__19444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1960',axiom,
! [Vvar__1961] :
( c_24__type__1960___24t(Vvar__1961)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__1961,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_19781',axiom,
! [Vvar__19782] :
( c_24__type__19781___24t(Vvar__19782)
<=> ! [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(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__19782,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_19829',axiom,
! [Vv__CANONICAL__0,Vvar__19830] :
( c_24__type__19829___24t(Vv__CANONICAL__0,Vvar__19830)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(Vvar__19830,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19839',axiom,
! [Vv__CANONICAL__0,Vvar__19840] :
( c_24__type__19839___24t(Vv__CANONICAL__0,Vvar__19840)
<=> ! [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(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(Vvar__19840,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_19932',axiom,
! [Vvar__19933] :
( c_24__type__19932___24t(Vvar__19933)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__19937___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__19952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__19933,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__5)),happ(Vv__CANONICAL__3,Vv__CANONICAL__6))) ) ) ) ) ) ) ) ) ).
fof('$_type_19937',axiom,
! [Vv__CANONICAL__0,Vvar__19938] :
( c_24__type__19937___24t(Vv__CANONICAL__0,Vvar__19938)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(happ(Vvar__19938,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_19952',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19953] :
( c_24__type__19952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19953)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__19953,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_19971',axiom,
! [Vvar__19972] :
( c_24__type__19971___24t(Vvar__19972)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__19980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__19972,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ) ) ).
fof('$_type_19980',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19981] :
( c_24__type__19980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19981)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__19981,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_20',axiom,
! [Vvar__21] :
( c_24__type__20___24t(Vvar__21)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__21,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__20013] :
( c_24__type__20012___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__20013)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__20013,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_20040',axiom,
! [Vvar__20041] :
( c_24__type__20040___24t(Vvar__20041)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__20041,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20043',axiom,
! [Vvar__20044] :
( c_24__type__20043___24t(Vvar__20044)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__20044,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20070',axiom,
! [Vvar__20071] :
( c_24__type__20070___24t(Vvar__20071)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__20071,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20147',axiom,
! [Vvar__20148] :
( c_24__type__20147___24t(Vvar__20148)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__20148,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20259',axiom,
! [Vvar__20260] :
( c_24__type__20259___24t(Vvar__20260)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__20260,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20292',axiom,
! [Vvar__20293] :
( c_24__type__20292___24t(Vvar__20293)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__20293,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20294',axiom,
! [Vvar__20295] :
( c_24__type__20294___24t(Vvar__20295)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__20295,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20371',axiom,
! [Vvar__20372] :
( c_24__type__20371___24t(Vvar__20372)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__20372,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20386',axiom,
! [Vvar__20387] :
( c_24__type__20386___24t(Vvar__20387)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(happ(happ(Vvar__20387,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_20388',axiom,
! [Vvar__20389] :
( c_24__type__20388___24t(Vvar__20389)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,happ(Vvar__20389,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20400',axiom,
! [Vvar__20401] :
( c_24__type__20400___24t(Vvar__20401)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__20401,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20449',axiom,
! [Vvar__20450] :
( c_24__type__20449___24t(Vvar__20450)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__20450,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20962',axiom,
! [Vvar__20963] :
( c_24__type__20962___24t(Vvar__20963)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__20963,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20973',axiom,
! [Vvar__20974] :
( c_24__type__20973___24t(Vvar__20974)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__20974,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21044',axiom,
! [Vvar__21045] :
( c_24__type__21044___24t(Vvar__21045)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__21045,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21070',axiom,
! [Vvar__21071] :
( c_24__type__21070___24t(Vvar__21071)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__21071,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21078',axiom,
! [Vvar__21079] :
( c_24__type__21078___24t(Vvar__21079)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(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__21079,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21088',axiom,
! [Vvar__21089] :
( c_24__type__21088___24t(Vvar__21089)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__21089,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21142',axiom,
! [Vvar__21143] :
( c_24__type__21142___24t(Vvar__21143)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__21143,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21145',axiom,
! [Vv__CANONICAL__0,Vvar__21146] :
( c_24__type__21145___24t(Vv__CANONICAL__0,Vvar__21146)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__21146,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_2134',axiom,
! [Vv__CANONICAL__0,Vvar__2135] :
( c_24__type__2134___24t(Vv__CANONICAL__0,Vvar__2135)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__2135,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_21359',axiom,
! [Vvar__21360] :
( c_24__type__21359___24t(Vvar__21360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__21360,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2157',axiom,
! [Vvar__2158] :
( c_24__type__2157___24t(Vvar__2158)
<=> ! [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__2158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21577] :
( c_24__type__21576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21577)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21577,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21669',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21670] :
( c_24__type__21669___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21670)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21670,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2174',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2175] :
( c_24__type__2174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2175)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2175,Vv__CANONICAL__2)) ) ) ).
fof('$_type_21762',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21763] :
( c_24__type__21762___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21763)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21763,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2178',axiom,
! [Vvar__2179] :
( c_24__type__2178___24t(Vvar__2179)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2179,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2181',axiom,
! [Vv__CANONICAL__0,Vvar__2182] :
( c_24__type__2181___24t(Vv__CANONICAL__0,Vvar__2182)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2182,Vv__CANONICAL__1)) ) ) ).
fof('$_type_21844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21845] :
( c_24__type__21844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__21845)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__21845,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_21937',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__21938] :
( c_24__type__21937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__21938)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21938,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2198',axiom,
! [Vvar__2199] :
( c_24__type__2198___24t(Vvar__2199)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2199,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_22019',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__22020] :
( c_24__type__22019___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__22020)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__22020,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_22112',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__22113] :
( c_24__type__22112___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__22113)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22113,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_2215',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2216] :
( c_24__type__2215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2216)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2216,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2221',axiom,
! [Vvar__2222] :
( c_24__type__2221___24t(Vvar__2222)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__2222,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_2234',axiom,
! [Vvar__2235] :
( c_24__type__2234___24t(Vvar__2235)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2235,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22446',axiom,
! [Vvar__22447] :
( c_24__type__22446___24t(Vvar__22447)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__22447,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22468',axiom,
! [Vvar__22469] :
( c_24__type__22468___24t(Vvar__22469)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__22469,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22500',axiom,
! [Vvar__22501] :
( c_24__type__22500___24t(Vvar__22501)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__22501,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22505',axiom,
! [Vv__CANONICAL__0,Vvar__22506] :
( c_24__type__22505___24t(Vv__CANONICAL__0,Vvar__22506)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__22506,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_22521',axiom,
! [Vvar__22522] :
( c_24__type__22521___24t(Vvar__22522)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(Vvar__22522,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2257',axiom,
! [Vvar__2258] :
( c_24__type__2257___24t(Vvar__2258)
<=> ! [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__2258,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_22572',axiom,
! [Vvar__22573] :
( c_24__type__22572___24t(Vvar__22573)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__22573,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_22590',axiom,
! [Vvar__22591] :
( c_24__type__22590___24t(Vvar__22591)
<=> ! [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__22591,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_2262',axiom,
! [Vvar__2263] :
( c_24__type__2262___24t(Vvar__2263)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__2263,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_22621',axiom,
! [Vvar__22622] :
( c_24__type__22621___24t(Vvar__22622)
<=> ! [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__22622,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_22650',axiom,
! [Vvar__22651] :
( c_24__type__22650___24t(Vvar__22651)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__22651,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_22657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22658] :
( c_24__type__22657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22658)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22658,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22695] :
( c_24__type__22694___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22695)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22695,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22718',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22719] :
( c_24__type__22718___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22719)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22719,Vv__CANONICAL__3)) ) ) ).
fof('$_type_2274',axiom,
! [Vvar__2275] :
( c_24__type__2274___24t(Vvar__2275)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2275,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22765',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22766] :
( c_24__type__22765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__22766)
<=> ! [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__22766,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_22800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22801] :
( c_24__type__22800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22801)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22801,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22803',axiom,
! [Vvar__22804] :
( c_24__type__22803___24t(Vvar__22804)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22804,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2297',axiom,
! [Vvar__2298] :
( c_24__type__2297___24t(Vvar__2298)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2302',axiom,
! [Vvar__2303] :
( c_24__type__2302___24t(Vvar__2303)
<=> ! [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__2303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_2314',axiom,
! [Vvar__2315] :
( c_24__type__2314___24t(Vvar__2315)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__2315,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23249',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23250] :
( c_24__type__23249___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23250)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23250,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23350',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23351] :
( c_24__type__23350___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23351)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23351,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23452] :
( c_24__type__23451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23452)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23452,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23541',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23542] :
( c_24__type__23541___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23542)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__23542,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_23642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23643] :
( c_24__type__23642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23643)
<=> ! [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__23643,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_23743',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23744] :
( c_24__type__23743___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23744)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23744,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_23844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23845] :
( c_24__type__23844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23845)
<=> ! [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__23845,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_24041',axiom,
! [Vvar__24042] :
( c_24__type__24041___24t(Vvar__24042)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__24042,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24044',axiom,
! [Vvar__24045] :
( c_24__type__24044___24t(Vvar__24045)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__24045,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24047',axiom,
! [Vvar__24048] :
( c_24__type__24047___24t(Vvar__24048)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24048,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24053',axiom,
! [Vvar__24054] :
( c_24__type__24053___24t(Vvar__24054)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__24054,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24071',axiom,
! [Vvar__24072] :
( c_24__type__24071___24t(Vvar__24072)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__24072,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24097',axiom,
! [Vvar__24098] :
( c_24__type__24097___24t(Vvar__24098)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2181___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__24098,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24149',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24150] :
( c_24__type__24149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24150)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24150,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24247',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24248] :
( c_24__type__24247___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24248)
<=> ! [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__24248,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_25203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25204] :
( c_24__type__25203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25204)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25204,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25549',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25550] :
( c_24__type__25549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25550)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25550,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25896] :
( c_24__type__25895___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25896)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25896,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26218',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26219] :
( c_24__type__26218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26219)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__26219,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_26564',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26565] :
( c_24__type__26564___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26565)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26565,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_2690',axiom,
! [Vv__CANONICAL__0,Vvar__2691] :
( c_24__type__2690___24t(Vv__CANONICAL__0,Vvar__2691)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__2691,Vv__CANONICAL__1)) ) ) ).
fof('$_type_26910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26911] :
( c_24__type__26910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26911)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26911,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_271',axiom,
! [Vv__CANONICAL__0,Vvar__272] :
( c_24__type__271___24t(Vv__CANONICAL__0,Vvar__272)
<=> ! [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__272,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_27256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27257] :
( c_24__type__27256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27257)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__27257,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_27602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27603] :
( c_24__type__27602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27603)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__27603,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_27948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27949] :
( c_24__type__27948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27949)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__27949,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_28271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__28272] :
( c_24__type__28271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__28272)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__28272,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_28617',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28618] :
( c_24__type__28617___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28618)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28618,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_287',axiom,
! [Vvar__288] :
( c_24__type__287___24t(Vvar__288)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__288,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28964] :
( c_24__type__28963___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28964)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__28964,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_290',axiom,
! [Vvar__291] :
( c_24__type__290___24t(Vvar__291)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__291,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29286',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29287] :
( c_24__type__29286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29287)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__29287,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_29609',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29610] :
( c_24__type__29609___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__29610)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__29610,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_29955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29956] :
( c_24__type__29955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29956)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__29956,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_301',axiom,
! [Vvar__302] :
( c_24__type__301___24t(Vvar__302)
<=> ! [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__302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30132',axiom,
! [Vvar__30133] :
( c_24__type__30132___24t(Vvar__30133)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__30133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30137',axiom,
! [Vvar__30138] :
( c_24__type__30137___24t(Vvar__30138)
<=> ! [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__30138,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30145',axiom,
! [Vvar__30146] :
( c_24__type__30145___24t(Vvar__30146)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__30146,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30154',axiom,
! [Vvar__30155] :
( c_24__type__30154___24t(Vvar__30155)
<=> ! [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__30155,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30356',axiom,
! [Vvar__30357] :
( c_24__type__30356___24t(Vvar__30357)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__30357,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_30373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30374] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30374)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__30374,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_30382',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30383] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30383)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__30383,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30400',axiom,
! [Vvar__30401] :
( c_24__type__30400___24t(Vvar__30401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9009___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__30401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30421',axiom,
! [Vvar__30422] :
( c_24__type__30421___24t(Vvar__30422)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__30422,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_30426',axiom,
! [Vvar__30427] :
( c_24__type__30426___24t(Vvar__30427)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__30427,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30678] :
( c_24__type__30677___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30678)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30678,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30740',axiom,
! [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__30741] :
( c_24__type__30740___24t(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__30741)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30741,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_308',axiom,
! [Vvar__309] :
( c_24__type__308___24t(Vvar__309)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),happ(happ(Vvar__309,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30803',axiom,
! [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__30804] :
( c_24__type__30803___24t(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__30804)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30804,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30858] :
( c_24__type__30857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__30858)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__30858,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_30920',axiom,
! [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__30921] :
( c_24__type__30920___24t(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__30921)
<=> ! [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__30921,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_31108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31109] :
( c_24__type__31108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31109)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31109,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3112',axiom,
! [Vvar__3113] :
( c_24__type__3112___24t(Vvar__3113)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__271___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)
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) )
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__6)
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4) = Vv__CANONICAL__6
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5) = Vv__CANONICAL__6
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__5) = Vv__CANONICAL__6 ) ) ) ) ) )
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__7)
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__6) = Vv__CANONICAL__7
=> happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__6) = Vv__CANONICAL__7 ) ) ) ) ) )
=> cQuicksortComplexity_2esort__order_2eE___24t(happ(happ(Vvar__3113,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_31131',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31132] :
( c_24__type__31131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31132)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31132,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31155] :
( c_24__type__31154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31155)
<=> ! [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__31155,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_31177',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31178] :
( c_24__type__31177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31178)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31178,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31195',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31196] :
( c_24__type__31195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31196)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__31196,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_31221',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31222] :
( c_24__type__31221___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31222)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31222,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31240] :
( c_24__type__31239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__31240)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__31240,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_3134',axiom,
! [Vvar__3135] :
( c_24__type__3134___24t(Vvar__3135)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__3135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31349',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31350] :
( c_24__type__31349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31350)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31350,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31379',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31380] :
( c_24__type__31379___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31380)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31380,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31403',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31404] :
( c_24__type__31403___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31404)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31404,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31433',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31434] :
( c_24__type__31433___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31434)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31434,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_31463',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31464] :
( c_24__type__31463___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31464)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31464,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3148',axiom,
! [Vvar__3149] :
( c_24__type__3148___24t(Vvar__3149)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cQuicksortComplexity_2eutil_2edecision___24t(cQuicksortComplexity_2esort__order_2eEle___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__3149,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31488] :
( c_24__type__31487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31488)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31488,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31520',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31521] :
( c_24__type__31520___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31521)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31521,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31545] :
( c_24__type__31544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31545)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31545,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31571',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31572] :
( c_24__type__31571___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31572)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__31572,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_31970',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31971] :
( c_24__type__31970___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31971)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31971,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32183',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32184] :
( c_24__type__32183___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32184)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32184,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32396',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32397] :
( c_24__type__32396___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32397)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32397,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_324',axiom,
! [Vvar__325] :
( c_24__type__324___24t(Vvar__325)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__325,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32592] :
( c_24__type__32591___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__32592)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__32592,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_32804',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32805] :
( c_24__type__32804___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__32805)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32805,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_33017',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33018] :
( c_24__type__33017___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33018)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__33018,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_33230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__33231] :
( c_24__type__33230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__33231)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__33231,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_33443',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33444] :
( c_24__type__33443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33444)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__33444,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_33638',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__33639] :
( c_24__type__33638___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__33639)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__33639,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_33851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33852] :
( c_24__type__33851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__33852)
<=> ! [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__33852,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_34046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__34047] :
( c_24__type__34046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__34047)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__34047,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_34114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34115] :
( c_24__type__34114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34115)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__34115,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_34133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34134] :
( c_24__type__34133___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34134)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34134,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34147',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34148] :
( c_24__type__34147___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34148)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__34148,Vv__CANONICAL__4)) ) ) ).
fof('$_type_34292',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34293] :
( c_24__type__34292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34293)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34293,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_34342',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34343] :
( c_24__type__34342___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34343)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__34343,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_34392',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34393] :
( c_24__type__34392___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34393)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__34393,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_34434',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34435] :
( c_24__type__34434___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34435)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__34435,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_34484',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34485] :
( c_24__type__34484___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34485)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__34485,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_34560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34561] :
( c_24__type__34560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34561)
<=> ! [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__34561,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_34568',axiom,
! [Vvar__34569] :
( c_24__type__34568___24t(Vvar__34569)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34569,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34672',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34673] :
( c_24__type__34672___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34673)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34673,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34717] :
( c_24__type__34716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34717)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34717,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_34752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34753] :
( c_24__type__34752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34753)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__34753,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_34796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34797] :
( c_24__type__34796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__34797)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__34797,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34817',axiom,
! [Vvar__34818] :
( c_24__type__34817___24t(Vvar__34818)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9009___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__34818,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_34851',axiom,
! [Vvar__34852] :
( c_24__type__34851___24t(Vvar__34852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__34852,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34889',axiom,
! [Vvar__34890] :
( c_24__type__34889___24t(Vvar__34890)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1116___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__34899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__34890,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34899',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34900] :
( c_24__type__34899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34900)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__34900,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_349',axiom,
! [Vvar__350] :
( c_24__type__349___24t(Vvar__350)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__350,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34943] :
( c_24__type__34942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34943)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34943,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_34981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34982] :
( c_24__type__34981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34982)
<=> ! [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__34982,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_35016',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35017] :
( c_24__type__35016___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35017)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35017,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_35051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35052] :
( c_24__type__35051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35052)
<=> ! [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__35052,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_35067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35068] :
( c_24__type__35067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35068)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__35068,Vv__CANONICAL__2)) ) ) ).
fof('$_type_35071',axiom,
! [Vvar__35072] :
( c_24__type__35071___24t(Vvar__35072)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__35072,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35089',axiom,
! [Vvar__35090] :
( c_24__type__35089___24t(Vvar__35090)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__35090,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35196',axiom,
! [Vvar__35197] :
( c_24__type__35196___24t(Vvar__35197)
<=> ! [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__35197,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__357] :
( c_24__type__356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__357)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__357,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_35658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35659] :
( c_24__type__35658___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35659)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35659,Vv__CANONICAL__3)) ) ) ).
fof('$_type_35683',axiom,
! [Vvar__35684] :
( c_24__type__35683___24t(Vvar__35684)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__35684,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35702',axiom,
! [Vvar__35703] :
( c_24__type__35702___24t(Vvar__35703)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__35703,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35706',axiom,
! [Vvar__35707] :
( c_24__type__35706___24t(Vvar__35707)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__20070___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__20070___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35707,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35714',axiom,
! [Vvar__35715] :
( c_24__type__35714___24t(Vvar__35715)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35715,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35742] :
( c_24__type__35741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35742)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__35742,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_35744',axiom,
! [Vvar__35745] :
( c_24__type__35744___24t(Vvar__35745)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(happ(Vvar__35745,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35815',axiom,
! [Vvar__35816] :
( c_24__type__35815___24t(Vvar__35816)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,happ(happ(Vvar__35816,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_365',axiom,
! [Vvar__366] :
( c_24__type__365___24t(Vvar__366)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),Vv__CANONICAL__1,happ(happ(Vvar__366,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37427',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37428] :
( c_24__type__37427___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37428)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__37428,Vv__CANONICAL__3)) ) ) ).
fof('$_type_37432',axiom,
! [Vv__CANONICAL__0,Vvar__37433] :
( c_24__type__37432___24t(Vv__CANONICAL__0,Vvar__37433)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__37433,Vv__CANONICAL__1)) ) ) ).
fof('$_type_37445',axiom,
! [Vvar__37446] :
( c_24__type__37445___24t(Vvar__37446)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__158___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__37450___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__37446,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_37450',axiom,
! [Vv__CANONICAL__0,Vvar__37451] :
( c_24__type__37450___24t(Vv__CANONICAL__0,Vvar__37451)
<=> ! [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__37451,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_37455',axiom,
! [Vvar__37456] :
( c_24__type__37455___24t(Vvar__37456)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__37456,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37460',axiom,
! [Vvar__37461] :
( c_24__type__37460___24t(Vvar__37461)
<=> ! [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__37461,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37748',axiom,
! [Vvar__37749] :
( c_24__type__37748___24t(Vvar__37749)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__37749,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_380',axiom,
! [Vvar__381] :
( c_24__type__380___24t(Vvar__381)
<=> ! [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__381,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38017',axiom,
! [Vvar__38018] :
( c_24__type__38017___24t(Vvar__38018)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cType___24t(Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__9,Vv__CANONICAL__11,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__9,Vv__CANONICAL__15)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__38018,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_38054',axiom,
! [Vvar__38055] :
( c_24__type__38054___24t(Vvar__38055)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__38055,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38074',axiom,
! [Vvar__38075] :
( c_24__type__38074___24t(Vvar__38075)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__38075,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38293',axiom,
! [Vvar__38294] :
( c_24__type__38293___24t(Vvar__38294)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__38294,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_38321',axiom,
! [Vvar__38322] :
( c_24__type__38321___24t(Vvar__38322)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38322,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38399',axiom,
! [Vvar__38400] :
( c_24__type__38399___24t(Vvar__38400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__38400,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_384',axiom,
! [Vvar__385] :
( c_24__type__384___24t(Vvar__385)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__385,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38433',axiom,
! [Vvar__38434] :
( c_24__type__38433___24t(Vvar__38434)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__8531___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__38434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_38461',axiom,
! [Vvar__38462] :
( c_24__type__38461___24t(Vvar__38462)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__38462,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38517',axiom,
! [Vvar__38518] :
( c_24__type__38517___24t(Vvar__38518)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___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__38518,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38662',axiom,
! [Vvar__38663] :
( c_24__type__38662___24t(Vvar__38663)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__38663,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38665',axiom,
! [Vvar__38666] :
( c_24__type__38665___24t(Vvar__38666)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__38666,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38667',axiom,
! [Vvar__38668] :
( c_24__type__38667___24t(Vvar__38668)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__38668,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38796',axiom,
! [Vvar__38797] :
( c_24__type__38796___24t(Vvar__38797)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9009___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__38797,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_38884',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38885] :
( c_24__type__38884___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38885)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__38885,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_38898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38899] :
( c_24__type__38898___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38899)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__38899,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_38905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38906] :
( c_24__type__38905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38906)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__38906,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_39011',axiom,
! [Vvar__39012] :
( c_24__type__39011___24t(Vvar__39012)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1116___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__34899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__39012,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_39021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39022] :
( c_24__type__39021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__39022)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__39022,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_39568',axiom,
! [Vvar__39569] :
( c_24__type__39568___24t(Vvar__39569)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__39569,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39606',axiom,
! [Vvar__39607] :
( c_24__type__39606___24t(Vvar__39607)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__39607,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_399',axiom,
! [Vvar__400] :
( c_24__type__399___24t(Vvar__400)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__400,Vv__CANONICAL__0)) ) ) ).
fof('$_type_417',axiom,
! [Vvar__418] :
( c_24__type__417___24t(Vvar__418)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__418,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42',axiom,
! [Vvar__43] :
( c_24__type__42___24t(Vvar__43)
<=> ! [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__43,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4273',axiom,
! [Vvar__4274] :
( c_24__type__4273___24t(Vvar__4274)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4274,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4276',axiom,
! [Vvar__4277] :
( c_24__type__4276___24t(Vvar__4277)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__1,happ(happ(Vvar__4277,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_434',axiom,
! [Vvar__435] :
( c_24__type__434___24t(Vvar__435)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__435,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4418',axiom,
! [Vvar__4419] :
( c_24__type__4418___24t(Vvar__4419)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4419,Vv__CANONICAL__0)) ) ) ).
fof('$_type_442',axiom,
! [Vvar__443] :
( c_24__type__442___24t(Vvar__443)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__443,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4421',axiom,
! [Vvar__4422] :
( c_24__type__4421___24t(Vvar__4422)
<=> ! [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__4422,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_444',axiom,
! [Vvar__445] :
( c_24__type__444___24t(Vvar__445)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(Vvar__445,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44926',axiom,
! [Vvar__44927] :
( c_24__type__44926___24t(Vvar__44927)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__44927,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_453',axiom,
! [Vvar__454] :
( c_24__type__453___24t(Vvar__454)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(happ(Vvar__454,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46775',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46776] :
( c_24__type__46775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__46776)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__46776,Vv__CANONICAL__3)) ) ) ).
fof('$_type_49369',axiom,
! [Vvar__49370] :
( c_24__type__49369___24t(Vvar__49370)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__49370,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_50003',axiom,
! [Vvar__50004] :
( c_24__type__50003___24t(Vvar__50004)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__50004,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_50008',axiom,
! [Vvar__50009] :
( c_24__type__50008___24t(Vvar__50009)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__50009,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50013',axiom,
! [Vvar__50014] :
( c_24__type__50013___24t(Vvar__50014)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__50014,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_50047',axiom,
! [Vvar__50048] :
( c_24__type__50047___24t(Vvar__50048)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__50051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__50048,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_50051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__50052] :
( c_24__type__50051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__50052)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__50052,Vv__CANONICAL__2)) ) ) ).
fof('$_type_54495',axiom,
! [Vvar__54496] :
( c_24__type__54495___24t(Vvar__54496)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__54496,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_56222',axiom,
! [Vvar__56223] :
( c_24__type__56222___24t(Vvar__56223)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__10] :
( c_24__type__38905___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__15181___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cType___24t(Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__30373___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__30382___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__46775___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__12,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__16)
=> ! [Vv__CANONICAL__17] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__7,Vv__CANONICAL__17)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__56223,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_56805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56806] :
( c_24__type__56805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56806)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__56806,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_57',axiom,
! [Vvar__58] :
( c_24__type__57___24t(Vvar__58)
<=> ! [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__58,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_59497',axiom,
! [Vvar__59498] :
( c_24__type__59497___24t(Vvar__59498)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__59498,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_59504',axiom,
! [Vvar__59505] :
( c_24__type__59504___24t(Vvar__59505)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__59505,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59533] :
( c_24__type__59532___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__59533)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__59533,Vv__CANONICAL__3)) ) ) ).
fof('$_type_59567',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__59568] :
( c_24__type__59567___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__59568)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__59568,Vv__CANONICAL__5)) ) ) ).
fof('$_type_59575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__59576] :
( c_24__type__59575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__59576)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__59576,Vv__CANONICAL__5)) ) ) ).
fof('$_type_59811',axiom,
! [Vvar__59812] :
( c_24__type__59811___24t(Vvar__59812)
<=> ! [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__59812,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_59870',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59871] :
( c_24__type__59870___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59871)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__59871,Vv__CANONICAL__4)) ) ) ).
fof('$_type_59900',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59901] :
( c_24__type__59900___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__59901)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__59901,Vv__CANONICAL__4)) ) ) ).
fof('$_type_59966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__59967] :
( c_24__type__59966___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__59967)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__59967,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_60022',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__60023] :
( c_24__type__60022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__60023)
<=> ! [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__60023,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_60134',axiom,
! [Vvar__60135] :
( c_24__type__60134___24t(Vvar__60135)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__60139___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__60135,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_60139',axiom,
! [Vv__CANONICAL__0,Vvar__60140] :
( c_24__type__60139___24t(Vv__CANONICAL__0,Vvar__60140)
<=> ! [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__60140,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_60178',axiom,
! [Vvar__60179] :
( c_24__type__60178___24t(Vvar__60179)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__60179,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_60192',axiom,
! [Vvar__60193] :
( c_24__type__60192___24t(Vvar__60193)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9009___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__60193,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_62352',axiom,
! [Vv__CANONICAL__0,Vvar__62353] :
( c_24__type__62352___24t(Vv__CANONICAL__0,Vvar__62353)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(Vvar__62353,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_type_62438',axiom,
! [Vvar__62439] :
( c_24__type__62438___24t(Vvar__62439)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__62439,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_635',axiom,
! [Vvar__636] :
( c_24__type__635___24t(Vvar__636)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(happ(Vvar__636,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_640',axiom,
! [Vvar__641] :
( c_24__type__640___24t(Vvar__641)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__641,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_654',axiom,
! [Vvar__655] :
( c_24__type__654___24t(Vvar__655)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2esort__order_2eEc___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cQuicksortComplexity_2esort__order_2eEle___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cQuicksortComplexity_2esort__order_2eEle___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1),happ(happ(happ(Vvar__655,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_669',axiom,
! [Vvar__670] :
( c_24__type__669___24t(Vvar__670)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__670,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_684',axiom,
! [Vvar__685] :
( c_24__type__684___24t(Vvar__685)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,happ(happ(happ(Vvar__685,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_694',axiom,
! [Vvar__695] :
( c_24__type__694___24t(Vvar__695)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__695,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_69977',axiom,
! [Vvar__69978] :
( c_24__type__69977___24t(Vvar__69978)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eBool_2eBvector_2eBvector___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__69978,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_70412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70413] :
( c_24__type__70412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__70413)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> cType___24t(happ(happ(Vvar__70413,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_70602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70603] :
( c_24__type__70602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70603)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__70603,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_70716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70717] :
( c_24__type__70716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70717)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__70717,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7075',axiom,
! [Vvar__7076] :
( c_24__type__7075___24t(Vvar__7076)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__7076,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7077',axiom,
! [Vvar__7078] :
( c_24__type__7077___24t(Vvar__7078)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__7078,Vv__CANONICAL__0)) ) ) ).
fof('$_type_70785',axiom,
! [Vvar__70786] :
( c_24__type__70785___24t(Vvar__70786)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__70790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__70796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__70814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4),Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__70786,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_70790',axiom,
! [Vv__CANONICAL__0,Vvar__70791] :
( c_24__type__70790___24t(Vv__CANONICAL__0,Vvar__70791)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cType___24t(happ(happ(Vvar__70791,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_70796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70797] :
( c_24__type__70796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70797)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__70797,Vv__CANONICAL__2),happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)))) ) ) ).
fof('$_type_70814',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70815] :
( c_24__type__70814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__70815)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> t(happ(happ(happ(happ(Vvar__70815,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3)),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4))) ) ) ) ) ) ).
fof('$_type_7083',axiom,
! [Vvar__7084] :
( c_24__type__7083___24t(Vvar__7084)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__7084,Vv__CANONICAL__0)) ) ) ).
fof('$_type_70859',axiom,
! [Vvar__70860] :
( c_24__type__70859___24t(Vvar__70860)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__70860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7086',axiom,
! [Vvar__7087] :
( c_24__type__7086___24t(Vvar__7087)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__7087,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_70883',axiom,
! [Vvar__70884] :
( c_24__type__70883___24t(Vvar__70884)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1)),happ(happ(happ(Vvar__70884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_716',axiom,
! [Vv__CANONICAL__0,Vvar__717] :
( c_24__type__716___24t(Vv__CANONICAL__0,Vvar__717)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(happ(Vvar__717,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_71654',axiom,
! [Vvar__71655] :
( c_24__type__71654___24t(Vvar__71655)
<=> ! [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__71655,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('$_type_7267',axiom,
! [Vvar__7268] :
( c_24__type__7267___24t(Vvar__7268)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__7268,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7284',axiom,
! [Vvar__7285] :
( c_24__type__7284___24t(Vvar__7285)
<=> ! [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__7285,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7286',axiom,
! [Vvar__7287] :
( c_24__type__7286___24t(Vvar__7287)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__7287,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7296',axiom,
! [Vvar__7297] :
( c_24__type__7296___24t(Vvar__7297)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__7297,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_72983',axiom,
! [Vvar__72984] :
( c_24__type__72983___24t(Vvar__72984)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2enat__below_2enatBelow___24a1(Vv__CANONICAL__0),c_24__lam__72987___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),c_24__prop__72988___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__72984,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73023',axiom,
! [Vvar__73024] :
( c_24__type__73023___24t(Vvar__73024)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3),happ(happ(happ(happ(happ(Vvar__73024,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_73048',axiom,
! [Vvar__73049] :
( c_24__type__73048___24t(Vvar__73049)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__73051___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__73054___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__73062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__73049,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_73051',axiom,
! [Vvar__73052] :
( c_24__type__73051___24t(Vvar__73052)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__73052,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73054',axiom,
! [Vv__CANONICAL__0,Vvar__73055] :
( c_24__type__73054___24t(Vv__CANONICAL__0,Vvar__73055)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__73055,Vv__CANONICAL__1),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1)),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1))) ) ) ).
fof('$_type_73062',axiom,
! [Vv__CANONICAL__0,Vvar__73063] :
( c_24__type__73062___24t(Vv__CANONICAL__0,Vvar__73063)
<=> ! [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] :
( t(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)))
=> t(happ(happ(happ(Vvar__73063,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_7312',axiom,
! [Vvar__7313] :
( c_24__type__7312___24t(Vvar__7313)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__7313,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_73137',axiom,
! [Vvar__73138] :
( c_24__type__73137___24t(Vvar__73138)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( c_24__type__73141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__73138,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_73141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73142] :
( c_24__type__73141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73142)
<=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2epred___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> t(happ(Vvar__73142,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_73158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73159] :
( c_24__type__73158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73159)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(Vvar__73159,Vv__CANONICAL__2)) ) ) ).
fof('$_type_73188',axiom,
! [Vvar__73189] :
( c_24__type__73188___24t(Vvar__73189)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__73189,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_73211',axiom,
! [Vvar__73212] :
( c_24__type__73211___24t(Vvar__73212)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__73215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__73226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__73212,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_73215',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73216] :
( c_24__type__73215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73216)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__73216,Vv__CANONICAL__2)) ) ) ).
fof('$_type_73226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73227] :
( c_24__type__73226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73227)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__73227,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__4))) ) ) ) ).
fof('$_type_7324',axiom,
! [Vvar__7325] :
( c_24__type__7324___24t(Vvar__7325)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__7325,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_73256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73257] :
( c_24__type__73256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73257)
<=> ! [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__73257,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_73311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73312] :
( c_24__type__73311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73312)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__73312,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_73322',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73323] :
( c_24__type__73322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73323)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3),happ(happ(Vvar__73323,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_73347',axiom,
! [Vvar__73348] :
( c_24__type__73347___24t(Vvar__73348)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__73359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__4),happ(happ(happ(happ(happ(happ(Vvar__73348,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_73359',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73360] :
( c_24__type__73359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73360)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__73360,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7336',axiom,
! [Vvar__7337] :
( c_24__type__7336___24t(Vvar__7337)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__7337,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_73371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73372] :
( c_24__type__73371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73372)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__73372,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7338',axiom,
! [Vvar__7339] :
( c_24__type__7338___24t(Vvar__7339)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__7339,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73383',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73384] :
( c_24__type__73383___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73384)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__73384,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_73388',axiom,
! [Vvar__73389] :
( c_24__type__73388___24t(Vvar__73389)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),happ(happ(happ(Vvar__73389,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_73390',axiom,
! [Vvar__73391] :
( c_24__type__73390___24t(Vvar__73391)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,happ(Vvar__73391,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73396',axiom,
! [Vvar__73397] :
( c_24__type__73396___24t(Vvar__73397)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,happ(happ(Vvar__73397,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73399',axiom,
! [Vvar__73400] :
( c_24__type__73399___24t(Vvar__73400)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,happ(happ(Vvar__73400,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73404',axiom,
! [Vvar__73405] :
( c_24__type__73404___24t(Vvar__73405)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,happ(happ(happ(Vvar__73405,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7341',axiom,
! [Vv__CANONICAL__0,Vvar__7342] :
( c_24__type__7341___24t(Vv__CANONICAL__0,Vvar__7342)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__7342,Vv__CANONICAL__1)) ) ) ).
fof('$_type_73418',axiom,
! [Vvar__73419] :
( c_24__type__73418___24t(Vvar__73419)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__73419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_73438',axiom,
! [Vvar__73439] :
( c_24__type__73438___24t(Vvar__73439)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__73439,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73456',axiom,
! [Vvar__73457] :
( c_24__type__73456___24t(Vvar__73457)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__73458___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__73457,Vv__CANONICAL__0),Vv__CANONICAL__1),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73458',axiom,
! [Vvar__73459] :
( c_24__type__73458___24t(Vvar__73459)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__73459,Vv__CANONICAL__0)) ) ) ).
fof('$_type_73477',axiom,
! [Vvar__73478] :
( c_24__type__73477___24t(Vvar__73478)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__73480___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__73483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__73488___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__73478,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_73480',axiom,
! [Vvar__73481] :
( c_24__type__73480___24t(Vvar__73481)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__73481,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_73483',axiom,
! [Vv__CANONICAL__0,Vvar__73484] :
( c_24__type__73483___24t(Vv__CANONICAL__0,Vvar__73484)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__73484,Vv__CANONICAL__1),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eVectors_2eFin_2eF1___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_73488',axiom,
! [Vv__CANONICAL__0,Vvar__73489] :
( c_24__type__73488___24t(Vv__CANONICAL__0,Vvar__73489)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__73489,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eVectors_2eFin_2eFS___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ).
fof('$_type_73721',axiom,
! [Vvar__73722] :
( c_24__type__73721___24t(Vvar__73722)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),happ(happ(happ(Vvar__73722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_73738',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73739] :
( c_24__type__73738___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73739)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__73739,Vv__CANONICAL__2)) ) ) ).
fof('$_type_73744',axiom,
! [Vvar__73745] :
( c_24__type__73744___24t(Vvar__73745)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__73745,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_73761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73762] :
( c_24__type__73761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73762)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__73762,Vv__CANONICAL__2)) ) ) ).
fof('$_type_73767',axiom,
! [Vvar__73768] :
( c_24__type__73767___24t(Vvar__73768)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__73768,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eprojT1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_type_73790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73791] :
( c_24__type__73790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73791)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cType___24t(happ(happ(Vvar__73791,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_73828',axiom,
! [Vvar__73829] :
( c_24__type__73828___24t(Vvar__73829)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__73833___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__73851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__73829,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_73833',axiom,
! [Vv__CANONICAL__0,Vvar__73834] :
( c_24__type__73833___24t(Vv__CANONICAL__0,Vvar__73834)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(happ(Vvar__73834,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_73851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73852] :
( c_24__type__73851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73852)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> t(happ(happ(happ(happ(Vvar__73852,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3)),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ) ).
fof('$_type_73912',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73913] :
( c_24__type__73912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73913)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__73913,Vv__CANONICAL__2)) ) ) ).
fof('$_type_73926',axiom,
! [Vvar__73927] :
( c_24__type__73926___24t(Vvar__73927)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__73929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__73927,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_73929',axiom,
! [Vv__CANONICAL__0,Vvar__73930] :
( c_24__type__73929___24t(Vv__CANONICAL__0,Vvar__73930)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__73930,Vv__CANONICAL__1)) ) ) ).
fof('$_type_73950',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73951] :
( c_24__type__73950___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__73951)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> cType___24t(happ(happ(Vvar__73951,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_73980',axiom,
! [Vvar__73981] :
( c_24__type__73980___24t(Vvar__73981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__70790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__73996___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__73981,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_73996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73997] :
( c_24__type__73996___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__73997)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(happ(Vvar__73997,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__75,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_74078',axiom,
! [Vvar__74079] :
( c_24__type__74078___24t(Vvar__74079)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__73215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__74091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__74079,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_74091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__74092] :
( c_24__type__74091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__74092)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__74092,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__1,Vv__CANONICAL__4))) ) ) ) ).
fof('$_type_74137',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__74138] :
( c_24__type__74137___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__74138)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> cType___24t(happ(happ(happ(Vvar__74138,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ).
fof('$_type_74359',axiom,
! [Vvar__74360] :
( c_24__type__74359___24t(Vvar__74360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__74370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__0)),cCoq_2eVectors_2eVectorDef_2enil___24a1(Vv__CANONICAL__1)))
=> ! [Vv__CANONICAL__4] :
( c_24__type__74411___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__74360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_74370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__74371] :
( c_24__type__74370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__74371)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cType___24t(happ(happ(happ(Vvar__74371,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_type_74411',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__74412] :
( c_24__type__74411___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__74412)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5))
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(happ(happ(Vvar__74412,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),happ(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3)),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__3,Vv__CANONICAL__4)),cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__1,Vv__CANONICAL__8,Vv__CANONICAL__3,Vv__CANONICAL__5))) ) ) ) ) ) ) ) ).
fof('$_type_74436',axiom,
! [Vvar__74437] :
( c_24__type__74436___24t(Vvar__74437)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(Vvar__74437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_74645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__74646] :
( c_24__type__74645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__74646)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(Vvar__74646,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_74668',axiom,
! [Vvar__74669] :
( c_24__type__74668___24t(Vvar__74669)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__74669,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_74680',axiom,
! [Vvar__74681] :
( c_24__type__74680___24t(Vvar__74681)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__3,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__74681,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_74860',axiom,
! [Vvar__74861] :
( c_24__type__74860___24t(Vvar__74861)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eFin_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__74861,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_74877',axiom,
! [Vvar__74878] :
( c_24__type__74877___24t(Vvar__74878)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__3,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__74878,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_74896',axiom,
! [Vvar__74897] :
( c_24__type__74896___24t(Vvar__74897)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__74897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_74915',axiom,
! [Vvar__74916] :
( c_24__type__74915___24t(Vvar__74916)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__74916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_75031',axiom,
! [Vvar__75032] :
( c_24__type__75031___24t(Vvar__75032)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__75032,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_75054',axiom,
! [Vvar__75055] :
( c_24__type__75054___24t(Vvar__75055)
<=> ! [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_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(happ(happ(Vvar__75055,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_75300',axiom,
! [Vvar__75301] :
( c_24__type__75300___24t(Vvar__75301)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eArith_2ePlus_2etail__plus___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(happ(happ(Vvar__75301,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_75315',axiom,
! [Vvar__75316] :
( c_24__type__75315___24t(Vvar__75316)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__75316,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_75430',axiom,
! [Vvar__75431] :
( c_24__type__75430___24t(Vvar__75431)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__19980___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__2,Vv__CANONICAL__4,happ(happ(happ(happ(happ(happ(happ(Vvar__75431,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_75470',axiom,
! [Vvar__75471] :
( c_24__type__75470___24t(Vvar__75471)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__75477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__75471,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ) ) ) ) ).
fof('$_type_75477',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75478] :
( c_24__type__75477___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75478)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__75478,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_75510',axiom,
! [Vvar__75511] :
( c_24__type__75510___24t(Vvar__75511)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__34899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(happ(happ(Vvar__75511,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ) ) ) ) ) ).
fof('$_type_75625',axiom,
! [Vvar__75626] :
( c_24__type__75625___24t(Vvar__75626)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__75639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__75626,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__2) ) ) ) ) ) ) ) ) ) ).
fof('$_type_75639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75640] :
( c_24__type__75639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75640)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__75640,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__2) ) ) ) ) ).
fof('$_type_75801',axiom,
! [Vvar__75802] :
( c_24__type__75801___24t(Vvar__75802)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__75815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__2,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__75802,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ).
fof('$_type_75815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75816] :
( c_24__type__75815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__75816)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__75816,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_75905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75906] :
( c_24__type__75905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75906)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(Vvar__75906,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_type_76096',axiom,
! [Vvar__76097] :
( c_24__type__76096___24t(Vvar__76097)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8531___24t(Vv__CANONICAL__0,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)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(happ(Vvar__76097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_76776',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76777] :
( c_24__type__76776___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76777)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__76777,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_76788',axiom,
! [Vvar__76789] :
( c_24__type__76788___24t(Vvar__76789)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1017___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__76794___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__76789,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_76794',axiom,
! [Vv__CANONICAL__0,Vvar__76795] :
( c_24__type__76794___24t(Vv__CANONICAL__0,Vvar__76795)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__76795,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ).
fof('$_type_76797',axiom,
! [Vvar__76798] :
( c_24__type__76797___24t(Vvar__76798)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__76798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_76814',axiom,
! [Vvar__76815] :
( c_24__type__76814___24t(Vvar__76815)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__76816___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__76817___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(Vvar__76815,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_76834',axiom,
! [Vvar__76835] :
( c_24__type__76834___24t(Vvar__76835)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> t(happ(happ(Vvar__76835,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_76843',axiom,
! [Vvar__76844] :
( c_24__type__76843___24t(Vvar__76844)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__73051___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__76844,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_77018',axiom,
! [Vvar__77019] :
( c_24__type__77018___24t(Vvar__77019)
<=> ! [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_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__77019,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7705',axiom,
! [Vvar__7706] :
( c_24__type__7705___24t(Vvar__7706)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7706,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7711',axiom,
! [Vvar__7712] :
( c_24__type__7711___24t(Vvar__7712)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__7712,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_77116',axiom,
! [Vvar__77117] :
( c_24__type__77116___24t(Vvar__77117)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__77117,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_77134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__77135] :
( c_24__type__77134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__77135)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2),happ(happ(Vvar__77135,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_77141',axiom,
! [Vvar__77142] :
( c_24__type__77141___24t(Vvar__77142)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__77142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_77157',axiom,
! [Vvar__77158] :
( c_24__type__77157___24t(Vvar__77158)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8308___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(Vvar__77158,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_type_77169',axiom,
! [Vvar__77170] :
( c_24__type__77169___24t(Vvar__77170)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__77170,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7769',axiom,
! [Vvar__7770] :
( c_24__type__7769___24t(Vvar__7770)
<=> ! [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__7770,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_7791',axiom,
! [Vvar__7792] :
( c_24__type__7791___24t(Vvar__7792)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__7792,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_78',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79] :
( c_24__type__78___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__79,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_7803',axiom,
! [Vvar__7804] :
( c_24__type__7803___24t(Vvar__7804)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__7804,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_7825',axiom,
! [Vvar__7826] :
( c_24__type__7825___24t(Vvar__7826)
<=> ! [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__7826,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7847] :
( c_24__type__7846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7847)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__7847,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_7883',axiom,
! [Vvar__7884] :
( c_24__type__7883___24t(Vvar__7884)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7890___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__7884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_7890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7891] :
( c_24__type__7890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7891)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__7891,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7907',axiom,
! [Vvar__7908] :
( c_24__type__7907___24t(Vvar__7908)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__7908,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7910',axiom,
! [Vv__CANONICAL__0,Vvar__7911] :
( c_24__type__7910___24t(Vv__CANONICAL__0,Vvar__7911)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__7911,Vv__CANONICAL__1)) ) ) ).
fof('$_type_7927',axiom,
! [Vvar__7928] :
( c_24__type__7927___24t(Vvar__7928)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7910___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__7928,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7961',axiom,
! [Vvar__7962] :
( c_24__type__7961___24t(Vvar__7962)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__7962,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8',axiom,
! [Vvar__9] :
( c_24__type__8___24t(Vvar__9)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__9,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8007',axiom,
! [Vvar__8008] :
( c_24__type__8007___24t(Vvar__8008)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(Vvar__8008,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8034',axiom,
! [Vvar__8035] :
( c_24__type__8034___24t(Vvar__8035)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__8035,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8058',axiom,
! [Vvar__8059] :
( c_24__type__8058___24t(Vvar__8059)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__8059,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8077',axiom,
! [Vvar__8078] :
( c_24__type__8077___24t(Vvar__8078)
<=> ! [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)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__8078,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8110',axiom,
! [Vv__CANONICAL__0,Vvar__8111] :
( c_24__type__8110___24t(Vv__CANONICAL__0,Vvar__8111)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__8111,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_8136',axiom,
! [Vvar__8137] :
( c_24__type__8136___24t(Vvar__8137)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,happ(happ(Vvar__8137,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8143',axiom,
! [Vvar__8144] :
( c_24__type__8143___24t(Vvar__8144)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__8144,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8161',axiom,
! [Vvar__8162] :
( c_24__type__8161___24t(Vvar__8162)
<=> ! [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__8162,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8191',axiom,
! [Vvar__8192] :
( c_24__type__8191___24t(Vvar__8192)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__8192,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8216',axiom,
! [Vv__CANONICAL__0,Vvar__8217] :
( c_24__type__8216___24t(Vv__CANONICAL__0,Vvar__8217)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__8217,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8237',axiom,
! [Vv__CANONICAL__0,Vvar__8238] :
( c_24__type__8237___24t(Vv__CANONICAL__0,Vvar__8238)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__8238,Vv__CANONICAL__1)) ) ) ).
fof('$_type_8241',axiom,
! [Vv__CANONICAL__0,Vvar__8242] :
( c_24__type__8241___24t(Vv__CANONICAL__0,Vvar__8242)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__8242,Vv__CANONICAL__1)) ) ) ).
fof('$_type_8254',axiom,
! [Vvar__8255] :
( c_24__type__8254___24t(Vvar__8255)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__8255,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_83',axiom,
! [Vvar__84] :
( c_24__type__83___24t(Vvar__84)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__84,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8305',axiom,
! [Vvar__8306] :
( c_24__type__8305___24t(Vvar__8306)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__8306,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_8308',axiom,
! [Vv__CANONICAL__0,Vvar__8309] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vvar__8309)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__8309,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_8319',axiom,
! [Vvar__8320] :
( c_24__type__8319___24t(Vvar__8320)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__8320,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_85',axiom,
! [Vvar__86] :
( c_24__type__85___24t(Vvar__86)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__86,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8531',axiom,
! [Vv__CANONICAL__0,Vvar__8532] :
( c_24__type__8531___24t(Vv__CANONICAL__0,Vvar__8532)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8532,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_8542',axiom,
! [Vvar__8543] :
( c_24__type__8542___24t(Vvar__8543)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8531___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__8543,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8791',axiom,
! [Vvar__8792] :
( c_24__type__8791___24t(Vvar__8792)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8792,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8796',axiom,
! [Vvar__8797] :
( c_24__type__8796___24t(Vvar__8797)
<=> ! [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__8797,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9004',axiom,
! [Vvar__9005] :
( c_24__type__9004___24t(Vvar__9005)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__8308___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__8531___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__9024___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__9005,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_9009',axiom,
! [Vv__CANONICAL__0,Vvar__9010] :
( c_24__type__9009___24t(Vv__CANONICAL__0,Vvar__9010)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9010,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9024',axiom,
! [Vv__CANONICAL__0,Vvar__9025] :
( c_24__type__9024___24t(Vv__CANONICAL__0,Vvar__9025)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__9025,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_9242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9243] :
( c_24__type__9242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9243)
<=> ! [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__9243,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_9277',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9278] :
( c_24__type__9277___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9278)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9278,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_9317',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9318] :
( c_24__type__9317___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9318)
<=> ! [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__9318,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_9456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9457] :
( c_24__type__9456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9457)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9457,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_9467',axiom,
! [Vvar__9468] :
( c_24__type__9467___24t(Vvar__9468)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__9468,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9571',axiom,
! [Vvar__9572] :
( c_24__type__9571___24t(Vvar__9572)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__9572,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_9577',axiom,
! [Vv__CANONICAL__0,Vvar__9578] :
( c_24__type__9577___24t(Vv__CANONICAL__0,Vvar__9578)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9578,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9599',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9600] :
( c_24__type__9599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9600)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__9600,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_9614',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9615] :
( c_24__type__9614___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__9615)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> t(happ(Vvar__9615,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_962',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__963] :
( c_24__type__962___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__963)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cType___24t(happ(happ(Vvar__963,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__21070___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__301___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.Factorial.fact',axiom,
c_24__type__8___24t(cCoq_2eArith_2eFactorial_2efact) ).
fof('$_typeof_Coq.Arith.Mult.mult_acc',axiom,
c_24__type__77141___24t(cCoq_2eArith_2eMult_2emult__acc) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__35702___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__301___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__301___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__35706___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le_alt',axiom,
c_24__type__301___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__60134___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__83___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.gtof',axiom,
c_24__type__10686___24t(cCoq_2eArith_2eWf__nat_2egtof) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__10686___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__7086___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__21088___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.BVand',axiom,
c_24__type__73404___24t(cCoq_2eBool_2eBvector_2eBVand) ).
fof('$_typeof_Coq.Bool.Bvector.BVeq',axiom,
c_24__type__73418___24t(cCoq_2eBool_2eBvector_2eBVeq) ).
fof('$_typeof_Coq.Bool.Bvector.BVor',axiom,
c_24__type__73404___24t(cCoq_2eBool_2eBvector_2eBVor) ).
fof('$_typeof_Coq.Bool.Bvector.BVxor',axiom,
c_24__type__73404___24t(cCoq_2eBool_2eBvector_2eBVxor) ).
fof('$_typeof_Coq.Bool.Bvector.Bcons',axiom,
c_24__type__73388___24t(cCoq_2eBool_2eBvector_2eBcons) ).
fof('$_typeof_Coq.Bool.Bvector.Bhigh',axiom,
c_24__type__73396___24t(cCoq_2eBool_2eBvector_2eBhigh) ).
fof('$_typeof_Coq.Bool.Bvector.Blow',axiom,
c_24__type__62438___24t(cCoq_2eBool_2eBvector_2eBlow) ).
fof('$_typeof_Coq.Bool.Bvector.Bneg',axiom,
c_24__type__73399___24t(cCoq_2eBool_2eBvector_2eBneg) ).
fof('$_typeof_Coq.Bool.Bvector.Bnil',axiom,
cCoq_2eVectors_2eVectorDef_2et___24t(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eBool_2eBvector_2eBnil) ).
fof('$_typeof_Coq.Bool.Bvector.Bsign',axiom,
c_24__type__62438___24t(cCoq_2eBool_2eBvector_2eBsign) ).
fof('$_typeof_Coq.Bool.Bvector.Bvect_false',axiom,
c_24__type__73390___24t(cCoq_2eBool_2eBvector_2eBvect__false) ).
fof('$_typeof_Coq.Bool.Bvector.Bvect_true',axiom,
c_24__type__73390___24t(cCoq_2eBool_2eBvector_2eBvect__true) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__158___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__20070___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__35714___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__20449___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__20292___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.cardinal',axiom,
c_24__type__20400___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elements',axiom,
c_24__type__20388___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__39606___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
c_24__type__20371___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).
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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.xelements',axiom,
c_24__type__20386___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__399___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__7286___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__8___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__7284___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__7086___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__1355___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__1343___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__7324___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__37455___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__37460___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__42___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__20___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__37445___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__7267___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__7338___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__20___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__7086___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__7312___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__7296___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__7336___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__7296___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__7086___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__1843___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__8161___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__20070___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.iter',axiom,
c_24__type__77157___24t(cCoq_2eInit_2eNat_2eiter) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__8161___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__8191___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__20070___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.shiftr',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2eshiftr) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.sqrt_iter',axiom,
c_24__type__8191___24t(cCoq_2eInit_2eNat_2esqrt__iter) ).
fof('$_typeof_Coq.Init.Nat.square',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2esquare) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__8___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__83___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__8161___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__10___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__301___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__301___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__301___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__2198___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__35089___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__2297___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__2302___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__2257___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__2221___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__73744___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__73767___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__2262___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__2178___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__35071___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__2234___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__2274___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__9467___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Init.Wf.well_founded_induction_type',axiom,
c_24__type__9571___24t(cCoq_2eInit_2eWf_2ewell__founded__induction__type) ).
fof('$_typeof_Coq.Lists.List.ForallPairs',axiom,
c_24__type__38517___24t(cCoq_2eLists_2eList_2eForallPairs) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__57___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.combine',axiom,
c_24__type__8034___24t(cCoq_2eLists_2eList_2ecombine) ).
fof('$_typeof_Coq.Lists.List.existsb',axiom,
c_24__type__7907___24t(cCoq_2eLists_2eList_2eexistsb) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__7927___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.firstn',axiom,
c_24__type__8077___24t(cCoq_2eLists_2eList_2efirstn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__7883___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__22650___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__22590___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.incl',axiom,
c_24__type__8058___24t(cCoq_2eLists_2eList_2eincl) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__22621___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.lel',axiom,
c_24__type__8058___24t(cCoq_2eLists_2eList_2elel) ).
fof('$_typeof_Coq.Lists.List.list_prod',axiom,
c_24__type__8034___24t(cCoq_2eLists_2eList_2elist__prod) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__74___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__7769___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.nth_default',axiom,
c_24__type__7803___24t(cCoq_2eLists_2eList_2enth__default) ).
fof('$_typeof_Coq.Lists.List.nth_error',axiom,
c_24__type__7791___24t(cCoq_2eLists_2eList_2enth__error) ).
fof('$_typeof_Coq.Lists.List.nth_ok',axiom,
c_24__type__38461___24t(cCoq_2eLists_2eList_2enth__ok) ).
fof('$_typeof_Coq.Lists.List.partition',axiom,
c_24__type__7961___24t(cCoq_2eLists_2eList_2epartition) ).
fof('$_typeof_Coq.Lists.List.removelast',axiom,
c_24__type__7825___24t(cCoq_2eLists_2eList_2eremovelast) ).
fof('$_typeof_Coq.Lists.List.repeat',axiom,
c_24__type__8143___24t(cCoq_2eLists_2eList_2erepeat) ).
fof('$_typeof_Coq.Lists.List.rev',axiom,
c_24__type__7825___24t(cCoq_2eLists_2eList_2erev) ).
fof('$_typeof_Coq.Lists.List.rev_append',axiom,
c_24__type__1355___24t(cCoq_2eLists_2eList_2erev__append) ).
fof('$_typeof_Coq.Lists.List.seq',axiom,
c_24__type__8136___24t(cCoq_2eLists_2eList_2eseq) ).
fof('$_typeof_Coq.Lists.List.skipn',axiom,
c_24__type__8077___24t(cCoq_2eLists_2eList_2eskipn) ).
fof('$_typeof_Coq.Lists.List.split',axiom,
c_24__type__8007___24t(cCoq_2eLists_2eList_2esplit) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__7825___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.ListDec.decidable_eq',axiom,
c_24__type__22803___24t(cCoq_2eLists_2eListDec_2edecidable__eq) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__34889___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__34889___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__39011___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__39011___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__21142___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.FinFun.Finite',axiom,
c_24__type__22803___24t(cCoq_2eLogic_2eFinFun_2eFinite) ).
fof('$_typeof_Coq.Logic.FinFun.Full',axiom,
c_24__type__38321___24t(cCoq_2eLogic_2eFinFun_2eFull) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__7705___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__7705___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.Logic.FinFun.bFun',axiom,
c_24__type__7711___24t(cCoq_2eLogic_2eFinFun_2ebFun) ).
fof('$_typeof_Coq.Logic.FinFun.bInjective',axiom,
c_24__type__7711___24t(cCoq_2eLogic_2eFinFun_2ebInjective) ).
fof('$_typeof_Coq.Logic.FinFun.bSurjective',axiom,
c_24__type__7711___24t(cCoq_2eLogic_2eFinFun_2ebSurjective) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__35683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__59504___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__30426___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__1846___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__35683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.of_nat',axiom,
c_24__type__20043___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__30426___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__20040___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.Bv2N',axiom,
c_24__type__69977___24t(cCoq_2eNArith_2eNdigits_2eBv2N) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__35706___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_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__7083___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__1___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__7075___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__7075___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__4421___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__20147___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__60192___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__20259___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__20259___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__4418___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__20147___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__7075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__60178___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__8254___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qminus',axiom,
c_24__type__49369___24t(cCoq_2eQArith_2eQArith__base_2eQminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__24053___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__24041___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__24044___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__24047___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__24047___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__24041___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__24041___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__24044___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__24041___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__59811___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.sum_nat_f_O',axiom,
c_24__type__12512___24t(cCoq_2eReals_2eRfunctions_2esum__nat__f__O) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__34851___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__2157___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__20___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__2157___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__71654___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.ByteVector.ByteVector',axiom,
c_24__type__158___24t(cCoq_2eStrings_2eByteVector_2eByteVector) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__2314___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__1960___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__301___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__301___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.F1',axiom,
c_24__type__22521___24t(cCoq_2eVectors_2eFin_2eF1) ).
fof('$_typeof_Coq.Vectors.Fin.FS',axiom,
c_24__type__35744___24t(cCoq_2eVectors_2eFin_2eFS) ).
fof('$_typeof_Coq.Vectors.Fin.L_R',axiom,
c_24__type__73721___24t(cCoq_2eVectors_2eFin_2eL__R) ).
fof('$_typeof_Coq.Vectors.Fin.case0',axiom,
c_24__type__73456___24t(cCoq_2eVectors_2eFin_2ecase0) ).
fof('$_typeof_Coq.Vectors.Fin.caseS',axiom,
c_24__type__73477___24t(cCoq_2eVectors_2eFin_2ecaseS) ).
fof('$_typeof_Coq.Vectors.Fin.of_nat_lt',axiom,
c_24__type__35815___24t(cCoq_2eVectors_2eFin_2eof__nat__lt) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__158___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.append',axiom,
c_24__type__75054___24t(cCoq_2eVectors_2eVectorDef_2eappend) ).
fof('$_typeof_Coq.Vectors.VectorDef.case0',axiom,
c_24__type__73926___24t(cCoq_2eVectors_2eVectorDef_2ecase0) ).
fof('$_typeof_Coq.Vectors.VectorDef.caseS',axiom,
c_24__type__73980___24t(cCoq_2eVectors_2eVectorDef_2ecaseS) ).
fof('$_typeof_Coq.Vectors.VectorDef.caseS\'',axiom,
c_24__type__74078___24t(cCoq_2eVectors_2eVectorDef_2ecaseS_27) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__442___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.const',axiom,
c_24__type__74436___24t(cCoq_2eVectors_2eVectorDef_2econst) ).
fof('$_typeof_Coq.Vectors.VectorDef.fold_left',axiom,
c_24__type__75470___24t(cCoq_2eVectors_2eVectorDef_2efold__left) ).
fof('$_typeof_Coq.Vectors.VectorDef.fold_left2',axiom,
c_24__type__75801___24t(cCoq_2eVectors_2eVectorDef_2efold__left2) ).
fof('$_typeof_Coq.Vectors.VectorDef.fold_right',axiom,
c_24__type__75510___24t(cCoq_2eVectors_2eVectorDef_2efold__right) ).
fof('$_typeof_Coq.Vectors.VectorDef.fold_right2',axiom,
c_24__type__75625___24t(cCoq_2eVectors_2eVectorDef_2efold__right2) ).
fof('$_typeof_Coq.Vectors.VectorDef.hd',axiom,
c_24__type__669___24t(cCoq_2eVectors_2eVectorDef_2ehd) ).
fof('$_typeof_Coq.Vectors.VectorDef.last',axiom,
c_24__type__669___24t(cCoq_2eVectors_2eVectorDef_2elast) ).
fof('$_typeof_Coq.Vectors.VectorDef.map',axiom,
c_24__type__349___24t(cCoq_2eVectors_2eVectorDef_2emap) ).
fof('$_typeof_Coq.Vectors.VectorDef.map2',axiom,
c_24__type__75430___24t(cCoq_2eVectors_2eVectorDef_2emap2) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__434___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.nth',axiom,
c_24__type__74668___24t(cCoq_2eVectors_2eVectorDef_2enth) ).
fof('$_typeof_Coq.Vectors.VectorDef.nth_order',axiom,
c_24__type__74680___24t(cCoq_2eVectors_2eVectorDef_2enth__order) ).
fof('$_typeof_Coq.Vectors.VectorDef.of_list',axiom,
c_24__type__694___24t(cCoq_2eVectors_2eVectorDef_2eof__list) ).
fof('$_typeof_Coq.Vectors.VectorDef.rect2',axiom,
c_24__type__74359___24t(cCoq_2eVectors_2eVectorDef_2erect2) ).
fof('$_typeof_Coq.Vectors.VectorDef.rectS',axiom,
c_24__type__70785___24t(cCoq_2eVectors_2eVectorDef_2erectS) ).
fof('$_typeof_Coq.Vectors.VectorDef.replace',axiom,
c_24__type__74860___24t(cCoq_2eVectors_2eVectorDef_2ereplace) ).
fof('$_typeof_Coq.Vectors.VectorDef.replace_order',axiom,
c_24__type__74877___24t(cCoq_2eVectors_2eVectorDef_2ereplace__order) ).
fof('$_typeof_Coq.Vectors.VectorDef.rev',axiom,
c_24__type__75315___24t(cCoq_2eVectors_2eVectorDef_2erev) ).
fof('$_typeof_Coq.Vectors.VectorDef.rev_append',axiom,
c_24__type__75054___24t(cCoq_2eVectors_2eVectorDef_2erev__append) ).
fof('$_typeof_Coq.Vectors.VectorDef.rev_append_tail',axiom,
c_24__type__75300___24t(cCoq_2eVectors_2eVectorDef_2erev__append__tail) ).
fof('$_typeof_Coq.Vectors.VectorDef.shiftin',axiom,
c_24__type__74915___24t(cCoq_2eVectors_2eVectorDef_2eshiftin) ).
fof('$_typeof_Coq.Vectors.VectorDef.shiftout',axiom,
c_24__type__70859___24t(cCoq_2eVectors_2eVectorDef_2eshiftout) ).
fof('$_typeof_Coq.Vectors.VectorDef.shiftrepeat',axiom,
c_24__type__70883___24t(cCoq_2eVectors_2eVectorDef_2eshiftrepeat) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__417___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t_rec',axiom,
c_24__type__73828___24t(cCoq_2eVectors_2eVectorDef_2et__rec) ).
fof('$_typeof_Coq.Vectors.VectorDef.t_rect',axiom,
c_24__type__73828___24t(cCoq_2eVectors_2eVectorDef_2et__rect) ).
fof('$_typeof_Coq.Vectors.VectorDef.take',axiom,
c_24__type__75031___24t(cCoq_2eVectors_2eVectorDef_2etake) ).
fof('$_typeof_Coq.Vectors.VectorDef.tl',axiom,
c_24__type__70859___24t(cCoq_2eVectors_2eVectorDef_2etl) ).
fof('$_typeof_Coq.Vectors.VectorDef.to_list',axiom,
c_24__type__324___24t(cCoq_2eVectors_2eVectorDef_2eto__list) ).
fof('$_typeof_Coq.Vectors.VectorDef.uncons',axiom,
c_24__type__74896___24t(cCoq_2eVectors_2eVectorDef_2euncons) ).
fof('$_typeof_Coq.Vectors.VectorEq.eqb',axiom,
c_24__type__76096___24t(cCoq_2eVectors_2eVectorEq_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__1277___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__1277___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__1277___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__1277___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__1277___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__20962___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__380___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__1271___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__10880___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__380___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__380___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__20973___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__1274___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__384___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__380___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__21044___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__380___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__384___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__20962___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__10880___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength',axiom,
c_24__type__10895___24t(cCoq_2eZArith_2eZcomplements_2eZlength) ).
fof('$_typeof_Coq.ZArith.Zcomplements.Zlength_aux',axiom,
c_24__type__10892___24t(cCoq_2eZArith_2eZcomplements_2eZlength__aux) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__301___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Zpower.shift_nat',axiom,
c_24__type__77169___24t(cCoq_2eZArith_2eZpower_2eshift__nat) ).
fof('$_typeof_Coq.funind.Recdef.iter',axiom,
c_24__type__8305___24t(cCoq_2efunind_2eRecdef_2eiter) ).
fof('$_typeof_Coq.funind.Recdef.max_type',axiom,
c_24__type__8319___24t(cCoq_2efunind_2eRecdef_2emax__type) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__21359___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__24097___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__24071___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__20___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzAdd',axiom,
c_24__type__50013___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__38665___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzIn',axiom,
c_24__type__38662___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzIn) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulC',axiom,
c_24__type__50008___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzMulE',axiom,
c_24__type__50013___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzSquare',axiom,
c_24__type__50003___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__38667___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__8161___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
c_24__type__50047___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__35196___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__7296___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_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.make_conj',axiom,
c_24__type__24097___24t(cCoq_2emicromega_2eZMicromega_2emake__conj) ).
fof('$_typeof_Coq.micromega.ZMicromega.make_impl',axiom,
c_24__type__24071___24t(cCoq_2emicromega_2eZMicromega_2emake__impl) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__1274___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.setoid_ring.BinList.jump',axiom,
c_24__type__21078___24t(cCoq_2esetoid__ring_2eBinList_2ejump) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__22446___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEeval',axiom,
c_24__type__38017___24t(cCoq_2esetoid__ring_2eField__theory_2eFEeval) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__37748___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__22500___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__38293___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__38074___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__38054___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__22468___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__38054___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__44926___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__44926___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__30426___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__35683___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__38399___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__22572___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__38433___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__7086___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__8791___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__8796___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__30154___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__30356___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__8796___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__8796___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__30145___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__30132___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__8542___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__30137___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__20___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pphi_pow',axiom,
c_24__type__56222___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__54495___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__38796___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__9004___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__34568___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__34568___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__34817___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__7284___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__30426___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__30421___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__30400___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_ceil_log2_S',axiom,
c_24__type__8319___24t(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_floor_log2_S',axiom,
c_24__type__8319___24t(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S) ).
fof('$_typeof_QuicksortComplexity.arith_lems.log2ceil',axiom,
c_24__type__8___24t(cQuicksortComplexity_2earith__lems_2elog2ceil) ).
fof('$_typeof_QuicksortComplexity.arith_lems.pow',axiom,
c_24__type__83___24t(cQuicksortComplexity_2earith__lems_2epow) ).
fof('$_typeof_QuicksortComplexity.arith_lems.sqrd',axiom,
c_24__type__8___24t(cQuicksortComplexity_2earith__lems_2esqrd) ).
fof('$_typeof_QuicksortComplexity.list_utils.Partitioning',axiom,
c_24__type__20___24t(cQuicksortComplexity_2elist__utils_2ePartitioning) ).
fof('$_typeof_QuicksortComplexity.list_utils.add',axiom,
c_24__type__15187___24t(cQuicksortComplexity_2elist__utils_2eadd) ).
fof('$_typeof_QuicksortComplexity.list_utils.concat',axiom,
c_24__type__15081___24t(cQuicksortComplexity_2elist__utils_2econcat) ).
fof('$_typeof_QuicksortComplexity.list_utils.count',axiom,
c_24__type__15059___24t(cQuicksortComplexity_2elist__utils_2ecount) ).
fof('$_typeof_QuicksortComplexity.list_utils.insert_everywhere',axiom,
c_24__type__18598___24t(cQuicksortComplexity_2elist__utils_2einsert__everywhere) ).
fof('$_typeof_QuicksortComplexity.list_utils.me',axiom,
c_24__type__19443___24t(cQuicksortComplexity_2elist__utils_2eme) ).
fof('$_typeof_QuicksortComplexity.list_utils.merges',axiom,
c_24__type__19781___24t(cQuicksortComplexity_2elist__utils_2emerges) ).
fof('$_typeof_QuicksortComplexity.list_utils.perms',axiom,
c_24__type__18603___24t(cQuicksortComplexity_2elist__utils_2eperms) ).
fof('$_typeof_QuicksortComplexity.list_utils.product',axiom,
c_24__type__8034___24t(cQuicksortComplexity_2elist__utils_2eproduct) ).
fof('$_typeof_QuicksortComplexity.list_utils.repeat',axiom,
c_24__type__15099___24t(cQuicksortComplexity_2elist__utils_2erepeat) ).
fof('$_typeof_QuicksortComplexity.list_utils.splits',axiom,
c_24__type__18586___24t(cQuicksortComplexity_2elist__utils_2esplits) ).
fof('$_typeof_QuicksortComplexity.nat_below.Snb',axiom,
c_24__type__453___24t(cQuicksortComplexity_2enat__below_2eSnb) ).
fof('$_typeof_QuicksortComplexity.nat_below.mkNatBelow',axiom,
c_24__type__308___24t(cQuicksortComplexity_2enat__below_2emkNatBelow) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow',axiom,
c_24__type__158___24t(cQuicksortComplexity_2enat__below_2enatBelow) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow_eq_dec',axiom,
c_24__type__76814___24t(cQuicksortComplexity_2enat__below_2enatBelow__eq__dec) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow_rec',axiom,
c_24__type__76788___24t(cQuicksortComplexity_2enat__below_2enatBelow__rec) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow_rect',axiom,
c_24__type__76788___24t(cQuicksortComplexity_2enat__below_2enatBelow__rect) ).
fof('$_typeof_QuicksortComplexity.nat_below.nb0',axiom,
c_24__type__444___24t(cQuicksortComplexity_2enat__below_2enb0) ).
fof('$_typeof_QuicksortComplexity.nat_below.nb_val',axiom,
c_24__type__171___24t(cQuicksortComplexity_2enat__below_2enb__val) ).
fof('$_typeof_QuicksortComplexity.nat_seqs.nats',axiom,
c_24__type__8136___24t(cQuicksortComplexity_2enat__seqs_2enats) ).
fof('$_typeof_QuicksortComplexity.sort_order.Build_E',axiom,
c_24__type__3112___24t(cQuicksortComplexity_2esort__order_2eBuild__E) ).
fof('$_typeof_QuicksortComplexity.sort_order.E',axiom,
cType___24t(cQuicksortComplexity_2esort__order_2eE) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ec',axiom,
c_24__type__287___24t(cQuicksortComplexity_2esort__order_2eEc) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ecmp',axiom,
c_24__type__635___24t(cQuicksortComplexity_2esort__order_2eEcmp) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ege',axiom,
c_24__type__640___24t(cQuicksortComplexity_2esort__order_2eEge) ).
fof('$_typeof_QuicksortComplexity.sort_order.Egeb',axiom,
c_24__type__3134___24t(cQuicksortComplexity_2esort__order_2eEgeb) ).
fof('$_typeof_QuicksortComplexity.sort_order.Egt',axiom,
c_24__type__640___24t(cQuicksortComplexity_2esort__order_2eEgt) ).
fof('$_typeof_QuicksortComplexity.sort_order.Egtb',axiom,
c_24__type__3134___24t(cQuicksortComplexity_2esort__order_2eEgtb) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ele',axiom,
c_24__type__640___24t(cQuicksortComplexity_2esort__order_2eEle) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ele_dec',axiom,
c_24__type__3148___24t(cQuicksortComplexity_2esort__order_2eEle__dec) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ele_le_dec',axiom,
c_24__type__654___24t(cQuicksortComplexity_2esort__order_2eEle__le__dec) ).
fof('$_typeof_QuicksortComplexity.sort_order.Eleb',axiom,
c_24__type__3134___24t(cQuicksortComplexity_2esort__order_2eEleb) ).
fof('$_typeof_QuicksortComplexity.sort_order.Elt',axiom,
c_24__type__640___24t(cQuicksortComplexity_2esort__order_2eElt) ).
fof('$_typeof_QuicksortComplexity.sort_order.Eltb',axiom,
c_24__type__3134___24t(cQuicksortComplexity_2esort__order_2eEltb) ).
fof('$_typeof_QuicksortComplexity.util.decision',axiom,
c_24__type__4273___24t(cQuicksortComplexity_2eutil_2edecision) ).
fof('$_typeof_QuicksortComplexity.util.ext_eq',axiom,
c_24__type__39568___24t(cQuicksortComplexity_2eutil_2eext__eq) ).
fof('$_typeof_QuicksortComplexity.util.on',axiom,
c_24__type__19932___24t(cQuicksortComplexity_2eutil_2eon) ).
fof('$_typeof_QuicksortComplexity.util.uncurry',axiom,
c_24__type__19971___24t(cQuicksortComplexity_2eutil_2euncurry) ).
fof('$_typeof_QuicksortComplexity.util.unsum_bool',axiom,
c_24__type__59497___24t(cQuicksortComplexity_2eutil_2eunsum__bool) ).
fof('$_typeof_QuicksortComplexity.vec.R',axiom,
c_24__type__76843___24t(cQuicksortComplexity_2evec_2eR) ).
fof('$_typeof_QuicksortComplexity.vec.S_rect',axiom,
c_24__type__73211___24t(cQuicksortComplexity_2evec_2eS__rect) ).
fof('$_typeof_QuicksortComplexity.vec.Xlt',axiom,
c_24__type__1111___24t(cQuicksortComplexity_2evec_2eXlt) ).
fof('$_typeof_QuicksortComplexity.vec.app',axiom,
c_24__type__73023___24t(cQuicksortComplexity_2evec_2eapp) ).
fof('$_typeof_QuicksortComplexity.vec.drop',axiom,
c_24__type__77116___24t(cQuicksortComplexity_2evec_2edrop) ).
fof('$_typeof_QuicksortComplexity.vec.from_list',axiom,
c_24__type__694___24t(cQuicksortComplexity_2evec_2efrom__list) ).
fof('$_typeof_QuicksortComplexity.vec.head',axiom,
c_24__type__669___24t(cQuicksortComplexity_2evec_2ehead) ).
fof('$_typeof_QuicksortComplexity.vec.insert_ordered',axiom,
c_24__type__73347___24t(cQuicksortComplexity_2evec_2einsert__ordered) ).
fof('$_typeof_QuicksortComplexity.vec.insertion_sort',axiom,
c_24__type__1242___24t(cQuicksortComplexity_2evec_2einsertion__sort) ).
fof('$_typeof_QuicksortComplexity.vec.map',axiom,
c_24__type__349___24t(cQuicksortComplexity_2evec_2emap) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow0_rect',axiom,
c_24__type__76834___24t(cQuicksortComplexity_2evec_2enatBelow0__rect) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow_S_bla',axiom,
c_24__type__73137___24t(cQuicksortComplexity_2evec_2enatBelow__S__bla) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow_S_inv',axiom,
c_24__type__72983___24t(cQuicksortComplexity_2evec_2enatBelow__S__inv) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow_S_inv\'',axiom,
c_24__type__1044___24t(cQuicksortComplexity_2evec_2enatBelow__S__inv_27) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow_rect',axiom,
c_24__type__1014___24t(cQuicksortComplexity_2evec_2enatBelow__rect) ).
fof('$_typeof_QuicksortComplexity.vec.natBelow_rect_S',axiom,
c_24__type__73048___24t(cQuicksortComplexity_2evec_2enatBelow__rect__S) ).
fof('$_typeof_QuicksortComplexity.vec.nats',axiom,
c_24__type__365___24t(cQuicksortComplexity_2evec_2enats) ).
fof('$_typeof_QuicksortComplexity.vec.nb_nats',axiom,
c_24__type__4276___24t(cQuicksortComplexity_2evec_2enb__nats) ).
fof('$_typeof_QuicksortComplexity.vec.nof',axiom,
c_24__type__171___24t(cQuicksortComplexity_2evec_2enof) ).
fof('$_typeof_QuicksortComplexity.vec.nth',axiom,
c_24__type__1083___24t(cQuicksortComplexity_2evec_2enth) ).
fof('$_typeof_QuicksortComplexity.vec.plusnb',axiom,
c_24__type__1100___24t(cQuicksortComplexity_2evec_2eplusnb) ).
fof('$_typeof_QuicksortComplexity.vec.remove',axiom,
c_24__type__73188___24t(cQuicksortComplexity_2evec_2eremove) ).
fof('$_typeof_QuicksortComplexity.vec.tail',axiom,
c_24__type__684___24t(cQuicksortComplexity_2evec_2etail) ).
fof('$_typeof_QuicksortComplexity.vec.take',axiom,
c_24__type__77018___24t(cQuicksortComplexity_2evec_2etake) ).
fof('$_typeof_QuicksortComplexity.vec.to_list',axiom,
c_24__type__324___24t(cQuicksortComplexity_2evec_2eto__list) ).
fof('$_typeof_T',axiom,
cQuicksortComplexity_2esort__order_2eE___24t(cT) ).
fof('$_typeof_b',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cb) ).
fof('$_typeof_indices.contents.Index',axiom,
cType___24t(cindices_2econtents_2eIndex) ).
fof('$_typeof_indices.contents.IndexIn',axiom,
c_24__type__290___24t(cindices_2econtents_2eIndexIn) ).
fof('$_typeof_indices.contents.IndexSeq',axiom,
c_24__type__290___24t(cindices_2econtents_2eIndexSeq) ).
fof('$_typeof_indices.contents.IndexSeq_above',axiom,
c_24__type__290___24t(cindices_2econtents_2eIndexSeq__above) ).
fof('$_typeof_indices.contents.UE',axiom,
cQuicksortComplexity_2esort__order_2eE___24t(cindices_2econtents_2eUE) ).
fof('$_typeof_indices.contents.subscript',axiom,
c_24__type__1280___24t(cindices_2econtents_2esubscript) ).
fof('$_typeof_n',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cn) ).
fof('$_typeof_ol',axiom,
cCoq_2eInit_2eDatatypes_2elist___24t(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col) ).
fof('$_typeof_v',axiom,
cCoq_2eVectors_2eVectorDef_2et___24t(cindices_2econtents_2eIndex,cn,cv) ).
fof('Coq.Arith.Between.bet_emp',axiom,
! [V0__P] :
( c_24__type__10___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V1__k) ) ) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_S_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m),cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))
=> cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Gt.gt_Sn_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ p(cCoq_2eInit_2ePeano_2ele___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_Sn_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_0_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
=> cCoq_2eInit_2eDatatypes_2eO = V0__n ) ) ).
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_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_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_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_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_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.Max.max_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(V1__m,V0__n))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.Max.max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.Minus.minus_Sn_m',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Minus.minus_diag_reverse',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO = cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Minus.minus_n_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.Minus.minus_plus',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V0__n) = V1__m ) ) ).
fof('Coq.Arith.Minus.minus_plus_simpl_l_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_2esub___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.A\'A_left',axiom,
! [V0__A] :
( c_24__type__10___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [Vvar__4__m__60143] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__m__60143)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__4__m__60143,V1__z))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,Vvar__4__m__60143))
=> p(happ(V0__A,Vvar__4__m__60143)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( 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.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.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_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( 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_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.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_succ_r',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.divide_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__77171___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lbase',axiom,
! [V0__A] :
( c_24__type__10___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
=> ! [Vvar__3__m__72952] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__72952)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__3__m__72952,V1__z))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__z),Vvar__3__m__72952))
=> p(happ(V0__A,Vvar__3__m__72952)) ) ) ) ) ) ).
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_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
<=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',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))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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_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.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__301,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__10,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
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_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_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_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_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( 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_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eNat_2emul___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.rbase',axiom,
! [V0__A] :
( c_24__type__10___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
=> ! [Vvar__3__m__37334] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__37334)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__z,Vvar__3__m__37334))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__3__m__37334,V1__z))
=> p(happ(V0__A,Vvar__3__m__37334)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eO
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_diag',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__83,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__8,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2esub) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
fof('Coq.Arith.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_tail_plus',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_2eArith_2ePlus_2etail__plus___24a2(V0__n,V1__m) ) ) ).
fof('Coq.Arith.Wf_nat.gt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__10___24t(V1__P)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V2__n,V3__m)
=> p(happ(V1__P,V3__m)) ) )
=> p(happ(V1__P,V2__n)) ) )
=> p(happ(V1__P,V0__n)) ) ) ) ).
fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
! [V0__P] :
( c_24__type__301___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__10___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.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.orb_false_elim',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& V1__b2 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.cardinal_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s) = cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__s)) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.elements_1',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq,V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__s)) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.elements_2',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq,V1__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__s))
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s) ) ) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.elements_3w',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V0__s)) ) ).
fof('Coq.FSets.FSetPositive.PositiveSet.tree_ind',axiom,
! [V0__P] :
( c_24__type__20294___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf))
=> ( ! [V2__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V2__t)
=> ( p(happ(V0__P,V2__t))
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ! [V5__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V5__t)
=> ( p(happ(V0__P,V5__t))
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V2__t,V4__b,V5__t))) ) ) ) ) )
=> ! [V3__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V3__t)
=> p(happ(V0__P,V3__t)) ) ) ) ) ).
fof('Coq.Init.Datatypes.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.andb_true_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7341___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__10___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Datatypes.pair_equal_spec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__a1] :
( t(V2__a1,V0__A)
=> ! [V3__a2] :
( t(V3__a2,V0__A)
=> ! [V4__b1] :
( t(V4__b1,V1__B)
=> ! [V5__b2] :
( t(V5__b2,V1__B)
=> ( cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V2__a1,V4__b1) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a2,V5__b2)
<=> ( V2__a1 = V3__a2
& V4__b1 = V5__b2 ) ) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.eq_S',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__y) ) ) ) ).
fof('Coq.Init.Peano.eq_add_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Init.Peano.f_equal2_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__8216___24t(V0__B,V1__f)
=> ! [V2__x1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x1)
=> ! [V3__y1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y1)
=> ! [V4__x2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x2)
=> ! [V5__y2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y2)
=> ( V2__x1 = V3__y1
=> ( V4__x2 = V5__y2
=> happ(happ(V1__f,V2__x1),V4__x2) = happ(happ(V1__f,V3__y1),V5__y2) ) ) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__2134___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_0_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Init.Peano.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.Init.Peano.le_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__10___24t(V1__P)
=> ( p(happ(V1__P,V0__n))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V3__m))
=> ( p(happ(V1__P,V3__m))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V4__n))
=> p(happ(V1__P,V4__n)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.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.Init.Peano.nat_case',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__10___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) )
=> p(happ(V1__P,V0__n)) ) ) ) ) ).
fof('Coq.Init.Peano.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__301___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.Lists.List.Add_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l_27)
<=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__8110___24t(V0__A,V2__P)
=> ( ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> p(happ(happ(V2__P,V3__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l))) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l_27)
=> ( p(happ(happ(V2__P,V5__l),V6__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V5__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l_27))) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l)
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
& cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V4__l_27,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Add_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.In_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l)
=> ? [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
& p(cCoq_2eInit_2ePeano_2elt___24a2(V5__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V5__n,V1__l,V3__d) = V2__x ) ) ) ) ) ) ).
fof('Coq.Lists.List.In_nth_error',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__l)
=> ? [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
& cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V4__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V2__x) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_incl_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27))) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__7341___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_length_incl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l_27,V1__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Lists.List.NoDup_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__d] :
( t(V2__d,V0__A)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
<=> ! [V3__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__i)
=> ! [V4__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__j)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__i,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__j,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__i,V1__l,V2__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__j,V1__l,V2__d)
=> V3__i = V4__j ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.NoDup_nth_error',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
<=> ! [V2__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__i)
=> ! [V3__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__j)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__i,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__i) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__j)
=> V2__i = V3__j ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_comm_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Lists.List.app_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).
fof('Coq.Lists.List.app_nil_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.app_nil_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) = V1__l ) ) ).
fof('Coq.Lists.List.app_nth1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_nth2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)),V2__l_27,V3__d) ) ) ) ) ) ) ).
fof('Coq.Lists.List.combine_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V2__l,V3__l_27)) = cCoq_2eInit_2eNat_2emin___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.List.existsb_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7910___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> ( cCoq_2eLists_2eList_2eexistsb___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2efalse
=> happ(V1__f,cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__n,V2__l,V4__d)) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.filter_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7910___24t(V0__A,V1__f)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l))
<=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V3__l)
& happ(V1__f,V2__x) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('Coq.Lists.List.firstn_all',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V1__l) = V1__l ) ) ).
fof('Coq.Lists.List.firstn_all2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) = V2__l ) ) ) ) ).
fof('Coq.Lists.List.firstn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_app_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1),V1__n),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.firstn_le_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l)),V1__n)) ) ) ) ).
fof('Coq.Lists.List.firstn_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l)) = cCoq_2eInit_2eNat_2emin___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)) ) ) ) ).
fof('Coq.Lists.List.firstn_length_le',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V2__n,V1__l)) = V2__n ) ) ) ) ).
fof('Coq.Lists.List.firstn_removelast',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,V2__l)) = cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.firstn_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l)) = cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__x),V2__l)) ) ) ) ).
fof('Coq.Lists.List.firstn_skipn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = V2__l ) ) ) ).
fof('Coq.Lists.List.firstn_skipn_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__x,V2__l) = cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__x),cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l))) ) ) ) ).
fof('Coq.Lists.List.fold_left_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2efold__left___24a5(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__7895___24a1(V0__A),V1__l,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
fof('Coq.Lists.List.in_app_or',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,V3__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__b,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.in_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l)) ) ) ) ).
fof('Coq.Lists.List.in_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V4__x),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_map_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__B)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V1__B,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l))
<=> ? [V5__x] :
( t(V5__x,V0__A)
& happ(V2__f,V5__x) = V4__y
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V3__l) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_Add_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__u] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__u)
=> ! [V4__v] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__v)
=> ( ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,V2__l)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__a,V2__l),V4__v)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(V0__A,V1__a,V3__u,V4__v)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__l,V3__u) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.incl_tran',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__n)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__m)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V2__m,V3__n)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ) ).
fof('Coq.Lists.List.length_zero_iff_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eO
<=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('Coq.Lists.List.map_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).
fof('Coq.Lists.List.map_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__78___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__7846___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__B,V2__C,V4__g,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__f,V5__l)) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V2__C,c_24__lam__7860___24a5(V0__A,V1__B,V2__C,V3__f,V4__g),V5__l) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_default_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> cCoq_2eLists_2eList_2enth__default___24a4(V0__A,V3__d,V2__l,V1__n) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_In',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__x)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_None',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n)) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_Some',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) != cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_app1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V3__n) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_app2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V3__n))
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l_27,cCoq_2eInit_2eNat_2esub___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l))) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_error_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,V2__n) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__a)
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V1__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V6__l2))
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V5__l1) = V2__n ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_indep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ! [V4__d_27] :
( t(V4__d_27,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V4__d_27) ) ) ) ) ) ) ).
fof('Coq.Lists.List.nth_overflow',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__n))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V1__l,V3__d) = V3__d ) ) ) ) ) ).
fof('Coq.Lists.List.nth_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> ? [V5__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l1)
& ? [V6__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V5__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,cCoq_2eLists_2eList_2enth___24a4(V0__A,V1__n,V2__l,V3__d),V6__l2))
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V5__l1) = V1__n ) ) ) ) ) ) ) ).
fof('Coq.Lists.List.partition_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7910___24t(V0__A,V1__f)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
=> ! [V4__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
=> ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V3__l1,V4__l2)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l1),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V4__l2)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.prod_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eLists_2eList_2elist__prod___24a4(V0__A,V1__B,V2__l,V3__l_27)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,V3__l_27)) ) ) ) ) ).
fof('Coq.Lists.List.removelast_firstn',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l)))
=> cCoq_2eLists_2eList_2eremovelast___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__l)) = cCoq_2eLists_2eList_2efirstn___24a3(V0__A,V1__n,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.repeat_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2erepeat___24a3(V0__A,V1__x,V2__n)) = V2__n ) ) ) ).
fof('Coq.Lists.List.rev_app_distr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__y)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__x,V2__y)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__y),cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__x)) ) ) ) ).
fof('Coq.Lists.List.rev_involutive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = V1__l ) ) ).
fof('Coq.Lists.List.rev_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) ) ) ).
fof('Coq.Lists.List.rev_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__d] :
( t(V2__d,V0__A)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V3__n,cCoq_2eLists_2eList_2erev___24a2(V0__A,V1__l),V2__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),V1__l,V2__d) ) ) ) ) ) ).
fof('Coq.Lists.List.seq_length',axiom,
! [V0__len] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__len)
=> ! [V1__start] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__start)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eLists_2eList_2eseq___24a2(V1__start,V0__len)) = V0__len ) ) ).
fof('Coq.Lists.List.skipn_all',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.List.skipn_all2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n))
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ) ).
fof('Coq.Lists.List.skipn_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l1)
=> ! [V3__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l2)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l1,V3__l2)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l1),cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V1__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l1)),V3__l2)) ) ) ) ) ).
fof('Coq.Lists.List.skipn_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__n,V2__l)) = cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__n) ) ) ) ).
fof('Coq.Lists.List.skipn_none',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ).
fof('Coq.Lists.List.skipn_rev',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2eskipn___24a3(V0__A,V1__x,cCoq_2eLists_2eList_2erev___24a2(V0__A,V2__l)) = cCoq_2eLists_2eList_2erev___24a2(V0__A,cCoq_2eLists_2eList_2efirstn___24a3(V0__A,cCoq_2eInit_2eNat_2esub___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l),V1__x),V2__l)) ) ) ) ).
fof('Coq.Lists.List.split_length_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V2__l))) = cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l) ) ) ) ).
fof('Coq.Lists.List.split_length_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V1__B,cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B),cCoq_2eLists_2eList_2esplit___24a3(V0__A,V1__B,V2__l))) = cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V2__l) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1116___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1116___24t(V0__A,V1__eqA)
=> ! [V2__P] :
( c_24__type__8110___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27)
=> ( p(happ(happ(V1__eqA,V4__x),V5__x_27))
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V6__l,V7__l_27)
=> ( p(happ(happ(V2__P,V6__l),V7__l_27))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__x_27,V7__l_27))) ) ) ) ) ) ) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V5__l,V6__l)
=> p(happ(happ(V2__P,V5__l),V6__l)) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqlistA_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__1116___24t(V0__A,V1__eqA)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l_27) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__46___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__59577___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.FinFun.bInjective_bSurjective',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__f] :
( c_24__type__8___24t(V1__f)
=> ( cCoq_2eLogic_2eFinFun_2ebFun___24a2(V0__n,V1__f)
=> ( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V0__n,V1__f) ) ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__7077___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Sorting.Permutation.NoDup_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V1__l)
<=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V2__l_27) ) )
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.NoDup_Permutation_bis',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V2__l_27)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_Equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V1__l)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l_27) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__8110___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V4__l,V5__l_27)
=> ( p(happ(happ(V1__P,V4__l),V5__l_27))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V5__l_27))) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,V6__l))),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__y,V6__l)))) ) ) )
=> ( ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ! [V6__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l_27)
=> ! [V7__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V5__l,V6__l_27)
=> ( p(happ(happ(V1__P,V5__l),V6__l_27))
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l_27,V7__l_27_27)
=> ( p(happ(happ(V1__P,V6__l_27),V7__l_27_27))
=> p(happ(happ(V1__P,V5__l),V7__l_27_27)) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V7__l)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V6__l,V7__l)
=> p(happ(happ(V1__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_length\'',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8237___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2elength___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.Permutation_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V3__l,V4__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l_27)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_middle',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l1)
=> ! [V2__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l2)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,V2__l2)),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V2__l2))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__d] :
( t(V3__d,V0__A)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
<=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27) = c_24__let__4__n__8244___24a2(V0__A,V1__l)
& ? [V5__f] :
( c_24__type__8241___24t(V0__A,V5__f)
& cCoq_2eLogic_2eFinFun_2ebFun___24a2(c_24__let__4__n__8244___24a2(V0__A,V1__l),V5__f)
& cCoq_2eLogic_2eFinFun_2ebInjective___24a2(c_24__let__4__n__8244___24a2(V0__A,V1__l),V5__f)
& ! [V6__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__x)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V6__x,c_24__let__4__n__8244___24a2(V0__A,V1__l)))
=> cCoq_2eLists_2eList_2enth___24a4(V0__A,V6__x,V2__l_27,V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,happ(V5__f,V6__x),V1__l,V3__d) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nth_error',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
<=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)
& ? [V3__f] :
( c_24__type__8241___24t(V0__A,V3__f)
& cCoq_2eLogic_2eFinFun_2eInjective___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l_27,V4__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,happ(V3__f,V4__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_nth_error_bis',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
<=> ? [V3__f] :
( c_24__type__8241___24t(V0__A,V3__f)
& cCoq_2eLogic_2eFinFun_2eInjective___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,V3__f)
& cCoq_2eLogic_2eFinFun_2ebFun___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V2__l_27,V4__n) = cCoq_2eLists_2eList_2enth__error___24a3(V0__A,V1__l,happ(V3__f,V4__n)) ) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V1__l) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ).
fof('Coq.Sorting.Permutation.perm_skip',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,V3__l_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V2__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V3__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__y,V3__l))) ) ) ) ) ).
fof('Coq.Sorting.Permutation.perm_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__l_27_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l_27,V3__l_27_27)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V3__l_27_27) ) ) ) ) ) ) ).
fof('Coq.Vectors.Fin.t_ind',axiom,
! [V0__P] :
( c_24__type__73438___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)),cCoq_2eVectors_2eFin_2eF1___24a1(V1__n))) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__t] :
( cCoq_2eVectors_2eFin_2et___24t(V2__n,V3__t)
=> ( p(happ(happ(V0__P,V2__n),V3__t))
=> p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eVectors_2eFin_2eFS___24a2(V2__n,V3__t))) ) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__t] :
( cCoq_2eVectors_2eFin_2et___24t(V3__n,V4__t)
=> p(happ(happ(V0__P,V3__n),V4__t)) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists2_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__x1] :
( t(V4__x1,V0__A)
=> ! [V5__x2] :
( t(V5__x2,V1__B)
=> ! [V6__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V6__v1)
=> ! [V7__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V3__m,V7__v2)
=> ( p(happ(happ(V2__P,V4__x1),V5__x2))
=> cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x1,V3__m,V6__v1),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V5__x2,V3__m,V7__v2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists2_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__x1] :
( t(V4__x1,V0__A)
=> ! [V5__x2] :
( t(V5__x2,V1__B)
=> ! [V6__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V6__v1)
=> ! [V7__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V3__m,V7__v2)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,V3__m,V6__v1,V7__v2)
=> cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x1,V3__m,V6__v1),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V5__x2,V3__m,V7__v2)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists2_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__P] :
( c_24__type__75905___24t(V0__A,V1__B,V3__P)
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x1] :
( t(V5__x1,V0__A)
=> ! [V6__x2] :
( t(V6__x2,V1__B)
=> ! [V7__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V7__v1)
=> ! [V8__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V4__m,V8__v2)
=> ( p(happ(happ(V2__P,V5__x1),V6__x2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x1,V4__m,V7__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V6__x2,V4__m,V8__v2))) ) ) ) ) ) )
=> ( ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ! [V6__x1] :
( t(V6__x1,V0__A)
=> ! [V7__x2] :
( t(V7__x2,V1__B)
=> ! [V8__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__m,V8__v1)
=> ! [V9__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V5__m,V9__v2)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,V5__m,V8__v1,V9__v2)
=> ( p(happ(happ(happ(V3__P,V5__m),V8__v1),V9__v2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V6__x1,V5__m,V8__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V7__x2,V5__m,V9__v2))) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__t)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V6__n,V8__t)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,V6__n,V7__t,V8__t)
=> p(happ(happ(happ(V3__P,V6__n),V7__t),V8__t)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists2_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__P] :
( c_24__type__75905___24t(V0__A,V1__B,V3__P)
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x1] :
( t(V5__x1,V0__A)
=> ! [V6__x2] :
( t(V6__x2,V1__B)
=> ! [V7__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V7__v1)
=> ! [V8__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V4__m,V8__v2)
=> ( p(happ(happ(V2__P,V5__x1),V6__x2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x1,V4__m,V7__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V6__x2,V4__m,V8__v2))) ) ) ) ) ) )
=> ( ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ! [V6__x1] :
( t(V6__x1,V0__A)
=> ! [V7__x2] :
( t(V7__x2,V1__B)
=> ! [V8__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__m,V8__v1)
=> ! [V9__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V5__m,V9__v2)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,V5__m,V8__v1,V9__v2)
=> ( p(happ(happ(happ(V3__P,V5__m),V8__v1),V9__v2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V6__x1,V5__m,V8__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V7__x2,V5__m,V9__v2))) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__t)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V6__n,V8__t)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V0__A,V1__B,V2__P,V6__n,V7__t,V8__t)
=> p(happ(happ(happ(V3__P,V6__n),V7__t),V8__t)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__v)
=> ( p(happ(V1__P,V3__x))
=> cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V2__m,V4__v)) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__v)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,V2__m,V4__v)
=> cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V2__m,V4__v)) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V5__v)
=> ( p(happ(V1__P,V4__x))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x,V3__m,V5__v))) ) ) ) )
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,V4__m,V6__v)
=> ( p(happ(happ(V2__P,V4__m),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__m,V6__v))) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__t)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,V5__n,V6__t)
=> p(happ(happ(V2__P,V5__n),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Exists_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V5__v)
=> ( p(happ(V1__P,V4__x))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x,V3__m,V5__v))) ) ) ) )
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,V4__m,V6__v)
=> ( p(happ(happ(V2__P,V4__m),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__m,V6__v))) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__t)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(V0__A,V1__P,V5__n,V6__t)
=> p(happ(happ(V2__P,V5__n),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall2_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__x1] :
( t(V4__x1,V0__A)
=> ! [V5__x2] :
( t(V5__x2,V1__B)
=> ! [V6__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V6__v1)
=> ! [V7__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V3__m,V7__v2)
=> ( p(happ(happ(V2__P,V4__x1),V5__x2))
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,V3__m,V6__v1,V7__v2)
=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x1,V3__m,V6__v1),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V5__x2,V3__m,V7__v2)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall2_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__P] :
( c_24__type__75905___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)),cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__B)))
=> ( ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ! [V6__x1] :
( t(V6__x1,V0__A)
=> ! [V7__x2] :
( t(V7__x2,V1__B)
=> ! [V8__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__m,V8__v1)
=> ! [V9__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V5__m,V9__v2)
=> ( p(happ(happ(V2__P,V6__x1),V7__x2))
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,V5__m,V8__v1,V9__v2)
=> ( p(happ(happ(happ(V3__P,V5__m),V8__v1),V9__v2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V6__x1,V5__m,V8__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V7__x2,V5__m,V9__v2))) ) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__t)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V6__n,V8__t)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,V6__n,V7__t,V8__t)
=> p(happ(happ(happ(V3__P,V6__n),V7__t),V8__t)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall2_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__15153___24t(V0__A,V1__B,V2__P)
=> ! [V3__P] :
( c_24__type__75905___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)),cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__B)))
=> ( ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ! [V6__x1] :
( t(V6__x1,V0__A)
=> ! [V7__x2] :
( t(V7__x2,V1__B)
=> ! [V8__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__m,V8__v1)
=> ! [V9__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V5__m,V9__v2)
=> ( p(happ(happ(V2__P,V6__x1),V7__x2))
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,V5__m,V8__v1,V9__v2)
=> ( p(happ(happ(happ(V3__P,V5__m),V8__v1),V9__v2))
=> p(happ(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V6__x1,V5__m,V8__v1)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V7__x2,V5__m,V9__v2))) ) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__t)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V6__n,V8__t)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V0__A,V1__B,V2__P,V6__n,V7__t,V8__t)
=> p(happ(happ(happ(V3__P,V6__n),V7__t),V8__t)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V4__v)
=> ( p(happ(V1__P,V3__x))
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,V2__n,V4__v)
=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V2__n,V4__v)) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v)
=> ( p(happ(V1__P,V5__x))
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,V4__n,V6__v)
=> ( p(happ(happ(V2__P,V4__n),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__n,V6__v))) ) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,V5__n,V6__v)
=> p(happ(happ(V2__P,V5__n),V6__v)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.Forall_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2181___24t(V0__A,V1__P)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v)
=> ( p(happ(V1__P,V5__x))
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,V4__n,V6__v)
=> ( p(happ(happ(V2__P,V4__n),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__n,V6__v))) ) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(V0__A,V1__P,V5__n,V6__v)
=> p(happ(happ(V2__P,V5__n),V6__v)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.In_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V3__v)
=> cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__a,V2__m,V3__v)) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.In_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__v)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,V2__m,V4__v)
=> cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V2__m,V4__v)) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.In_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V4__v)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__a,V3__m,V4__v))) ) )
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,V4__m,V6__v)
=> ( p(happ(happ(V2__P,V4__m),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__m,V6__v))) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__t)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,V5__n,V6__t)
=> p(happ(happ(V2__P,V5__n),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.In_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__A,V2__P)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V4__v)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__a,V3__m,V4__v))) ) )
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__m,V6__v)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,V4__m,V6__v)
=> ( p(happ(happ(V2__P,V4__m),V6__v))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__x,V4__m,V6__v))) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__t)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(V0__A,V1__a,V5__n,V6__t)
=> p(happ(happ(V2__P,V5__n),V6__t)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1180___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V3__h] :
( t(V3__h,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> ( p(happ(happ(V1__P,V4__n),V5__t))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> p(happ(happ(V1__P,V4__n),V5__t)) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorDef.t_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__1180___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V3__h] :
( t(V3__h,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> ( p(happ(happ(V1__P,V4__n),V5__t))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> p(happ(happ(V1__P,V4__n),V5__t)) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorEq.eqb_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__A__beq] :
( c_24__type__8531___24t(V0__A,V1__A__beq)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( happ(happ(V1__A__beq,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2etrue
<=> V2__x = V3__y ) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__v1)
=> ! [V5__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__v2)
=> ( cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V3__n,V3__n,V4__v1,V5__v2) = cCoq_2eInit_2eDatatypes_2etrue
<=> V4__v1 = V5__v2 ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorEq.eqb_nat_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__A__beq] :
( c_24__type__8531___24t(V0__A,V1__A__beq)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__v1)
=> ! [V5__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__v2)
=> ( cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V0__A,V1__A__beq,V2__m,V3__n,V4__v1,V5__v2) = cCoq_2eInit_2eDatatypes_2etrue
=> V2__m = V3__n ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.append_comm_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
=> ! [V4__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__w)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__a,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m),cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,V1__n,V2__m,V3__v,V4__w)) = cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__m,cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__a,V1__n,V3__v),V4__w) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.cons_inj',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a1] :
( t(V1__a1,V0__A)
=> ! [V2__a2] :
( t(V2__a2,V0__A)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__v1)
=> ! [V5__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__v2)
=> ( cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__a1,V3__n,V4__v1) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__a2,V3__n,V5__v2)
=> ( V1__a1 = V2__a2
& V4__v1 = V5__v2 ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.eq_nth_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v1] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__v1)
=> ! [V3__v2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v2)
=> ( ! [V4__p1] :
( cCoq_2eVectors_2eFin_2et___24t(V1__n,V4__p1)
=> ! [V5__p2] :
( cCoq_2eVectors_2eFin_2et___24t(V1__n,V5__p2)
=> ( V4__p1 = V5__p2
=> cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V1__n,V2__v1,V4__p1) = cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V1__n,V3__v2,V5__p2) ) ) )
<=> V2__v1 = V3__v2 ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.fold_left_right_assoc_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__7890___24t(V0__A,V1__B,V2__f)
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> ! [V5__c] :
( t(V5__c,V1__B)
=> happ(happ(V2__f,happ(happ(V2__f,V3__a),V4__b)),V5__c) = happ(happ(V2__f,happ(happ(V2__f,V3__a),V5__c)),V4__b) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V4__n,V5__v)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> cCoq_2eVectors_2eVectorDef_2efold__left___24a6(V1__B,V0__A,V2__f,V6__a,V4__n,V5__v) = cCoq_2eVectors_2eVectorDef_2efold__right___24a6(V1__B,V0__A,c_24__lam__76031___24a4(V0__A,V1__B,V2__f,V4__n),V4__n,V5__v,V6__a) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.nth_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__v)
=> ! [V5__p1] :
( cCoq_2eVectors_2eFin_2et___24t(V3__n,V5__p1)
=> ! [V6__p2] :
( cCoq_2eVectors_2eFin_2et___24t(V3__n,V6__p2)
=> ( V5__p1 = V6__p2
=> cCoq_2eVectors_2eVectorDef_2enth___24a4(V1__B,V3__n,cCoq_2eVectors_2eVectorDef_2emap___24a5(V0__A,V1__B,V2__f,V3__n,V4__v),V5__p1) = happ(V2__f,cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V3__n,V4__v,V6__p2)) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.nth_map2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__19980___24t(V0__A,V1__B,V2__C,V3__f)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ! [V6__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V4__n,V6__w)
=> ! [V7__p1] :
( cCoq_2eVectors_2eFin_2et___24t(V4__n,V7__p1)
=> ! [V8__p2] :
( cCoq_2eVectors_2eFin_2et___24t(V4__n,V8__p2)
=> ! [V9__p3] :
( cCoq_2eVectors_2eFin_2et___24t(V4__n,V9__p3)
=> ( V7__p1 = V8__p2
=> ( V8__p2 = V9__p3
=> cCoq_2eVectors_2eVectorDef_2enth___24a4(V2__C,V4__n,cCoq_2eVectors_2eVectorDef_2emap2___24a7(V0__A,V1__B,V2__C,V3__f,V4__n,V5__v,V6__w),V7__p1) = happ(happ(V3__f,cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V4__n,V5__v,V8__p2)),cCoq_2eVectors_2eVectorDef_2enth___24a4(V1__B,V4__n,V6__w,V9__p3)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.nth_order_last',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)))
=> cCoq_2eVectors_2eVectorDef_2enth__order___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v,V1__n) = cCoq_2eVectors_2eVectorDef_2elast___24a3(V0__A,V1__n,V2__v) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.shiftin_last',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> cCoq_2eVectors_2eVectorDef_2elast___24a3(V0__A,V2__n,cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V0__A,V2__n,V1__a,V3__v)) = V1__a ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.shiftin_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> ! [V4__k1] :
( cCoq_2eVectors_2eFin_2et___24t(V2__n,V4__k1)
=> ! [V5__k2] :
( cCoq_2eVectors_2eFin_2et___24t(V2__n,V5__k2)
=> ( V4__k1 = V5__k2
=> cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V0__A,V2__n,V1__a,V3__v),cCoq_2eVectors_2eFin_2eL__R___24a3(V2__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V4__k1)) = cCoq_2eVectors_2eVectorDef_2enth___24a4(V0__A,V2__n,V3__v,V5__k2) ) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.shiftrepeat_last',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> cCoq_2eVectors_2eVectorDef_2elast___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eVectors_2eVectorDef_2eshiftrepeat___24a3(V0__A,V1__n,V2__v)) = cCoq_2eVectors_2eVectorDef_2elast___24a3(V0__A,V1__n,V2__v) ) ) ) ).
fof('Coq.Vectors.VectorSpec.splitat_append',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
=> ! [V4__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__w)
=> cCoq_2eVectors_2eVectorDef_2esplitat___24a4(V0__A,V1__n,V2__m,cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,V1__n,V2__m,V3__v,V4__w)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V1__n),cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V2__m),V3__v,V4__w) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.take_O',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__n))
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
=> cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V1__n,cCoq_2eInit_2eDatatypes_2eO,V3__v) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.take_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__v)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V4__w)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V3__m)))
=> cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V3__m),V1__n,cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,V1__n,V3__m,V2__v,V4__w)) = V2__v ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.take_idem',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__p,V2__n))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__p,V1__p))
=> cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V1__p,V1__p,cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V2__n,V1__p,V3__v)) = cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V2__n,V1__p,V3__v) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.take_prf_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__p,V2__n))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__p,V2__n))
=> cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V2__n,V1__p,V3__v) = cCoq_2eVectors_2eVectorDef_2etake___24a4(V0__A,V2__n,V1__p,V3__v) ) ) ) ) ) ) ).
fof('Coq.Vectors.VectorSpec.to_list_of_list_opp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eVectors_2eVectorDef_2eof__list___24a2(V0__A,V1__l)) = V1__l ) ) ).
fof('Coq.Vectors.VectorSpec.uncons_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
=> cCoq_2eVectors_2eVectorDef_2euncons___24a3(V0__A,V1__n,cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__a,V1__n,V3__v)) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V1__n),V2__a,V3__v) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.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__21049___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.Zcomplements.Zlength_correct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eZArith_2eZcomplements_2eZlength___24a2(V0__A,V1__l) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_iff',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.Nat2Z.is_nonneg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n))) ) ).
fof('Coq.ZArith.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.cardinal_0',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ? [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V1__l)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V1__l)
& ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive),V2__x,V1__l) ) )
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V0__s) = cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V1__l) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__85___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__85___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__85___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__85___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__85___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__85___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__85___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__85___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__85___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__85___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__85___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__85___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__85___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__85___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__85___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__85___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__9009___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__8308___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1116___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_R',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__9009___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__8308___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__1116___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__9009___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__8308___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1116___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9009___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__8308___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__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,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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.ARth_SRth',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__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___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)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__9009___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__8308___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__9009___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.SReqe_Reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__9009___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__1116___24t(V0__R,V3__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,V3__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V0__R),V3__req) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_reqe',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__9009___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__8308___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__1116___24t(V0__R,V4__req)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9009___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__8308___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9009___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__8308___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8308___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__38884___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__38884___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__38884___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__38898___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__38905___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__15181___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__9009___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__9009___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__9009___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__8308___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1116___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__38884___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__38884___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__38884___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__38898___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__38905___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__15181___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__9009___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__1116___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__56805___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__7890___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Transitive_le',axiom,
cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('QuicksortComplexity.arith_lems.le_exists_plus',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ? [V3__d] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__d)
& V1__y = cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V3__d) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.lt_exists_plus',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ? [V3__d] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__d)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V3__d)) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_inv_perm',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V2__l)
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l_27)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__X,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,V1__x,V4__l_27),V2__l) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.In_map_inv',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__78___24t(V0__T,V1__U,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l)
=> ! [V4__y] :
( t(V4__y,V1__U)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V1__U,V4__y,cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V2__f,V3__l))
=> ? [V6__x] :
( t(V6__x,V0__T)
& happ(V2__f,V6__x) = V4__y
& cCoq_2eLists_2eList_2eIn___24a3(V0__T,V6__x,V3__l) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.NoDup_incl_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__b)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__a) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__b)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V1__a)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,V1__a,V2__b)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__a,V2__b) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.NoDup_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__y,V3__l)
=> ( happ(V2__f,V4__x) = happ(V2__f,V5__y)
=> V4__x = V5__y ) ) ) ) )
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V3__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V1__B,cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V3__l)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Permutation_concatMap',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__15203___24t(V0__T,V1__U,V2__f)
=> ! [V3__g] :
( c_24__type__15203___24t(V0__T,V1__U,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__l)
=> ( ! [V5__x] :
( t(V5__x,V0__T)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__T,V5__x,V4__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__U,happ(V2__f,V5__x),happ(V3__g,V5__x)) ) )
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__U,cQuicksortComplexity_2elist__utils_2econcat___24a2(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),V2__f,V4__l)),cQuicksortComplexity_2elist__utils_2econcat___24a2(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),V3__g,V4__l))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Permutation_incl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__b)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__X,V1__a,V2__b)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__X,V1__a,V2__b) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Permutation_length_morphism',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__8237___24a1(V0__T),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__T),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2elength___24a1(V0__T)) ) ).
fof('QuicksortComplexity.list_utils.Permutation_perms',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__19829___24a1(V0__T),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__T),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T))),cQuicksortComplexity_2elist__utils_2eperms___24a1(V0__T)) ) ).
fof('QuicksortComplexity.list_utils.Permuted_Permutation_map',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__T,V2__R)
=> ! [V3__f] :
( c_24__type__78___24t(V0__T,V1__U,V3__f)
=> ( ! [V4__x] :
( t(V4__x,V0__T)
=> ! [V5__y] :
( t(V5__y,V0__T)
=> ( p(happ(happ(V2__R,V4__x),V5__y))
=> happ(V3__f,V4__x) = happ(V3__f,V5__y) ) ) )
=> ! [V5__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__a)
=> ! [V6__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V6__b)
=> ( cQuicksortComplexity_2elist__utils_2ePermuted___24a4(V0__T,V2__R,V5__a,V6__b)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V3__f,V5__a),cCoq_2eLists_2eList_2emap___24a4(V0__T,V1__U,V3__f,V6__b)) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Reflexive_Transitive',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__T)) ) ).
fof('QuicksortComplexity.list_utils.add_same',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__c)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V1__l)
=> ( ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__x,V1__l)
=> V2__x = V0__c ) )
=> cQuicksortComplexity_2elist__utils_2eadd___24a1(V1__l) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,V1__l),V0__c) ) ) ) ).
fof('QuicksortComplexity.list_utils.app_nil_r',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__T,V1__l,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) = V1__l ) ) ).
fof('QuicksortComplexity.list_utils.complementary_filter_perm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__A,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V2__l,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__p,V2__l),cCoq_2eLists_2eList_2efilter___24a3(V0__A,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2enegb,V1__p),V2__l))) ) ) ) ).
fof('QuicksortComplexity.list_utils.concat_repeat',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__c] :
( t(V3__c,V0__T)
=> cQuicksortComplexity_2elist__utils_2econcat___24a2(V0__T,cQuicksortComplexity_2elist__utils_2erepeat___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__n,cQuicksortComplexity_2elist__utils_2erepeat___24a3(V0__T,V2__m,V3__c))) = cQuicksortComplexity_2elist__utils_2erepeat___24a3(V0__T,cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m),V3__c) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.count_le',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V2__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V2__l))) ) ) ) ).
fof('QuicksortComplexity.list_utils.count_lt',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__X,V1__p)
=> ! [V2__v] :
( t(V2__v,V0__X)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V2__v,V3__l)
=> ( happ(V1__p,V2__v) = cCoq_2eInit_2eDatatypes_2efalse
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V3__l))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.eR_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__15153___24t(V0__A,V1__B,V2__R)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V1__B)
=> ( p(happ(happ(V2__R,V3__a),V4__b))
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l_27)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V6__l,V7__l_27)
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V6__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V4__b,V7__l_27)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.eR_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__15153___24t(V0__A,V1__B,V2__R)
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__15153___24t(V0__A,V1__B,V2__R)
=> ! [V3__P] :
( c_24__type__15170___24t(V0__A,V1__B,V3__P)
=> ( p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)))
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V1__B)
=> ( p(happ(happ(V2__R,V5__a),V6__b))
=> ! [V8__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V8__l)
=> ! [V9__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V9__l_27)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V8__l,V9__l_27)
=> ( p(happ(happ(V3__P,V8__l),V9__l_27))
=> p(happ(happ(V3__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V5__a,V8__l)),cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V6__b,V9__l_27))) ) ) ) ) ) ) )
=> ! [V6__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V6__l)
=> ! [V7__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V7__l)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V1__B,V2__R,V6__l,V7__l)
=> p(happ(happ(V3__P,V6__l),V7__l)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_le_S',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,V1__b)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele,V0__a,V1__b)
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele,cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,V0__a),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,V1__b)) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__1116___24t(V0__A,V1__R)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__b)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__A,V0__A,V1__R,V2__a,V3__b)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__a) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__b) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_map_map',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__15181___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__15181___24t(V0__X,V1__Y,V3__g)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__Y,V4__l)
=> ! [V5__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V5__R)
=> ( ! [V6__x] :
( t(V6__x,V1__Y)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V1__Y,V6__x,V4__l)
=> p(happ(happ(V5__R,happ(V2__f,V6__x)),happ(V3__g,V6__x))) ) )
=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V0__X,V0__X,V5__R,cCoq_2eLists_2eList_2emap___24a4(V1__Y,V0__X,V2__f,V4__l),cCoq_2eLists_2eList_2emap___24a4(V1__Y,V0__X,V3__g,V4__l)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.elemsR_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cQuicksortComplexity_2elist__utils_2eelemsR___24a3(V0__A,V0__A,V1__R)) ) ) ) ).
fof('QuicksortComplexity.list_utils.empty_nil',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V1__x)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V1__x) = cCoq_2eInit_2eDatatypes_2eO
=> V1__x = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) ) ) ).
fof('QuicksortComplexity.list_utils.filter_none',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,V2__l)
=> happ(V1__p,V3__x) = cCoq_2eInit_2eDatatypes_2efalse ) )
<=> cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.filter_perm',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__15070___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7910___24a1(V0__X),c_24__type__15075___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2epointwise__relation___24a3(V0__X,cCoq_2eInit_2eDatatypes_2ebool,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__X),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__X),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__X))),cCoq_2eLists_2eList_2efilter___24a1(V0__X)) ) ).
fof('QuicksortComplexity.list_utils.incl_In',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V2__l)
=> ! [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__l_27)
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__X,V2__l,V4__l_27)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,V4__l_27) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_0_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2eO
<=> V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_concat',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cQuicksortComplexity_2elist__utils_2econcat___24a2(V0__T,V1__l)) = cQuicksortComplexity_2elist__utils_2eadd___24a1(cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2elength___24a1(V0__T),V1__l)) ) ) ).
fof('QuicksortComplexity.list_utils.length_excl_counts',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V2__l) = cCoq_2eInit_2eNat_2eadd___24a2(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V2__l),cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2enegb,V1__p),V2__l)) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_filter',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__X,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,cCoq_2eLists_2eList_2efilter___24a3(V0__X,V1__p,V2__l)) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V2__l) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_filter_le',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( c_24__type__7910___24t(V0__T,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eLists_2eList_2efilter___24a3(V0__T,V1__p,V2__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_in_splits',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V2__p)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),V2__p,cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V1__l))
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V2__p))) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V1__l) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_insert_everywhere',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a3(V0__T,V1__x,V2__l)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l)) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_merges',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( c_24__type__83___24t(V1__F)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__a)
=> ! [V3__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__b)
=> ! [V4__r] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V4__r)
=> ( ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> happ(happ(V1__F,cCoq_2eInit_2eDatatypes_2eO),V5__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
=> ( ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> happ(happ(V1__F,V6__n),cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
=> ( ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ! [V8__n_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V8__n_27)
=> cCoq_2eInit_2eNat_2eadd___24a2(happ(happ(V1__F,V7__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V8__n_27)),happ(happ(V1__F,cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n)),V8__n_27)) = happ(happ(V1__F,cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V8__n_27)) ) )
=> ( cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(V0__T,V2__a,V3__b,V4__r)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V4__r) = happ(happ(V1__F,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__a)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V3__b)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_merges_mor',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__19839___24a1(V0__T),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),c_24__type__19829___24a1(V0__T),cQuicksortComplexity_2eutil_2eon___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,c_24__lam__19843,cCoq_2eInit_2eDatatypes_2elength___24a1(V0__T),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cQuicksortComplexity_2eutil_2eon___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,c_24__lam__19843,cCoq_2eInit_2eDatatypes_2elength___24a1(V0__T),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cQuicksortComplexity_2eutil_2eon___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2enat,c_24__lam__19843,cCoq_2eInit_2eDatatypes_2elength___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)))),cQuicksortComplexity_2elist__utils_2emerges___24a1(V0__T)) ) ).
fof('QuicksortComplexity.list_utils.length_ne_0_ne_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l) != cCoq_2eInit_2eDatatypes_2eO
=> V1__l != cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) ) ) ) ).
fof('QuicksortComplexity.list_utils.length_perms',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cQuicksortComplexity_2elist__utils_2eperms___24a2(V0__T,V1__l)) = cCoq_2eArith_2eFactorial_2efact___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V1__l)) ) ) ).
fof('QuicksortComplexity.list_utils.length_repeat',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__c] :
( t(V1__c,V0__T)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cQuicksortComplexity_2elist__utils_2erepeat___24a3(V0__T,V2__n,V1__c)) = V2__n ) ) ) ).
fof('QuicksortComplexity.list_utils.length_splits',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V1__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V1__l) ) ) ).
fof('QuicksortComplexity.list_utils.map_Permutation_mor',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__78___24t(V0__T,V1__U,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__18558___24a2(V0__T,V1__U),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__T),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V1__U)),cCoq_2eLists_2eList_2emap___24a3(V0__T,V1__U,V2__f)) ) ) ) ).
fof('QuicksortComplexity.list_utils.map_concat_map',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__V] :
( cType___24t(V2__V)
=> ! [V3__g] :
( c_24__type__15203___24t(V0__T,V1__U,V3__g)
=> ! [V4__f] :
( c_24__type__7846___24t(V0__T,V1__U,V2__V,V4__f)
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V1__U,V2__V,V4__f,cQuicksortComplexity_2elist__utils_2econcat___24a2(V1__U,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),V3__g,V5__l))) = cQuicksortComplexity_2elist__utils_2econcat___24a2(V2__V,cCoq_2eLists_2eList_2emap___24a4(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V2__V),cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__U),cCoq_2eInit_2eDatatypes_2elist___24a1(V2__V),cCoq_2eLists_2eList_2emap___24a3(V1__U,V2__V,V4__f),V3__g),V5__l)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.map_length_filter_permuted_splits',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__T,V1__l,V2__l_27)
=> ! [V4__p] :
( c_24__type__8531___24t(V0__T,V4__p)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2enat,c_24__lam__19867___24a2(V0__T,V4__p),cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V1__l)),cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__T,cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T)),cCoq_2eInit_2eDatatypes_2enat,c_24__lam__19872___24a2(V0__T,V4__p),cQuicksortComplexity_2elist__utils_2esplits___24a2(V0__T,V2__l_27))) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.map_repeat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__c] :
( t(V3__c,V1__B)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V5__x,V4__l)
=> happ(V2__f,V5__x) = V3__c ) )
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__B,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V4__l),V3__c) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.merges_nil_r',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__a)
=> cQuicksortComplexity_2elist__utils_2emerges___24a3(V0__T,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T))) ) ) ).
fof('QuicksortComplexity.list_utils.merges_real_eq',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__a)
=> ! [V2__b] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__b)
=> cQuicksortComplexity_2elist__utils_2emerges___24a3(V0__T,V1__a,V2__b) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809___24a3(V0__T,V1__a,V2__b) ) ) ) ).
fof('QuicksortComplexity.list_utils.perms_are_perms',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__a)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),V2__a,cQuicksortComplexity_2elist__utils_2eperms___24a2(V0__T,V1__l))
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__T,V2__a,V1__l) ) ) ) ) ).
fof('QuicksortComplexity.nat_below.cond_eq_eq',axiom,
! [V0__T] :
( c_24__type__158___24t(V0__T)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__c] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__c)
=> ! [V3__x] :
( t(V3__x,happ(V0__T,cCoq_2eInit_2eNat_2eadd___24a2(V2__c,V1__n)))
=> ! [V4__y] :
( t(V4__y,happ(V0__T,cCoq_2eInit_2eNat_2eadd___24a2(V2__c,V1__n)))
=> cQuicksortComplexity_2enat__below_2econd__eq___24a6(V0__T,V1__n,V1__n,V2__c,V3__x,V4__y) = c_24__prop__3021___24a5(V0__T,V1__n,V2__c,V3__x,V4__y) ) ) ) ) ) ).
fof('QuicksortComplexity.nat_below.cond_eq_neq',axiom,
! [V0__T] :
( c_24__type__158___24t(V0__T)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__c] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__c)
=> ! [V4__x] :
( t(V4__x,happ(V0__T,cCoq_2eInit_2eNat_2eadd___24a2(V3__c,V1__n)))
=> ! [V5__y] :
( t(V5__y,happ(V0__T,cCoq_2eInit_2eNat_2eadd___24a2(V3__c,V2__m)))
=> ( V1__n != V2__m
=> cQuicksortComplexity_2enat__below_2econd__eq___24a6(V0__T,V1__n,V2__m,V3__c,V4__x,V5__y) = c_24True ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.nat_below.natBelow_ind',axiom,
! [V0__P] :
( c_24__type__76797___24t(V0__P)
=> ( ! [V1__v] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__v)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__v,V2__p))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V1__v,V2__p))) ) )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__n] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V2__n,V3__n)
=> p(happ(happ(V0__P,V2__n),V3__n)) ) ) ) ) ).
fof('QuicksortComplexity.nat_below.natBelow_uneq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V2__y)
=> ( cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__x) != cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V2__y)
=> V1__x != V2__y ) ) ) ) ).
fof('QuicksortComplexity.nat_below.natBelow_unique',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V2__y)
=> ( cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__x) = cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('QuicksortComplexity.nat_seqs.nats_Sb',axiom,
! [V0__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__w)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> cQuicksortComplexity_2enat__seqs_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__b),V0__w) = cCoq_2eLists_2eList_2emap___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS,cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V0__w)) ) ) ).
fof('QuicksortComplexity.nat_seqs.nats_length',axiom,
! [V0__w] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__w)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__seqs_2enats___24a2(V1__b,V0__w)) = V0__w ) ) ).
fof('QuicksortComplexity.skip_list.SkipList_head',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l_27)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__l,V3__l_27)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V1__x,V2__l),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V1__x,V3__l_27)) ) ) ) ) ) ).
fof('QuicksortComplexity.skip_list.SkipList_incl',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__y)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__x)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__x,V1__y)
=> cCoq_2eLists_2eList_2eincl___24a3(V0__T,V2__x,V1__y) ) ) ) ) ).
fof('QuicksortComplexity.skip_list.SkipList_refl',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__l)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V1__l,V1__l) ) ) ).
fof('QuicksortComplexity.skip_list.SkipList_tail',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V3__l_27)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__l,V3__l_27)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V1__x,V3__l_27)) ) ) ) ) ) ).
fof('QuicksortComplexity.skip_list.SkipList_trans',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V1__y)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__x)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__x,V1__y)
=> ! [V4__z] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V4__z)
=> ( cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V1__y,V4__z)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__T,V2__x,V4__z) ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.EO',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e),cQuicksortComplexity_2esort__order_2eEle___24a1(V0__e)) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_apply_sym',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V3__c)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V3__c)
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V1__x) = V3__c ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_eq_trans_l',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ! [V4__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V4__c)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eEq
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V3__z) = V4__c
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = V4__c ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_eq_trans_r',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ! [V4__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V4__c)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = V4__c
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V3__z) = cCoq_2eInit_2eDatatypes_2eEq
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = V4__c ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_ge_gt_trans',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ( cQuicksortComplexity_2esort__order_2eEge___24a3(V0__e,V1__x,V2__y)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V3__z) = cCoq_2eInit_2eDatatypes_2eGt
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_inv_sym',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V3__c)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) != cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V3__c)
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V1__x) != V3__c ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_le_lt_trans',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V3__z) = cCoq_2eInit_2eDatatypes_2eLt
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_lt_le_trans',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eLt
=> ( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V2__y,V3__z))
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_refl',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V1__x) = cCoq_2eInit_2eDatatypes_2eEq ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_sym',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V1__x)) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ecmp_trans',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V3__z)
=> ! [V4__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V4__c)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V2__y) = V4__c
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V2__y,V3__z) = V4__c
=> cQuicksortComplexity_2esort__order_2eEcmp___24a3(V0__e,V1__x,V3__z) = V4__c ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ege_Ele',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( cQuicksortComplexity_2esort__order_2eEge___24a3(V0__e,V1__x,V2__y)
=> p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V2__y,V1__x)) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ege_preorder',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e),cQuicksortComplexity_2esort__order_2eEge___24a1(V0__e)) ) ).
fof('QuicksortComplexity.sort_order.Egeb_preorder',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e),c_24__lam__3159___24a1(V0__e)) ) ).
fof('QuicksortComplexity.sort_order.Egeb_true',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( cQuicksortComplexity_2esort__order_2eEge___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEgeb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Egtb_true',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( cQuicksortComplexity_2esort__order_2eEgt___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEgtb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ele_Ege',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
=> cQuicksortComplexity_2esort__order_2eEge___24a3(V0__e,V2__y,V1__x) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Ele_nlt',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
=> ~ cQuicksortComplexity_2esort__order_2eElt___24a3(V0__e,V2__y,V1__x) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Eleb_preorder',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e),c_24__lam__3155___24a1(V0__e)) ) ).
fof('QuicksortComplexity.sort_order.Eleb_true',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
<=> cQuicksortComplexity_2esort__order_2eEleb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Elt_irrefl',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ~ cQuicksortComplexity_2esort__order_2eElt___24a3(V0__e,V1__x,V1__x) ) ) ).
fof('QuicksortComplexity.sort_order.Eltb_true',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( cQuicksortComplexity_2esort__order_2eElt___24a3(V0__e,V1__x,V2__y)
<=> cQuicksortComplexity_2esort__order_2eEltb___24a3(V0__e,V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('QuicksortComplexity.sort_order.Enle_le',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ! [V1__x] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V0__e,V2__y)
=> ( ~ p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V1__x,V2__y))
=> p(cQuicksortComplexity_2esort__order_2eEle___24a3(V0__e,V2__y,V1__x)) ) ) ) ) ).
fof('QuicksortComplexity.sort_order.preorder_impl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__P)
=> ! [V2__Q] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> ( p(happ(happ(V1__P,V3__x),V4__y))
<=> p(happ(happ(V2__Q,V3__x),V4__y)) ) ) )
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__P)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V2__Q) ) ) ) ) ) ).
fof('QuicksortComplexity.util.conj_prod',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
& p(V1__B) )
=> p(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) ) ) ) ).
fof('QuicksortComplexity.util.pair_rel_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__Ra] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__Ra)
=> ! [V3__Rb] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__Rb)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__a_27] :
( t(V5__a_27,V0__A)
=> ! [V6__b] :
( t(V6__b,V1__B)
=> ( p(happ(happ(V2__Ra,V4__a),V5__a_27))
=> cQuicksortComplexity_2eutil_2epair__rel___24a6(V0__A,V1__B,V2__Ra,V3__Rb,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__a,V6__b),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V5__a_27,V6__b)) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.pair_rel_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__Ra] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__Ra)
=> ! [V3__Rb] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__Rb)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V1__B)
=> ! [V6__b_27] :
( t(V6__b_27,V1__B)
=> ( p(happ(happ(V3__Rb,V5__b),V6__b_27))
=> cQuicksortComplexity_2eutil_2epair__rel___24a6(V0__A,V1__B,V2__Ra,V3__Rb,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__a,V5__b),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__a,V6__b_27)) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.well_founded_pairs',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__Ra] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__Ra)
=> ! [V3__Rb] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__Rb)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V2__Ra)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V1__B,V3__Rb)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2epair__rel___24a4(V0__A,V1__B,V2__Ra,V3__Rb)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_as_nb_val',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__x)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V0__n),V2__m,V3__l)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__x),cQuicksortComplexity_2evec_2eto__list___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__m,cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V0__n),cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__below_2enb__val___24a1(V0__n),V2__m,V3__l)))
=> cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V0__n),V1__x,cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V0__n),V2__m,V3__l)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_inv_perm',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V3__v)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V1__x,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V3__v))
=> ? [V5__v_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V2__n,V5__v_27)
& cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V1__x,V2__n,V5__v_27),V3__v) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V4__n,V5__v))
=> cCoq_2eLists_2eList_2eIn___24a3(V1__B,happ(V2__f,V3__a),cQuicksortComplexity_2evec_2eto__list___24a3(V1__B,V4__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V4__n,V5__v))) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_nats_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n),V1__x)
=> cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)),V1__x,cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)),V0__n,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n))) ) ) ).
fof('QuicksortComplexity.vec.In_nats_S',axiom,
! [V0__v] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__v)
=> ! [V1__u] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__u)
=> ! [V2__w] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(V1__u,V0__v),V2__w)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__u,V0__v)),V2__w,cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__u,V0__v)),V0__v,cQuicksortComplexity_2evec_2enats___24a2(V1__u,V0__v)))
=> cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__u,V0__v))),cQuicksortComplexity_2enat__below_2eSnb___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__u,V0__v),V2__w),cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__u),V0__v)),V0__v,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__u),V0__v))) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_nats_inv',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(V1__y,V0__z),V2__x)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__y,V0__z)),V2__x,cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__y,V0__z)),V0__z,cQuicksortComplexity_2evec_2enats___24a2(V1__y,V0__z)))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__y,V0__z),V2__x)))
& p(cCoq_2eInit_2ePeano_2elt___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__y,V0__z),V2__x),cCoq_2eInit_2eNat_2eadd___24a2(V0__z,V1__y))) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_nb_nats',axiom,
! [V0__v] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__v)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd___24a2(V0__v,V2__m),cQuicksortComplexity_2evec_2eto__list___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__v,V1__n)),cQuicksortComplexity_2evec_2enb__nats___24a2(V2__m,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__v,V1__n))))) ) ) ) ).
fof('QuicksortComplexity.vec.In_nb_nats\'',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__x))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__n)))
=> cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V0__x,cQuicksortComplexity_2evec_2eto__list___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__n,cQuicksortComplexity_2evec_2enb__nats___24a2(V1__m,V2__n))) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_nb_nats_inv',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2enat,V2__x,cQuicksortComplexity_2evec_2eto__list___24a3(cCoq_2eInit_2eDatatypes_2enat,V0__z,cQuicksortComplexity_2evec_2enb__nats___24a2(V1__y,V0__z)))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V2__x))
& p(cCoq_2eInit_2ePeano_2elt___24a2(V2__x,cCoq_2eInit_2eNat_2eadd___24a2(V0__z,V1__y))) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__n,V2__i)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__A,cQuicksortComplexity_2evec_2enth___24a4(V0__A,V1__n,V3__v,V2__i),cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V3__v)) ) ) ) ) ).
fof('QuicksortComplexity.vec.In_vec_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V2__n,V3__v))
=> ? [V5__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V2__n,V5__i)
& V1__a = cQuicksortComplexity_2evec_2enth___24a4(V0__A,V2__n,V3__v,V5__i) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.List_Permutation',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V2__a)
=> ! [V3__b] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V3__b)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V1__n,V2__a,V3__b)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__X,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V1__n,V2__a),cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V1__n,V3__b)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.List_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__l)
=> ! [V4__f] :
( c_24__type__356___24t(V0__A,V1__B,V2__n,V4__f)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V4__f,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V2__n,V3__l)) = cQuicksortComplexity_2evec_2eto__list___24a3(V1__B,V2__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V4__f,V2__n,V3__l)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.NoDup_incl_Permutation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__a)
=> ! [V3__b] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__b)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V2__a))
=> ( cCoq_2eLists_2eList_2eincl___24a3(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V2__a),cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V3__b))
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V1__n,V2__a,V3__b) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.NoDup_nats',axiom,
! [V0__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__y)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> cCoq_2eLists_2eList_2eNoDup___24a2(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,V0__y)),cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,V0__y)),V0__y,cQuicksortComplexity_2evec_2enats___24a2(V1__x,V0__y))) ) ) ).
fof('QuicksortComplexity.vec.Permutation_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__62352___24t(V0__A,V1__P)
=> ( p(happ(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ! [V6__v_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__v_27)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V4__n,V5__v,V6__v_27)
=> ( p(happ(happ(happ(V1__P,V4__n),V5__v),V6__v_27))
=> p(happ(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V4__n,V5__v)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__x,V4__n,V6__v_27))) ) ) ) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__l)
=> p(happ(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n))),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__y,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x,V6__n,V7__l))),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V4__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V5__y,V6__n,V7__l)))) ) ) ) )
=> ( ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__l)
=> ! [V7__l_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V7__l_27)
=> ! [V8__l_27_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V8__l_27_27)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V5__n,V6__l,V7__l_27)
=> ( p(happ(happ(happ(V1__P,V5__n),V6__l),V7__l_27))
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V5__n,V7__l_27,V8__l_27_27)
=> ( p(happ(happ(happ(V1__P,V5__n),V7__l_27),V8__l_27_27))
=> p(happ(happ(happ(V1__P,V5__n),V6__l),V8__l_27_27)) ) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V7__t)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V6__n,V8__t)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V6__n,V7__t,V8__t)
=> p(happ(happ(happ(V1__P,V6__n),V7__t),V8__t)) ) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.Permutation_mapping',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V2__a)
=> ! [V3__b] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V3__b)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V1__n,V2__a,V3__b)
=> ? [V5__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V1__n),V1__n,V5__l)
& ! [V6__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__n,V6__x)
=> cCoq_2eLists_2eList_2eIn___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V1__n),V6__x,cQuicksortComplexity_2evec_2eto__list___24a3(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V1__n),V1__n,V5__l)) )
& cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V1__n),V0__X,cQuicksortComplexity_2evec_2enth___24a3(V0__X,V1__n,V3__b),V1__n,V5__l) = V2__a ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.SkipList_remove',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__nb] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__nb)
=> ! [V3__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V3__l)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,cQuicksortComplexity_2evec_2eremove___24a4(V0__A,V1__n,V3__l,V2__nb)),cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V3__l)) ) ) ) ) ).
fof('QuicksortComplexity.vec.SkipList_tail',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,cQuicksortComplexity_2evec_2etail___24a3(V1__n,V0__A,V2__v)),cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)) ) ) ) ).
fof('QuicksortComplexity.vec.Vcons_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__h] :
( t(V1__h,V0__A)
=> ! [V2__h_27] :
( t(V2__h_27,V0__A)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__t)
=> ! [V5__t_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__t_27)
=> ( V1__h = V2__h_27
=> ( V4__t = V5__t_27
=> cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__h,V3__n,V4__t) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__h_27,V3__n,V5__t_27) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.Vcons_eq_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__h] :
( t(V1__h,V0__A)
=> ! [V2__h_27] :
( t(V2__h_27,V0__A)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__t)
=> ! [V5__t_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__t_27)
=> ( cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__h,V3__n,V4__t) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__h_27,V3__n,V5__t_27)
=> ( V1__h = V2__h_27
& V4__t = V5__t_27 ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.Xle_lt_trans',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> ( p(happ(happ(V1__Xle,V3__x),V4__y))
=> ! [V6__z] :
( t(V6__z,V0__X)
=> ( cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,V4__y,V6__z)
=> cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,V3__x,V6__z) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.Xle_nlt',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__y] :
( t(V4__y,V0__X)
=> ( p(happ(happ(V1__Xle,V3__x),V4__y))
=> ~ cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,V4__y,V3__x) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.Xlt_irrefl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ~ cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,V3__x,V3__x) ) ) ) ) ).
fof('QuicksortComplexity.vec.app_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__x] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__m,V2__x)
=> ! [V3__x_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__m,V3__x_27)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__y)
=> ! [V6__y_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V6__y_27)
=> ( V2__x = V3__x_27
=> ( V5__y = V6__y_27
=> cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__m,V2__x,V4__n,V5__y) = cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__m,V3__x_27,V4__n,V6__y_27) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.double_rect',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__75905___24t(V0__A,V1__B,V2__P)
=> ( p(happ(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)),cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__B)))
=> ( ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__v)
=> ! [V6__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V4__n,V6__w)
=> ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__y] :
( t(V8__y,V1__B)
=> ( p(happ(happ(happ(V2__P,V4__n),V5__v),V6__w))
=> p(happ(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V7__x,V4__n,V5__v)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,V8__y,V4__n,V6__w))) ) ) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__n,V6__v)
=> ! [V7__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__B,V5__n,V7__w)
=> p(happ(happ(happ(V2__P,V5__n),V6__v),V7__w)) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.eq_app_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__a] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__a)
=> ! [V4__b] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V4__b)
=> ! [V5__c] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V5__c)
=> ! [V6__d] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V6__d)
=> ( cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__n,V3__a,V2__m,V5__c) = cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__n,V4__b,V2__m,V6__d)
=> ( V3__a = V4__b
& V5__c = V6__d ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.eq_as_lists',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__x] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V2__x)
=> ! [V3__y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V3__y)
=> ( cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V1__n,V2__x) = cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V1__n,V3__y)
=> V2__x = V3__y ) ) ) ) ) ).
fof('QuicksortComplexity.vec.eq_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v),V1__n,cQuicksortComplexity_2evec_2etail___24a3(V1__n,V0__A,V2__v)) ) ) ) ).
fof('QuicksortComplexity.vec.eq_list',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__v)
=> ( cQuicksortComplexity_2evec_2efrom__list___24a2(V0__A,V1__l) = V2__v
=> V1__l = cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),V2__v) ) ) ) ) ).
fof('QuicksortComplexity.vec.eq_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eO,V1__v)
=> V1__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A) ) ) ).
fof('QuicksortComplexity.vec.ext_nth',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__x] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__x)
=> ! [V3__y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(V1__n),V0__A,cQuicksortComplexity_2evec_2enth___24a3(V0__A,V1__n,V2__x),cQuicksortComplexity_2evec_2enth___24a3(V0__A,V1__n,V3__y))
=> V2__x = V3__y ) ) ) ) ) ).
fof('QuicksortComplexity.vec.in_remove',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__x] :
( t(V1__x,V0__T)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V3__i)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V4__v)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__T,V1__x,cQuicksortComplexity_2evec_2eto__list___24a3(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V4__v))
=> ( V1__x != cQuicksortComplexity_2evec_2enth___24a4(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V4__v,V3__i)
=> cCoq_2eLists_2eList_2eIn___24a3(V0__T,V1__x,cQuicksortComplexity_2evec_2eto__list___24a3(V0__T,V2__n,cQuicksortComplexity_2evec_2eremove___24a4(V0__T,V2__n,V4__v,V3__i))) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.insert_ordered_permutes',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__XleDec] :
( c_24__type__73371___24t(V0__X,V1__Xle,V2__XleDec)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V4__n,V5__v)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n),cQuicksortComplexity_2evec_2einsert__ordered___24a6(V0__X,V1__Xle,V2__XleDec,V3__x,V4__n,V5__v),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V3__x,V4__n,V5__v)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.insert_ordered_preserves_sorted',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__XleDec] :
( c_24__type__77134___24t(V0__X,V1__Xle,V2__XleDec)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V5__v)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,V5__v)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),cQuicksortComplexity_2evec_2einsert__ordered___24a6(V0__X,V1__Xle,V2__XleDec,V4__x,V3__n,V5__v)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.insertion_sort_permutes',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__XleDec] :
( c_24__type__73383___24t(V0__X,V1__Xle,V2__XleDec)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__l)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V3__n,cQuicksortComplexity_2evec_2einsertion__sort___24a5(V0__X,V1__Xle,V2__XleDec,V3__n,V4__l),V4__l) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.insertion_sort_sorts',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__XleDec] :
( c_24__type__35741___24t(V0__X,V1__Xle,V2__XleDec)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__l)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,cQuicksortComplexity_2evec_2einsertion__sort___24a5(V0__X,V1__Xle,V2__XleDec,V3__n,V4__l)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__l)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V2__l)) = V1__n ) ) ) ).
fof('QuicksortComplexity.vec.list_round_trip',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cQuicksortComplexity_2evec_2efrom__list___24a2(V0__A,V1__l)) = V1__l ) ) ).
fof('QuicksortComplexity.vec.map_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__v)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ! [V6__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V5__m,V6__w)
=> cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eNat_2eadd___24a2(V3__n,V5__m),cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V3__n,V4__v,V5__m,V6__w)) = cQuicksortComplexity_2evec_2eapp___24a5(V1__B,V3__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V3__n,V4__v),V5__m,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V5__m,V6__w)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.map_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__h] :
( t(V3__h,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t)) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__B,happ(V2__f,V3__h),V4__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V4__n,V5__t)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.map_ext',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__78___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__78___24t(V0__X,V1__Y,V3__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__X,V1__Y,V2__f,V3__g)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V5__n,V6__v)
=> cQuicksortComplexity_2evec_2emap___24a5(V0__X,V1__Y,V2__f,V5__n,V6__v) = cQuicksortComplexity_2evec_2emap___24a5(V0__X,V1__Y,V3__g,V5__n,V6__v) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.map_map',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> ! [V3__f] :
( c_24__type__78___24t(V0__X,V1__Y,V3__f)
=> ! [V4__g] :
( c_24__type__7846___24t(V0__X,V1__Y,V2__Z,V4__g)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ! [V6__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V5__n,V6__v)
=> cQuicksortComplexity_2evec_2emap___24a5(V1__Y,V2__Z,V4__g,V5__n,cQuicksortComplexity_2evec_2emap___24a5(V0__X,V1__Y,V3__f,V5__n,V6__v)) = cQuicksortComplexity_2evec_2emap___24a5(V0__X,V2__Z,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,V1__Y,V2__Z,V4__g,V3__f),V5__n,V6__v) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.nats_S',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cQuicksortComplexity_2evec_2enats___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)) = cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V1__n))),cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n))),c_24__lam__363___24a2(V0__x,V1__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V1__n))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V0__x,V1__n),V1__n,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__x),V1__n))) ) ) ).
fof('QuicksortComplexity.vec.nats_plus',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> cQuicksortComplexity_2evec_2enats___24a2(V1__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V2__y)) = cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x),V2__y)),cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V2__y))),c_24__lam__73233___24a3(V0__x,V1__n,V2__y),cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V2__y),cQuicksortComplexity_2evec_2eapp___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x),V2__y)),V0__x,cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x)),cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x),V2__y)),cQuicksortComplexity_2evec_2eplusnb___24a2(V2__y,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x)),V0__x,cQuicksortComplexity_2evec_2enats___24a2(V1__n,V0__x)),V2__y,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x),V2__y))) ) ) ) ).
fof('QuicksortComplexity.vec.nb1',axiom,
! [V0__n] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n)
=> V0__n = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('QuicksortComplexity.vec.nb_nats_S',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> cQuicksortComplexity_2evec_2enb__nats___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n)) = cCoq_2eVectors_2eVectorDef_2econs___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__x,V1__n,cQuicksortComplexity_2evec_2enb__nats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__x),V1__n)) ) ) ).
fof('QuicksortComplexity.vec.nb_nats_plus',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> cQuicksortComplexity_2evec_2enb__nats___24a2(V1__n,cCoq_2eInit_2eNat_2eadd___24a2(V0__x,V2__y)) = cQuicksortComplexity_2evec_2eapp___24a5(cCoq_2eInit_2eDatatypes_2enat,V0__x,cQuicksortComplexity_2evec_2enb__nats___24a2(V1__n,V0__x),V2__y,cQuicksortComplexity_2evec_2enb__nats___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V0__x),V2__y)) ) ) ) ).
fof('QuicksortComplexity.vec.nb_val_eq_rec_r',axiom,
! [V0__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__k)
=> ! [V1__u] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__u)
=> ! [V2__n] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__u,V2__n)
=> ( V0__k = V1__u
=> cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__k,cCoq_2eInit_2eLogic_2eeq__rec__r___24a5(cCoq_2eInit_2eDatatypes_2enat,V1__u,cQuicksortComplexity_2enat__below_2enatBelow,V2__n,V0__k)) = cQuicksortComplexity_2enat__below_2enb__val___24a2(V1__u,V2__n) ) ) ) ) ).
fof('QuicksortComplexity.vec.nth_0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> cQuicksortComplexity_2evec_2enth___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v,cQuicksortComplexity_2enat__below_2enb0___24a1(V1__n)) = cQuicksortComplexity_2evec_2ehead___24a3(V0__A,V1__n,V2__v) ) ) ) ).
fof('QuicksortComplexity.vec.nth_S',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__p),V2__v)
=> ! [V3__n] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__p,V3__n)
=> cQuicksortComplexity_2evec_2enth___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__p),V2__v,cQuicksortComplexity_2enat__below_2eSnb___24a2(V1__p,V3__n)) = cQuicksortComplexity_2evec_2enth___24a4(V0__A,V1__p,cQuicksortComplexity_2evec_2etail___24a3(V1__p,V0__A,V2__v),V3__n) ) ) ) ) ).
fof('QuicksortComplexity.vec.nth_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V3__n,V4__i)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V5__v)
=> cQuicksortComplexity_2evec_2enth___24a4(V1__B,V3__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V3__n,V5__v),V4__i) = happ(V2__f,cQuicksortComplexity_2evec_2enth___24a4(V0__A,V3__n,V5__v,V4__i)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.nth_nats',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__m,V1__i)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__m),cQuicksortComplexity_2evec_2enth___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__m)),V0__m,cQuicksortComplexity_2evec_2enats___24a2(V2__n,V0__m),V1__i)) = cCoq_2eInit_2eNat_2eadd___24a2(V2__n,cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__m,V1__i)) ) ) ) ).
fof('QuicksortComplexity.vec.nth_nats3',axiom,
! [V0__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__m)
=> ! [V1__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__m,V1__i)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cQuicksortComplexity_2evec_2enth___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V0__m)),V0__m,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),V0__m),V1__i) = cQuicksortComplexity_2enat__below_2eSnb___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__m),cQuicksortComplexity_2evec_2enth___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__m)),V0__m,cQuicksortComplexity_2evec_2enats___24a2(V2__n,V0__m),V1__i)) ) ) ) ).
fof('QuicksortComplexity.vec.nth_nats_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__i)
=> cQuicksortComplexity_2evec_2enth___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)),V0__n,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n),V1__i) = V1__i ) ) ).
fof('QuicksortComplexity.vec.perm_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)) ) ).
fof('QuicksortComplexity.vec.perm_refl',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V2__v)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V1__n,V2__v,V2__v) ) ) ) ).
fof('QuicksortComplexity.vec.perm_skip',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__v)
=> ! [V4__v_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V4__v_27)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V2__n,V3__v,V4__v_27)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__x,V2__n,V3__v),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__x,V2__n,V4__v_27)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.perm_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__n,V4__l)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__y,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__x,V3__n,V4__l)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V2__y,V3__n,V4__l))) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.perm_sym',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__a] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V2__a)
=> ! [V3__b] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V1__n,V3__b)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V1__n,V2__a,V3__b)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__X,V1__n,V3__b,V2__a) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.perm_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__l)
=> ! [V3__l_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__l_27)
=> ! [V4__l_27_27] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V4__l_27_27)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V1__n,V2__l,V3__l_27)
=> ( cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V1__n,V3__l_27,V4__l_27_27)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__A,V1__n,V2__l,V4__l_27_27) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.remove_In',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V4__i)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V1__n,cQuicksortComplexity_2evec_2eremove___24a4(V0__X,V1__n,V2__v,V4__i)))
=> cCoq_2eLists_2eList_2eIn___24a3(V0__X,V3__x,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__v)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.remove_head',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__p)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__p),V2__v)
=> cQuicksortComplexity_2evec_2eremove___24a4(V0__T,V1__p,V2__v,cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eO,V1__p)) = cQuicksortComplexity_2evec_2etail___24a3(V1__p,V0__T,V2__v) ) ) ) ).
fof('QuicksortComplexity.vec.remove_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__i)
=> ! [V5__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V5__v)
=> cQuicksortComplexity_2evec_2eremove___24a4(V1__B,V3__n,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V5__v),V4__i) = cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V3__n,cQuicksortComplexity_2evec_2eremove___24a4(V0__A,V3__n,V5__v,V4__i)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.remove_perm',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__nb] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__nb)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V3__v)
=> cQuicksortComplexity_2evec_2ePermutation___24a4(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__T,cQuicksortComplexity_2evec_2enth___24a4(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V3__v,V2__nb),V1__n,cQuicksortComplexity_2evec_2eremove___24a4(V0__T,V1__n,V3__v,V2__nb)),V3__v) ) ) ) ) ).
fof('QuicksortComplexity.vec.remove_tail',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p))),V3__v)
=> cQuicksortComplexity_2evec_2eremove___24a4(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p)),V3__v,cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n),V2__p)) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__T,cQuicksortComplexity_2evec_2ehead___24a3(V0__T,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p)),V3__v),cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p),cQuicksortComplexity_2evec_2eremove___24a4(V0__T,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p),cQuicksortComplexity_2evec_2etail___24a3(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__p)),V0__T,V3__v),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V1__n,V2__p))) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_app',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__v] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__v)
=> ! [V4__w] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__w)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V3__v),cQuicksortComplexity_2evec_2efrom__list___24a2(V0__X,V3__v))
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,V4__w),cQuicksortComplexity_2evec_2efrom__list___24a2(V0__X,V4__w))
=> ( ! [V7__x] :
( t(V7__x,V0__X)
=> ! [V8__y] :
( t(V8__y,V0__X)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V7__x,V3__v)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V8__y,V4__w)
=> p(happ(happ(V1__Xle,V7__x),V8__y)) ) ) ) )
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__X,V3__v,V4__w)),cQuicksortComplexity_2evec_2efrom__list___24a2(V0__X,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__X,V3__v,V4__w))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_cons',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v)
=> ( p(happ(happ(V1__Xle,V2__x),cQuicksortComplexity_2evec_2ehead___24a3(V0__X,V3__n,V4__v)))
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_cons\'',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__v)
=> ( ! [V5__y] :
( t(V5__y,V0__X)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V5__y,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V3__n,V4__v))
=> p(happ(happ(V1__Xle,V2__x),V5__y)) ) )
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,V4__v)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__x,V3__n,V4__v)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_cons_inv',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__x,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__v))
=> p(happ(happ(V1__Xle,V2__x),cQuicksortComplexity_2evec_2ehead___24a3(V0__X,V3__n,V4__v))) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_cons_inv\'',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__x] :
( t(V3__x,V0__X)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__xs] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V4__n,V5__xs)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V3__x,V4__n,V5__xs))
=> ! [V7__x_27] :
( t(V7__x_27,V0__X)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__X,V7__x_27,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V4__n,V5__xs))
=> p(happ(happ(V1__Xle,V3__x),V7__x_27)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_ind',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__P] :
( c_24__type__1180___24t(V0__X,V2__P)
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__X)))
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V4__x,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__X)))) )
=> ( ! [V5__a] :
( t(V5__a,V0__X)
=> ! [V6__b] :
( t(V6__b,V0__X)
=> ! [V7__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__n)
=> ! [V8__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V7__n,V8__t)
=> ( p(happ(happ(V1__Xle,V5__a),V6__b))
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V6__b,V7__n,V8__t))
=> ( p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V6__b,V7__n,V8__t)))
=> p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n))),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V5__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V7__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V6__b,V7__n,V8__t)))) ) ) ) ) ) ) )
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> ! [V7__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V6__n,V7__t)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V6__n,V7__t)
=> p(happ(happ(V2__P,V6__n),V7__t)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_le_indices_le_values',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__v)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,V4__v)
=> ! [V6__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V3__n,V6__i)
=> ! [V7__j] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V3__n,V7__j)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(V3__n,V6__i),cQuicksortComplexity_2enat__below_2enb__val___24a2(V3__n,V7__j)))
=> p(happ(happ(V1__Xle,cQuicksortComplexity_2evec_2enth___24a4(V0__X,V3__n,V4__v,V6__i)),cQuicksortComplexity_2evec_2enth___24a4(V0__X,V3__n,V4__v,V7__j))) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_lt_values_lt_indices',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__X,V1__Xle)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__v)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,V4__v)
=> ! [V6__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V3__n,V6__i)
=> ! [V7__j] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V3__n,V7__j)
=> ( cQuicksortComplexity_2evec_2eXlt___24a4(V0__X,V1__Xle,cQuicksortComplexity_2evec_2enth___24a4(V0__X,V3__n,V4__v,V6__i),cQuicksortComplexity_2evec_2enth___24a4(V0__X,V3__n,V4__v,V7__j))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(V3__n,V6__i),cQuicksortComplexity_2enat__below_2enb__val___24a2(V3__n,V7__j))) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_more',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__a] :
( t(V2__a,V0__X)
=> ! [V3__b] :
( t(V3__b,V0__X)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V4__n,V5__t)
=> ( p(happ(happ(V1__Xle,V2__a),V3__b))
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V3__b,V4__n,V5__t))
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__a,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V3__b,V4__n,V5__t))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_nil',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__X)) ) ) ).
fof('QuicksortComplexity.vec.sorted_one',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__x,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__X))) ) ) ) ).
fof('QuicksortComplexity.vec.sorted_tail',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__1116___24t(V0__X,V1__Xle)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V3__n,V4__v)
=> ( cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__X,V2__x,V3__n,V4__v))
=> cQuicksortComplexity_2evec_2esorted___24a4(V0__X,V1__Xle,V3__n,V4__v) ) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m),V3__v)
=> V3__v = cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__n,cQuicksortComplexity_2evec_2etake___24a4(V0__A,V1__n,V2__m,V3__v),V2__m,cQuicksortComplexity_2evec_2edrop___24a4(V0__A,V1__n,V2__m,V3__v)) ) ) ) ) ).
fof('QuicksortComplexity.vec.tail_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__n,V3__l)
=> cQuicksortComplexity_2evec_2etail___24a3(V2__n,V0__A,cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V1__a,V2__n,V3__l)) = V3__l ) ) ) ) ).
fof('QuicksortComplexity.vec.tail_map',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__78___24t(V0__A,V1__B,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__l] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__l)
=> cQuicksortComplexity_2evec_2etail___24a3(V3__n,V1__B,cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n),V4__l)) = cQuicksortComplexity_2evec_2emap___24a5(V0__A,V1__B,V2__f,V3__n,cQuicksortComplexity_2evec_2etail___24a3(V3__n,V0__A,V4__l)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.to_list_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V2__v)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ! [V4__w] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V3__m,V4__w)
=> cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V3__m),cQuicksortComplexity_2evec_2eapp___24a5(V0__A,V1__n,V2__v,V3__m,V4__w)) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V1__n,V2__v),cQuicksortComplexity_2evec_2eto__list___24a3(V0__A,V3__m,V4__w)) ) ) ) ) ) ).
fof('QuicksortComplexity.vec.trans_plus_n_Sm',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,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) ) ) ).
fof('QuicksortComplexity.vec.val_Snb',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__x] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__x)
=> cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cQuicksortComplexity_2enat__below_2eSnb___24a2(V0__n,V1__x)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__x)) ) ) ).
fof('QuicksortComplexity.vec.val_nb0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cQuicksortComplexity_2enat__below_2enb0___24a1(V0__n)) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('QuicksortComplexity.vec.val_plusnb',axiom,
! [V0__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__y)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__nb] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V1__x,V2__nb)
=> cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,V0__y),cQuicksortComplexity_2evec_2eplusnb___24a3(V0__y,V1__x,V2__nb)) = cQuicksortComplexity_2enat__below_2enb__val___24a2(V1__x,V2__nb) ) ) ) ).
fof('QuicksortComplexity.vec.vec_round_trip',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__v] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__X,V2__n,V3__v)
=> ! [V4__f] :
( c_24__type__20012___24t(V0__X,V1__T,V2__n,V4__f)
=> happ(happ(V4__f,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__X,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V2__n,V3__v))),cQuicksortComplexity_2evec_2efrom__list___24a2(V0__X,cQuicksortComplexity_2evec_2eto__list___24a3(V0__X,V2__n,V3__v))) = happ(happ(V4__f,V2__n),V3__v) ) ) ) ) ) ).
fof('indices.contents.IndexSeq_cons_inv',axiom,
! [V0__b] :
( cindices_2econtents_2eIndex___24t(V0__b)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,V1__l)
=> ( cindices_2econtents_2eIndexSeq___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V0__b),cCoq_2eInit_2eDatatypes_2econs___24a3(cindices_2econtents_2eIndex,V0__b,V1__l))
=> cindices_2econtents_2eIndexSeq___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V0__b)),V1__l) ) ) ) ).
fof('indices.contents.IndexSeq_nil',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__b)
=> cindices_2econtents_2eIndexSeq___24a2(V0__b,cCoq_2eInit_2eDatatypes_2enil___24a1(cindices_2econtents_2eIndex)) ) ).
fof('indices.contents.IndexSeq_perm',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__b)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,V1__l)
=> ( cindices_2econtents_2eIndexSeq___24a2(V0__b,V1__l)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,V3__l_27)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(cindices_2econtents_2eIndex,V3__l_27,V1__l)
=> cindices_2econtents_2eIndexSeq___24a2(V0__b,V3__l_27) ) ) ) ) ) ).
fof('indices.contents.IndexSeq_uncons',axiom,
! [V0__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,V0__l)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cindices_2econtents_2eIndexSeq___24a2(V1__b,V0__l)
=> ( V0__l != cCoq_2eInit_2eDatatypes_2enil___24a1(cindices_2econtents_2eIndex)
=> ? [V4__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cindices_2econtents_2eIndex,V4__l_27)
& ? [V5__p] :
( cindices_2econtents_2eIndex___24t(V5__p)
& cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V5__p) = V1__b
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(cindices_2econtents_2eIndex,cCoq_2eInit_2eDatatypes_2econs___24a3(cindices_2econtents_2eIndex,V5__p,V4__l_27),V0__l) ) ) ) ) ) ) ).
fof('indices.contents.IndicesCorrect',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eEc___24t(cindices_2econtents_2eUE,V0__e)
=> ! [V1__e_27] :
( cQuicksortComplexity_2esort__order_2eEc___24t(cindices_2econtents_2eUE,V1__e_27)
=> ( cQuicksortComplexity_2esort__order_2eEcmp___24a3(cindices_2econtents_2eUE,V0__e,V1__e_27) = cCoq_2eInit_2eDatatypes_2eLt
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V0__e),cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V1__e_27))) ) ) ) ).
fof('indices.contents.IndicesCorrect_inv',axiom,
! [V0__x] :
( cindices_2econtents_2eIndex___24t(V0__x)
=> ! [V1__y] :
( cindices_2econtents_2eIndex___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V0__x),cQuicksortComplexity_2enat__below_2enb__val___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col),V1__y)))
=> p(cQuicksortComplexity_2esort__order_2eEle___24a3(cindices_2econtents_2eUE,V0__x,V1__y)) ) ) ) ).
fof('$adef_$_lam_992_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__992,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__992___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.Logic.False_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eLogic_2eFalse__rect,V_24X1) = cCoq_2eInit_2eLogic_2eFalse__rect___24a1(V_24X1) ).
fof('$adef_$_lam_827_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__827,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__827___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.seq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eseq,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eseq___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_30386_30389_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__30386__30389,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__30386__30389___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_75584_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__75584,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__75584___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.rev_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erev,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2erev___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('$adef_$_lam_76031_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76031,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76031___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.Ndigits.Bv2N_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eNdigits_2eBv2N,V_24X1),V_24X2) = cCoq_2eNArith_2eNdigits_2eBv2N___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_70844_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__70844,V_24X1),V_24X2) = c_24__lam__70844___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('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_$_fix_73712_v_CANONICAL_2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__73712__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__73712__v__CANONICAL__2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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_QuicksortComplexity.nat_seqs.nats_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__seqs_2enats,V_24X1),V_24X2) = cQuicksortComplexity_2enat__seqs_2enats___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_70842_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70842,V_24X1) = c_24__lam__70842___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.vec.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2eto__list,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_73122_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__73122,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__73122___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_QuicksortComplexity.vec.nb_nats_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2enb__nats,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2enb__nats___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.from_list_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2efrom__list,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2efrom__list___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Lists.List.repeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erepeat,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.last_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2elast,V_24X1) = cCoq_2eVectors_2eVectorDef_2elast___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_363_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__363,V_24X1),V_24X2) = c_24__lam__363___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_17_mkopp_pow_55943_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__55943,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__17__mkopp__pow__55943___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_lam_77034_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77034,V_24X1) = c_24__lam__77034___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Ecmp_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2esort__order_2eEcmp,V_24X1) = cQuicksortComplexity_2esort__order_2eEcmp___24a1(V_24X1) ).
fof('$adef_$_lam_1070_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1070,V_24X1),V_24X2) = c_24__lam__1070___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7070_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7070,V_24X1),V_24X2),V_24X3) = c_24__lam__7070___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74055_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74055,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74055___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_prop_22802_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22802,V_24X1),V_24X2),V_24X3) = c_24__prop__22802___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.Forall_$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('$adef_QuicksortComplexity.list_utils.concat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2econcat,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2econcat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Vectors.Fin.t$74763_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eVectors_2eFin_2et_2474763,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eVectors_2eFin_2et_2474763___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_76838_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__76838,V_24X1))
<=> c_24__lam__76838___24a1(V_24X1) ) ).
fof('$adef_QuicksortComplexity.vec.R_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2evec_2eR,V_24X1) = cQuicksortComplexity_2evec_2eR___24a1(V_24X1) ).
fof('$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_$_lam_1076_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1076,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1076___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_case_QuicksortComplexity.nat_below.natBelow$931_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Lists.List.partition_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2epartition,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2epartition___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_error_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2enth__error,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2enth__error___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1070_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1070,V_24X1),V_24X2),V_24X3) = c_24__lam__1070___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.Permutation_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2evec_2ePermutation,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2evec_2ePermutation___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_75401_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__75401,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__75401___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.list_utils.merges_spec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges__spec,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2emerges__spec___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_QuicksortComplexity.nat_below.natBelow_rect_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enatBelow__rect,V_24X1) = cQuicksortComplexity_2enat__below_2enatBelow__rect___24a1(V_24X1) ).
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('$adef_Coq.Vectors.VectorDef.t_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et__rec,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_75733_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__75733,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__75733___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.arith_lems.R_ceil_log2_S_0_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0,V_24X1) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(V_24X1) ).
fof('$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_QuicksortComplexity.vec.map_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2emap,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2emap___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.sort_order.Build_E_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2esort__order_2eBuild__E,V_24X1),V_24X2) = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.False_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eFalse__rect,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eFalse__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_QuicksortComplexity.sort_order.Build_E_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2esort__order_2eBuild__E,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2esort__order_2eBuild__E___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.le_alt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2ele__alt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_74583_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74583,V_24X1),V_24X2) = c_24__lam__74583___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.map_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2emap,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2emap___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_77148_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77148,V_24X1),V_24X2) = c_24__lam__77148___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.util.pair_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eutil_2epair__rel,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eutil_2epair__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.bSurjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebSurjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebSurjective___24a2(V_24X1,V_24X2) ) ).
fof('$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.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_72988_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__72988,V_24X1),V_24X2) = c_24__prop__72988___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.insertion_sort_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2einsertion__sort,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2einsertion__sort___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1212_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1212,V_24X1),V_24X2) = c_24__lam__1212___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.list_utils.Partitioning_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2ePartitioning,V_24X1) = cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Ecmp_eq_trans_l_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2esort__order_2eEcmp__eq__trans__l,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2esort__order_2eEcmp__eq__trans__l___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_18584_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__18584,V_24X1),V_24X2) = c_24__lam__18584___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_right_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2efold__right___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_72987_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__72987,V_24X1),V_24X2) = c_24__lam__72987___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.funind.Recdef.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2efunind_2eRecdef_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2efunind_2eRecdef_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.sort_order.Ecmp_sym_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEcmp__sym,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEcmp__sym___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.rev_append_tail_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erev__append__tail,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2erev__append__tail___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_60122_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__60122,V_24X1),V_24X2) = c_24__lam__60122___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_77034_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77034,V_24X1),V_24X2),V_24X3) = c_24__lam__77034___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_74812_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__74812,V_24X1),V_24X2),V_24X3) = c_24__lam__74812___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_19872_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__19872,V_24X1),V_24X2),V_24X3) = c_24__lam__19872___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_fix_19265_v_CANONICAL_2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__19265__v__CANONICAL__2,V_24X1),V_24X2),V_24X3) = c_24__fix__19265__v__CANONICAL__2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_15194_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__15194,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__15194___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1223_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1223,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1223___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1) = cCoq_2eVectors_2eVectorDef_2econs___24a1(V_24X1) ).
fof('$adef_$_lam_70879_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70879,V_24X1) = c_24__lam__70879___24a1(V_24X1) ).
fof('$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_QuicksortComplexity.vec.plusnb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2eplusnb,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2eplusnb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.take_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2etake,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2etake___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_11_subst_l_8800_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__8800,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__8800___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$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('$adef_$_lam_74234_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__74234,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__74234___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.Vectors.VectorDef.shiftin_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eshiftin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2eshiftin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.vec.natBelow_rect_S_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__rect__S,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2evec_2enatBelow__rect__S___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.util.on_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2eon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cQuicksortComplexity_2eutil_2eon___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_lam_72987_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__72987,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__72987___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.existsb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eexistsb,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eexistsb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.caseS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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_73670_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73670,V_24X1),V_24X2),V_24X3) = c_24__lam__73670___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_73670_$a1',axiom,
! [V_24X1] : happ(c_24__lam__73670,V_24X1) = c_24__lam__73670___24a1(V_24X1) ).
fof('$adef_$_lam_73181_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__73181,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__73181___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_73107_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73107,V_24X1),V_24X2),V_24X3) = c_24__lam__73107___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.util.unsum_bool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eutil_2eunsum__bool,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eutil_2eunsum__bool___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.cardinal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ecardinal___24a1(V_24X1) ).
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('$adef_Coq.Vectors.Fin.L_R_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eFin_2eL__R,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eFin_2eL__R___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.fold_right2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2efold__right2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2efold__right2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Init.Peano.eq_S_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2ePeano_2eeq__S,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2ePeano_2eeq__S___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.list_utils.product_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eproduct,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2elist__utils_2eproduct___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.nth_order_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2enth__order,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2enth__order___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_70879_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__70879,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__70879___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_38533_$a1',axiom,
! [V_24X1] : happ(c_24__lam__38533,V_24X1) = c_24__lam__38533___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.const_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2econst,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2econst___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_60164_$a1',axiom,
! [V_24X1] : happ(c_24__lam__60164,V_24X1) = c_24__lam__60164___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.util.uncurry_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2euncurry,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eutil_2euncurry___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_22814_$a1',axiom,
! [V_24X1] : happ(c_24__lam__22814,V_24X1) = c_24__lam__22814___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.util.pair_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2epair__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cQuicksortComplexity_2eutil_2epair__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_Coq.Vectors.VectorDef.case0_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecase0,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2ecase0___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Arith.Plus.plus_tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2eplus__tail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2eplus__tail__plus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.skipn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eskipn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eskipn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.take_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2etake,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2etake___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_70855_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70855,V_24X1) = c_24__lam__70855___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_$_fix_20117_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__20117__1__add__carry,V_24X1),V_24X2) = c_24__fix__20117__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$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('$adef_$_lam_74150_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74150,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74150___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Lists.List.map_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2emap___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.drop_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2edrop,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2edrop___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.skip_list.SkipList_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2eskip__list_2eSkipList,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2eskip__list_2eSkipList___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_case_Coq.Vectors.Fin.t$74763_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eVectors_2eFin_2et_2474763,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eVectors_2eFin_2et_2474763___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_$_lam_9527_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__9527,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__9527___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_74801_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74801,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74801___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_case_Coq.Init.Datatypes.list$24445_$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_2424445,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2424445___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.caseS\'_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS_27,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___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('$adef_$_case_Coq.Init.Datatypes.nat$59782_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2459782,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2459782___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_70833_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__70833,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__70833___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_35808_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35808,V_24X1) = c_24__lam__35808___24a1(V_24X1) ).
fof('$adef_Coq.Logic.FinFun.Surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eSurjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Vectors.VectorDef.t_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et__rect,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_3155_$a1',axiom,
! [V_24X1] : happ(c_24__lam__3155,V_24X1) = c_24__lam__3155___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.list_utils.NoDupL_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cQuicksortComplexity_2elist__utils_2eNoDupL,V_24X1),V_24X2))
<=> cQuicksortComplexity_2elist__utils_2eNoDupL___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_$_let_18_mkmult_pow_55944_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__55944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__18__mkmult__pow__55944___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.elements_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelements___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_$_lam_74055_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__74055,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__74055___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_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.Vectors.VectorDef.shiftout_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2eshiftout,V_24X1) = cCoq_2eVectors_2eVectorDef_2eshiftout___24a1(V_24X1) ).
fof('$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_$_lam_70419_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70419,V_24X1),V_24X2),V_24X3) = c_24__lam__70419___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('$adef_Coq.Vectors.VectorDef.of_list_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2eof__list,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2eof__list___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('$adef_Coq.Vectors.VectorDef.to_list_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eto__list,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2eto__list___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_992_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__992,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__992___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.append_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eappend,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2eappend___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_74150_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__74150,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__74150___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_70695_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__70695,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__70695___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1076_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1076,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1076___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.arith_lems.R_ceil_log2_S_1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.t_rect_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2et__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorDef_2et__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_70695_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__70695,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__70695___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_978_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__978,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__978___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_77148_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__77148,V_24X1),V_24X2),V_24X3) = c_24__lam__77148___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.bFun_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebFun,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebFun___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_73263_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73263,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73263___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_978_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__978,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__978___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_75760_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75760,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__75760___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_QuicksortComplexity.list_utils.Permuted_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2ePermuted,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2elist__utils_2ePermuted___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_77078_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__77078,V_24X1),V_24X2) = c_24__lam__77078___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_35806_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35806,V_24X1) = c_24__lam__35806___24a1(V_24X1) ).
fof('$adef_$_lam_70844_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70844,V_24X1) = c_24__lam__70844___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.perms_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2eperms,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2eperms___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_75760_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75760,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__75760___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_$_prop_21049_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__21049,V_24X1),V_24X2) = c_24__prop__21049___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.count_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2ecount,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.vec.natBelow0_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2enatBelow0__rect,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2enatBelow0__rect___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_74812_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74812,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74812___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.sort_order.Ecmp_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2esort__order_2eEcmp__trans,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2esort__order_2eEcmp__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.rev_append_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erev__append,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2erev__append___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_QuicksortComplexity.arith_lems.R_ceil_log2_S_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S,V_24X1),V_24X2) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.tail_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2etail,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2etail___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Vectors.VectorDef.Exists2_$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('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.combine_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecombine,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecombine___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.list_utils.merges_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2emerges,V_24X1) = cQuicksortComplexity_2elist__utils_2emerges___24a1(V_24X1) ).
fof('$adef_$_lam_4832_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4832,V_24X1),V_24X2) = c_24__lam__4832___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38501_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38501,V_24X1),V_24X2) = c_24__lam__38501___24a2(V_24X1,V_24X2) ).
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('$adef_QuicksortComplexity.nat_below.mkNatBelow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__below_2emkNatBelow,V_24X1),V_24X2) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$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('$adef_Coq.Vectors.VectorDef.caseS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.rectS_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erectS,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2erectS___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.split_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2esplit,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2esplit___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength,V_24X1),V_24X2) = cCoq_2eZArith_2eZcomplements_2eZlength___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('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorEq.eqb_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorEq_2eeqb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorEq_2eeqb___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_QuicksortComplexity.vec.natBelow_S_bla_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__S__bla,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2enatBelow__S__bla___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38501_$a1',axiom,
! [V_24X1] : happ(c_24__lam__38501,V_24X1) = c_24__lam__38501___24a1(V_24X1) ).
fof('$adef_$_lam_74282_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__74282,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__74282___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_70868_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__70868,V_24X1),V_24X2) = c_24__lam__70868___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.insert_ordered_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2einsert__ordered,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2evec_2einsert__ordered___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_case_Coq.Vectors.Fin.t$74541_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eVectors_2eFin_2et_2474541,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eVectors_2eFin_2et_2474541___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.ForallPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Vectors.VectorDef.take_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2etake,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2etake___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.arith_lems.sqrd_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2esqrd,V_24X1) = cQuicksortComplexity_2earith__lems_2esqrd___24a1(V_24X1) ).
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('$adef_$_lam_1212_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1212,V_24X1),V_24X2),V_24X3) = c_24__lam__1212___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_73122_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73122,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73122___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
fof('$adef_$_lam_76949_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__76949,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__76949___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_74632_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74632,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74632___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('$adef_QuicksortComplexity.vec.nats_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2enats,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2enats___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.rev_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2erev,V_24X1),V_24X2) = cCoq_2eLists_2eList_2erev___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$19809_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419809___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$24532_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2424532___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.Morphisms.pointwise_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eClasses_2eMorphisms_2epointwise__relation,V_24X1),V_24X2),V_24X3) = cCoq_2eClasses_2eMorphisms_2epointwise__relation___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_60122_$a1',axiom,
! [V_24X1] : happ(c_24__lam__60122,V_24X1) = c_24__lam__60122___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorEq.eqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorEq_2eeqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorEq_2eeqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.cons_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2econs___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.list_utils.add_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2eadd,V_24X1) = cQuicksortComplexity_2elist__utils_2eadd___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_QuicksortComplexity.vec.insertion_sort_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2einsertion__sort,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2einsertion__sort___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_73155_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73155,V_24X1),V_24X2) = c_24__lam__73155___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('$adef_QuicksortComplexity.sort_order.Ecmp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEcmp,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEcmp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_73615_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73615,V_24X1),V_24X2) = c_24__lam__73615___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.util.ext_eq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2eext__eq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_$_lam_74642_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74642,V_24X1),V_24X2) = c_24__lam__74642___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_75675_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__75675,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__75675___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_8872_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__8872,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__8872___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_719_$a1',axiom,
! [V_24X1] : happ(c_24__lam__719,V_24X1) = c_24__lam__719___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8048_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__8048,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__8048___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.caseS\'_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eFin_2ecaseS_27,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eFin_2ecaseS_27___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_indices.contents.IndexSeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cindices_2econtents_2eIndexSeq,V_24X1),V_24X2))
<=> cindices_2econtents_2eIndexSeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_var_6_p_30388_30390_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__30388__30390,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__30388__30390___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$70592_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_avoid_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__avoid___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$137_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24137,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24137___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.firstn_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efirstn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efirstn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73162_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73162,V_24X1),V_24X2),V_24X3) = c_24__lam__73162___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_lam_7860_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7860,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7860___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_QuicksortComplexity.util.decision_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eutil_2edecision,V_24X1) = cQuicksortComplexity_2eutil_2edecision___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Vectors.Fin.t$74541_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eVectors_2eFin_2et_2474541,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eVectors_2eFin_2et_2474541___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.sort_order.Ele_le_dec_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2esort__order_2eEle__le__dec,V_24X1) = cQuicksortComplexity_2esort__order_2eEle__le__dec___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('$adef_QuicksortComplexity.list_utils.splits_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2esplits,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2esplits___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.rect2_$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_2eVectors_2eVectorDef_2erect2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eVectors_2eVectorDef_2erect2___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_let_17_mkopp_pow_55943_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__17__mkopp__pow__55943,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__let__17__mkopp__pow__55943___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_QuicksortComplexity.sort_order.Ec_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2esort__order_2eEc,V_24X1) = cQuicksortComplexity_2esort__order_2eEc___24a1(V_24X1) ).
fof('$adef_$_lam_70833_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70833,V_24X1) = c_24__lam__70833___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.filter_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLists_2eList_2efilter,V_24X1) = cCoq_2eLists_2eList_2efilter___24a1(V_24X1) ).
fof('$adef_$_let_16_mkpow_55942_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__16__mkpow__55942,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__16__mkpow__55942___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_77078_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__77078,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__77078___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_74221_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__74221,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__74221___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_74889_$a1',axiom,
! [V_24X1] : happ(c_24__lam__74889,V_24X1) = c_24__lam__74889___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.Acc_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2eAcc__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_7895_$a1',axiom,
! [V_24X1] : happ(c_24__lam__7895,V_24X1) = c_24__lam__7895___24a1(V_24X1) ).
fof('$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_$_lam_74849_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__74849,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__74849___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_indices.contents.subscript_$a1',axiom,
! [V_24X1] : happ(cindices_2econtents_2esubscript,V_24X1) = cindices_2econtents_2esubscript___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_59577_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__59577,V_24X1),V_24X2) = c_24__prop__59577___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.nlt_0_r_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2enlt__0__r,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2enlt__0__r___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.vec.head_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2ehead,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2ehead___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_15194_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15194,V_24X1),V_24X2),V_24X3) = c_24__lam__15194___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Logic.eq_rect_r_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect__r,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eLogic_2eeq__rect__r___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73293_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73293,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73293___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.Mult.mult_acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eArith_2eMult_2emult__acc,V_24X1),V_24X2),V_24X3) = cCoq_2eArith_2eMult_2emult__acc___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.natBelow_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2enatBelow__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.Fin.case0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2ecase0,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2ecase0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_indices.contents.IndexSeq_above_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cindices_2econtents_2eIndexSeq__above,V_24X1),V_24X2))
<=> cindices_2econtents_2eIndexSeq__above___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esqrt,V_24X1) = cCoq_2eInit_2eNat_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEeval_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eField__theory_2eFEeval___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.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_QuicksortComplexity.vec.app_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2eapp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2eapp___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.tl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2etl,V_24X1) = cCoq_2eVectors_2eVectorDef_2etl___24a1(V_24X1) ).
fof('$adef_$_lam_73012_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73012,V_24X1),V_24X2) = c_24__lam__73012___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.fold_left2_$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_2eVectors_2eVectorDef_2efold__left2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eVectors_2eVectorDef_2efold__left2___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_prop_76816_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__76816,V_24X1),V_24X2),V_24X3) = c_24__prop__76816___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$70592_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2470592___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Egeb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEgeb,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEgeb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.replace_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ereplace,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2ereplace___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_QuicksortComplexity.sort_order.Ele_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEle,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEle___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.fold_right_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorDef_2efold__right___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Empty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty,V_24X1))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V_24X1) ) ).
fof('$adef_$_lam_73454_$a1',axiom,
! [V_24X1] : happ(c_24__lam__73454,V_24X1) = c_24__lam__73454___24a1(V_24X1) ).
fof('$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.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.merges_spec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges__spec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.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.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$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.Vectors.VectorDef.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.FinFun.Injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eInjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eInjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_73002_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73002,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73002___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bvector.Bvector_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBvector_2eBvector,V_24X1) = cCoq_2eBool_2eBvector_2eBvector___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2epair___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.sort_order.Ele_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2esort__order_2eEle,V_24X1) = cQuicksortComplexity_2esort__order_2eEle___24a1(V_24X1) ).
fof('$adef_$_lam_74423_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74423,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74423___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Arith.Le.le_S_n_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eLe_2ele__S__n,V_24X1),V_24X2) = cCoq_2eArith_2eLe_2ele__S__n___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_75728_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75728,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__75728___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_$_lam_73233_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73233,V_24X1),V_24X2),V_24X3) = c_24__lam__73233___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.util.on_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eutil_2eon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eutil_2eon___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.arith_lems.log2ceil_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2elog2ceil,V_24X1) = cQuicksortComplexity_2earith__lems_2elog2ceil___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bvector.BVeq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBvector_2eBVeq,V_24X1),V_24X2) = cCoq_2eBool_2eBvector_2eBVeq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Plus.plus_assoc_reverse_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eArith_2ePlus_2eplus__assoc__reverse,V_24X1),V_24X2),V_24X3) = cCoq_2eArith_2ePlus_2eplus__assoc__reverse___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.tl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2etl,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2etl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_QuicksortComplexity.vec.tail_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2etail,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2etail___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.Logic.FinFun.Full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2eFull,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2eFull___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_73615_$a1',axiom,
! [V_24X1] : happ(c_24__lam__73615,V_24X1) = c_24__lam__73615___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_$_lam_74221_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__74221,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__74221___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_lam_74573_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74573,V_24X1),V_24X2) = c_24__lam__74573___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.list_prod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2elist__prod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2elist__prod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_75355_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__75355,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__75355___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_QuicksortComplexity.vec.Xlt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2evec_2eXlt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2evec_2eXlt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.List.lel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2elel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2elel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_$_lam_74432_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74432,V_24X1),V_24X2) = c_24__lam__74432___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_19362_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__19362__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__19362__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.plusnb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2eplusnb,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2eplusnb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7860_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__7860,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__7860___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.nat_below.cond_eq_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2enat__below_2econd__eq,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2enat__below_2econd__eq___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74632_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74632,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74632___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_75009_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__75009,V_24X1),V_24X2) = c_24__lam__75009___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.False_ind_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eLogic_2eFalse__ind,V_24X1) = cCoq_2eInit_2eLogic_2eFalse__ind___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xelements_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exelements___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_76031_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__76031,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__76031___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_70842_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70842,V_24X1),V_24X2),V_24X3) = c_24__lam__70842___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.vec.nth_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2enth,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2enth___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Wf.well_founded_induction_type_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eWf_2ewell__founded__induction__type___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('$adef_$_lam_60171_$a1',axiom,
! [V_24X1] : happ(c_24__lam__60171,V_24X1) = c_24__lam__60171___24a1(V_24X1) ).
fof('$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_QuicksortComplexity.list_utils.elemsR_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.FinFun.Finite_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eFinFun_2eFinite,V_24X1))
<=> cCoq_2eLogic_2eFinFun_2eFinite___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_prop_4272_$a1',axiom,
! [V_24X1] : happ(c_24__prop__4272,V_24X1) = c_24__prop__4272___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.rev_append_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2erev__append,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2erev__append___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_75678_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__75678,V_24X1),V_24X2),V_24X3) = c_24__lam__75678___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.shiftl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1) = cCoq_2eInit_2eNat_2eshiftl___24a1(V_24X1) ).
fof('$adef_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.Vectors.VectorDef.shiftrepeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eshiftrepeat,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2eshiftrepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.nat_below.nb_val_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__below_2enb__val,V_24X1),V_24X2) = cQuicksortComplexity_2enat__below_2enb__val___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73233_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73233,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73233___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$19226_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419226___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_75020_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__75020,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__75020___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_74661_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74661,V_24X1),V_24X2) = c_24__lam__74661___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7074_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7074,V_24X1),V_24X2),V_24X3) = c_24__lam__7074___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.rect2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erect2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2erect2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_73957_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73957,V_24X1),V_24X2),V_24X3) = c_24__lam__73957___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74025_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74025,V_24X1),V_24X2) = c_24__lam__74025___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.nat_below.natBelow_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enatBelow,V_24X1) = cQuicksortComplexity_2enat__below_2enatBelow___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.list_utils.insert_everywhere_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2einsert__everywhere,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73002_$a1',axiom,
! [V_24X1] : happ(c_24__lam__73002,V_24X1) = c_24__lam__73002___24a1(V_24X1) ).
fof('$adef_$_lam_74804_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__74804,V_24X1),V_24X2),V_24X3) = c_24__lam__74804___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.funind.Recdef.cmt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2efunind_2eRecdef_2ecmt,V_24X1),V_24X2),V_24X3) = cCoq_2efunind_2eRecdef_2ecmt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_74801_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74801,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74801___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.vec.natBelow_rect_S_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__rect__S,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2enatBelow__rect__S___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_73155_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__73155,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__73155___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.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.QArith.QArith_base.Qminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQminus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQminus___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.sort_order.Ege_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2esort__order_2eEge,V_24X1) = cQuicksortComplexity_2esort__order_2eEge___24a1(V_24X1) ).
fof('$adef_$_prop_76817_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__76817,V_24X1),V_24X2),V_24X3) = c_24__prop__76817___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4830_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4830,V_24X1),V_24X2) = c_24__lam__4830___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_75733_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__75733,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__75733___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.vec.sorted_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2evec_2esorted,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2evec_2esorted___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_74573_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74573,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74573___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.nat_below.nb0_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enb0,V_24X1) = cQuicksortComplexity_2enat__below_2enb0___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Ege_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2esort__order_2eEge,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2esort__order_2eEge___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_lam_75535_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__75535,V_24X1),V_24X2),V_24X3) = c_24__lam__75535___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_18601_$a1',axiom,
! [V_24X1] : happ(c_24__lam__18601,V_24X1) = c_24__lam__18601___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$_lam_73181_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73181,V_24X1),V_24X2) = c_24__lam__73181___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_74837_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74837,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74837___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.sort_order.Egtb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEgtb,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEgtb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_$_lam_73293_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__73293,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__73293___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1),V_24X2),V_24X3) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.nat_below.natBelow_rec_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enatBelow__rec,V_24X1) = cQuicksortComplexity_2enat__below_2enatBelow__rec___24a1(V_24X1) ).
fof('$adef_$_lam_70866_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70866,V_24X1),V_24X2),V_24X3) = c_24__lam__70866___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.nof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2enof,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2enof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7895_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7895,V_24X1),V_24X2),V_24X3) = c_24__lam__7895___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.eq_rec_r_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rec__r,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eLogic_2eeq__rec__r___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.Zcomplements.Zlength_aux_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2eZlength__aux,V_24X1) = cCoq_2eZArith_2eZcomplements_2eZlength__aux___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.shiftrepeat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2eshiftrepeat,V_24X1) = cCoq_2eVectors_2eVectorDef_2eshiftrepeat___24a1(V_24X1) ).
fof('$adef_$_fix_75238_v_CANONICAL_3_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__75238__v__CANONICAL__3,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__75238__v__CANONICAL__3___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.splitat_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2esplitat,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2esplitat___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.list_utils.InP_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eInP,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2elist__utils_2eInP___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_QuicksortComplexity.list_utils.insert_everywhere_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2einsert__everywhere,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2einsert__everywhere___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.VectorDef.replace_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ereplace,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2ereplace___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_QuicksortComplexity.vec.take_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2etake,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2etake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.eq_rec_r_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rec__r,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rec__r___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.list_utils.repeat_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2erepeat,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2erepeat___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.app_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1) = cCoq_2eInit_2eDatatypes_2eapp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_19867_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__19867,V_24X1),V_24X2) = c_24__lam__19867___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73107_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73107,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73107___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_QuicksortComplexity.arith_lems.R_floor_log2_S_0_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0,V_24X1) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(V_24X1) ).
fof('$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.Vectors.VectorDef.fold_left_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorDef_2efold__left___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_75535_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__75535,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__75535___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_73263_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73263,V_24X1),V_24X2),V_24X3) = c_24__lam__73263___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.vec.natBelow_S_bla_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__S__bla,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2enatBelow__S__bla___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_19872_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__19872,V_24X1),V_24X2) = c_24__lam__19872___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pphi_pow_$a16',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16) = cCoq_2esetoid__ring_2eRing__polynom_2ePphi__pow___24a16(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16) ).
fof('$adef_Coq.Vectors.VectorDef.map_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2emap,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2emap___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.list_utils.me_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2eme,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2eme___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_$_lam_3155_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__3155,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__3155___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Program.Basics.compose_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.elemsR_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2eelemsR___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_60164_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__60164,V_24X1),V_24X2) = c_24__lam__60164___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.jump_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eBinList_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_QuicksortComplexity.list_utils.concat_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2econcat,V_24X1) = cQuicksortComplexity_2elist__utils_2econcat___24a1(V_24X1) ).
fof('$adef_$_lam_3159_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__3159,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__3159___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_77167_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77167,V_24X1) = c_24__lam__77167___24a1(V_24X1) ).
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('$adef_Coq.Vectors.VectorDef.In_$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('$adef_$_lam_75355_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__75355,V_24X1),V_24X2),V_24X3) = c_24__lam__75355___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_76949_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__76949,V_24X1),V_24X2) = c_24__lam__76949___24a2(V_24X1,V_24X2) ).
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('$adef_QuicksortComplexity.vec.app_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2eapp,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2eapp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8872_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__8872,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__8872___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_prop_77171_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__77171,V_24X1),V_24X2) = c_24__prop__77171___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_4_n_8244_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__n__8244,V_24X1),V_24X2) = c_24__let__4__n__8244___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.nle_succ_0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2enle__succ__0,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2enle__succ__0___24a1(V_24X1) ).
fof('$adef_$_lam_75584_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75584,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__75584___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_76867_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__76867,V_24X1),V_24X2),V_24X3) = c_24__lam__76867___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.sort_order.Elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2esort__order_2eElt,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2esort__order_2eElt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_case_QuicksortComplexity.nat_below.natBelow$931_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__QuicksortComplexity_2enat__below_2enatBelow_24931___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_prop_46_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__46,V_24X1),V_24X2) = c_24__prop__46___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$59804_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2459804___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$34547_$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_2434547,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_2434547___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_$_lam_19867_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__19867,V_24X1),V_24X2),V_24X3) = c_24__lam__19867___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_35811_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__35811,V_24X1),V_24X2) = c_24__lam__35811___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('$adef_$_lam_70821_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70821,V_24X1) = c_24__lam__70821___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74849_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74849,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74849___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.sort_order.Eltb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEltb,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEltb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74423_$a1',axiom,
! [V_24X1] : happ(c_24__lam__74423,V_24X1) = c_24__lam__74423___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_74889_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74889,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74889___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rfunctions.sum_nat_f_O_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2esum__nat__f__O,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2esum__nat__f__O___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_74837_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__74837,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__74837___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_fix_9407_v_CANONICAL_2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__fix__9407__v__CANONICAL__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__fix__9407__v__CANONICAL__2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_fix_24577_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__24577__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__24577__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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.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.Arith.Wf_nat.gtof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2egtof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2egtof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Nat.shiftr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftr,V_24X1) = cCoq_2eInit_2eNat_2eshiftr___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.nat_below.Snb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2enat__below_2eSnb,V_24X1),V_24X2) = cQuicksortComplexity_2enat__below_2eSnb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_70868_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70868,V_24X1) = c_24__lam__70868___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1223_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1223,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1223___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_QuicksortComplexity.vec.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.sqrt_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_3021_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__prop__3021,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__prop__3021___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Vectors.Fin.of_nat_lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eof__nat__lt,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eof__nat__lt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.nth_ok_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__ok,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__ok___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.map2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2emap2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2emap2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$19119_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419119___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.caseS_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_3159_$a1',axiom,
! [V_24X1] : happ(c_24__lam__3159,V_24X1) = c_24__lam__3159___24a1(V_24X1) ).
fof('$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_$_case_Coq.Numbers.BinNums.Z$59799_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2459799___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_60171_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__60171,V_24X1),V_24X2) = c_24__lam__60171___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.merges_ex_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2elist__utils_2emerges__ex,V_24X1),V_24X2) = cQuicksortComplexity_2elist__utils_2emerges__ex___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.map2_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2emap2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eVectors_2eVectorDef_2emap2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Eleb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2esort__order_2eEleb,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2esort__order_2eEleb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.nat_below.natBelow_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2enat__below_2enatBelow__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2enat__below_2enatBelow__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Vectors.VectorDef.caseS_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.Fin.caseS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eFin_2ecaseS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eFin_2ecaseS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.Arith.Lt.lt_S_n_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eLt_2elt__S__n,V_24X1),V_24X2) = cCoq_2eArith_2eLt_2elt__S__n___24a2(V_24X1,V_24X2) ).
fof('$adef_indices.contents.IndexIn_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cindices_2econtents_2eIndexIn,V_24X1),V_24X2))
<=> cindices_2econtents_2eIndexIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.removelast_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2eremovelast,V_24X1),V_24X2) = cCoq_2eLists_2eList_2eremovelast___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1) = cCoq_2eInit_2eDatatypes_2elength___24a1(V_24X1) ).
fof('$adef_$_lam_74804_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__74804,V_24X1),V_24X2) = c_24__lam__74804___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_363_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__363,V_24X1),V_24X2),V_24X3) = c_24__lam__363___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_$_lam_75675_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__75675,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__75675___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_74432_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74432,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74432___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.QArith.QArith_base.Qplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQplus,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQplus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_74642_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__74642,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__74642___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.funind.Recdef.max_type_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2efunind_2eRecdef_2emax__type,V_24X1),V_24X2) = cCoq_2efunind_2eRecdef_2emax__type___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_74282_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__74282,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__74282___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Vectors.VectorDef.replace_order_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ereplace__order,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2ereplace__order___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_719_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__719,V_24X1),V_24X2) = c_24__lam__719___24a2(V_24X1,V_24X2) ).
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('$adef_QuicksortComplexity.arith_lems.R_floor_log2_S_1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Lists.ListDec.decidable_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLists_2eListDec_2edecidable__eq,V_24X1))
<=> cCoq_2eLists_2eListDec_2edecidable__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_75401_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75401,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__lam__75401___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.ZArith.Zpower.shift_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eshift__nat,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eshift__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_76867_$a1',axiom,
! [V_24X1] : happ(c_24__lam__76867,V_24X1) = c_24__lam__76867___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_70746_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__70746,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__70746___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_19843_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__19843,V_24X1),V_24X2) = c_24__lam__19843___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_75728_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__75728,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__75728___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_QuicksortComplexity.vec.R_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2eR,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2eR___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$74984_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2474984___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.arith_lems.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2earith__lems_2epow,V_24X1),V_24X2) = cQuicksortComplexity_2earith__lems_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Peano.plus_n_O_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2ePeano_2eplus__n__O,V_24X1) = cCoq_2eInit_2ePeano_2eplus__n__O___24a1(V_24X1) ).
fof('$adef_$_lam_827_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__827,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__827___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_77166_$a1',axiom,
! [V_24X1] : happ(c_24__lam__77166,V_24X1) = c_24__lam__77166___24a1(V_24X1) ).
fof('$adef_$_lam_18584_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__18584,V_24X1),V_24X2),V_24X3) = c_24__lam__18584___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_60175_$a1',axiom,
! [V_24X1] : happ(c_24__lam__60175,V_24X1) = c_24__lam__60175___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.compare_$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('$adef_QuicksortComplexity.vec.remove_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2eremove,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2eremove___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_22813_$a1',axiom,
! [V_24X1] : happ(c_24__lam__22813,V_24X1) = c_24__lam__22813___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.sort_order.Egt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cQuicksortComplexity_2esort__order_2eEgt,V_24X1),V_24X2),V_24X3))
<=> cQuicksortComplexity_2esort__order_2eEgt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_QuicksortComplexity.list_utils.merges_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2emerges___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.add_assoc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eadd__assoc,V_24X1),V_24X2),V_24X3) = cCoq_2eArith_2ePeanoNat_2eNat_2eadd__assoc___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_default_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth__default,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth__default___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_70855_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__70855,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__70855___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_18_mkmult_pow_55944_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__18__mkmult__pow__55944,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__let__18__mkmult__pow__55944___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_QuicksortComplexity.vec.drop_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2evec_2edrop,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2evec_2edrop___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_70866_$a1',axiom,
! [V_24X1] : happ(c_24__lam__70866,V_24X1) = c_24__lam__70866___24a1(V_24X1) ).
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('$adef_$_lam_75678_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__75678,V_24X1),V_24X2) = c_24__lam__75678___24a2(V_24X1,V_24X2) ).
fof('$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.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_$_lam_74583_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__74583,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__74583___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Vectors.VectorDef.uncons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2euncons,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2euncons___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_73918_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__73918,V_24X1),V_24X2),V_24X3) = c_24__lam__73918___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.FinFun.bInjective_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eFinFun_2ebInjective,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_74234_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__74234,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__74234___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.fold_left2_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2efold__left2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eVectors_2eVectorDef_2efold__left2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_$_lam_73162_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__73162,V_24X1),V_24X2) = c_24__lam__73162___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.arith_lems.R_floor_log2_S_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S,V_24X1),V_24X2) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24a2(V_24X1,V_24X2) ).
fof('$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.Vectors.Fin.of_nat_lt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eFin_2eof__nat__lt,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eFin_2eof__nat__lt___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_QuicksortComplexity.arith_lems.ceil_log2_S_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2eceil__log2__S,V_24X1) = cQuicksortComplexity_2earith__lems_2eceil__log2__S___24a1(V_24X1) ).
fof('$adef_$_fix_156_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__156__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__156__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_16_mkpow_55942_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__let__16__mkpow__55942,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__let__16__mkpow__55942___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Vectors.VectorDef.caseS\'_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS_27,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2ecaseS_27___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Factorial.fact_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2eFactorial_2efact,V_24X1) = cCoq_2eArith_2eFactorial_2efact___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_$_lam_75013_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__75013,V_24X1),V_24X2),V_24X3) = c_24__lam__75013___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_18601_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__18601,V_24X1),V_24X2) = c_24__lam__18601___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_70723_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70723,V_24X1),V_24X2),V_24X3) = c_24__lam__70723___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_74661_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__74661,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__74661___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_9527_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__9527,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__9527___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.rect2_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erect2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eVectors_2eVectorDef_2erect2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_73012_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__73012,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__73012___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.vec.trans_plus_n_Sm_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2evec_2etrans__plus__n__Sm,V_24X1),V_24X2) = cQuicksortComplexity_2evec_2etrans__plus__n__Sm___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.nat_below.nb_val_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enb__val,V_24X1) = cQuicksortComplexity_2enat__below_2enb__val___24a1(V_24X1) ).
fof('$adef_$_lam_70821_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__70821,V_24X1),V_24X2),V_24X3) = c_24__lam__70821___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.vec.natBelow_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2enatBelow__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2enatBelow__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.incl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eincl,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eincl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.rectS_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2erectS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eVectors_2eVectorDef_2erectS___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.hd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2ehd,V_24X1) = cCoq_2eVectors_2eVectorDef_2ehd___24a1(V_24X1) ).
fof('$adef_$_lam_8048_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__8048,V_24X1),V_24X2),V_24X3) = c_24__lam__8048___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_$_lam_70746_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__70746,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__70746___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_QuicksortComplexity.vec.insert_ordered_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2evec_2einsert__ordered,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2evec_2einsert__ordered___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.QArith.QArith_base.Qopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQopp,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQopp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.list_utils.perms_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2eperms,V_24X1) = cQuicksortComplexity_2elist__utils_2eperms___24a1(V_24X1) ).
fof('$tdef_$_type_30421',axiom,
! [V_24Y] :
( c_24__type__30421___24t(V_24Y)
<=> t(V_24Y,c_24__type__30421) ) ).
fof('$tdef_$_type_9277',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9277___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9277___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_20292',axiom,
! [V_24Y] :
( c_24__type__20292___24t(V_24Y)
<=> t(V_24Y,c_24__type__20292) ) ).
fof('$tdef_$_type_73215',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73215___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73215___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27602',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__27602___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__27602___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_44926',axiom,
! [V_24Y] :
( c_24__type__44926___24t(V_24Y)
<=> t(V_24Y,c_24__type__44926) ) ).
fof('$tdef_$_type_27256',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__27256___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__27256___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_59504',axiom,
! [V_24Y] :
( c_24__type__59504___24t(V_24Y)
<=> t(V_24Y,c_24__type__59504) ) ).
fof('$tdef_$_type_19932',axiom,
! [V_24Y] :
( c_24__type__19932___24t(V_24Y)
<=> t(V_24Y,c_24__type__19932) ) ).
fof('$tdef_$_type_77141',axiom,
! [V_24Y] :
( c_24__type__77141___24t(V_24Y)
<=> t(V_24Y,c_24__type__77141) ) ).
fof('$tdef_$_type_1116',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1116___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1116___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22718',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22718___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22718___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29286',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__29286___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__29286___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_31487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31487___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_34342',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34342___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34342___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_34899',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34899___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34899___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38665',axiom,
! [V_24Y] :
( c_24__type__38665___24t(V_24Y)
<=> t(V_24Y,c_24__type__38665) ) ).
fof('$tdef_$_type_4418',axiom,
! [V_24Y] :
( c_24__type__4418___24t(V_24Y)
<=> t(V_24Y,c_24__type__4418) ) ).
fof('$tdef_$_type_59532',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__59532___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__59532___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_73980',axiom,
! [V_24Y] :
( c_24__type__73980___24t(V_24Y)
<=> t(V_24Y,c_24__type__73980) ) ).
fof('$tdef_$_type_2134',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2134___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2134___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8110',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8110___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8110___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8077',axiom,
! [V_24Y] :
( c_24__type__8077___24t(V_24Y)
<=> t(V_24Y,c_24__type__8077) ) ).
fof('$tdef_$_type_73256',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73256___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73256___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_60139',axiom,
! [V_24X1,V_24Y] :
( c_24__type__60139___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__60139___24a1(V_24X1)) ) ).
fof('$tdef_$_type_365',axiom,
! [V_24Y] :
( c_24__type__365___24t(V_24Y)
<=> t(V_24Y,c_24__type__365) ) ).
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_$_type_8058',axiom,
! [V_24Y] :
( c_24__type__8058___24t(V_24Y)
<=> t(V_24Y,c_24__type__8058) ) ).
fof('$tdef_$_type_171',axiom,
! [V_24Y] :
( c_24__type__171___24t(V_24Y)
<=> t(V_24Y,c_24__type__171) ) ).
fof('$tdef_$_type_37450',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37450___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37450___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18598',axiom,
! [V_24Y] :
( c_24__type__18598___24t(V_24Y)
<=> t(V_24Y,c_24__type__18598) ) ).
fof('$tdef_$_type_60192',axiom,
! [V_24Y] :
( c_24__type__60192___24t(V_24Y)
<=> t(V_24Y,c_24__type__60192) ) ).
fof('$tdef_$_type_33017',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__33017___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__33017___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_62352',axiom,
! [V_24X1,V_24Y] :
( c_24__type__62352___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__62352___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25203___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_73226',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73226___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73226___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_308',axiom,
! [V_24Y] :
( c_24__type__308___24t(V_24Y)
<=> t(V_24Y,c_24__type__308) ) ).
fof('$tdef_$_type_9599',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9599___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9599___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30137',axiom,
! [V_24Y] :
( c_24__type__30137___24t(V_24Y)
<=> t(V_24Y,c_24__type__30137) ) ).
fof('$tdef_$_type_21070',axiom,
! [V_24Y] :
( c_24__type__21070___24t(V_24Y)
<=> t(V_24Y,c_24__type__21070) ) ).
fof('$tdef_$_type_21044',axiom,
! [V_24Y] :
( c_24__type__21044___24t(V_24Y)
<=> t(V_24Y,c_24__type__21044) ) ).
fof('$tdef_$_type_20043',axiom,
! [V_24Y] :
( c_24__type__20043___24t(V_24Y)
<=> t(V_24Y,c_24__type__20043) ) ).
fof('$tdef_$_type_34716',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34716___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34716___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_37445',axiom,
! [V_24Y] :
( c_24__type__37445___24t(V_24Y)
<=> t(V_24Y,c_24__type__37445) ) ).
fof('$tdef_$_type_8791',axiom,
! [V_24Y] :
( c_24__type__8791___24t(V_24Y)
<=> t(V_24Y,c_24__type__8791) ) ).
fof('$tdef_$_type_7803',axiom,
! [V_24Y] :
( c_24__type__7803___24t(V_24Y)
<=> t(V_24Y,c_24__type__7803) ) ).
fof('$tdef_$_type_349',axiom,
! [V_24Y] :
( c_24__type__349___24t(V_24Y)
<=> t(V_24Y,c_24__type__349) ) ).
fof('$tdef_QuicksortComplexity.sort_order.Ec',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2esort__order_2eEc___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2esort__order_2eEc___24a1(V_24X1)) ) ).
fof('$tdef_$_type_77169',axiom,
! [V_24Y] :
( c_24__type__77169___24t(V_24Y)
<=> t(V_24Y,c_24__type__77169) ) ).
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_73383',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73383___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73383___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35089',axiom,
! [V_24Y] :
( c_24__type__35089___24t(V_24Y)
<=> t(V_24Y,c_24__type__35089) ) ).
fof('$tdef_$_type_73767',axiom,
! [V_24Y] :
( c_24__type__73767___24t(V_24Y)
<=> t(V_24Y,c_24__type__73767) ) ).
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_$_type_73950',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73950___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73950___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_75801',axiom,
! [V_24Y] :
( c_24__type__75801___24t(V_24Y)
<=> t(V_24Y,c_24__type__75801) ) ).
fof('$tdef_$_type_35714',axiom,
! [V_24Y] :
( c_24__type__35714___24t(V_24Y)
<=> t(V_24Y,c_24__type__35714) ) ).
fof('$tdef_$_type_31379',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31379___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31379___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_19952',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__19952___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__19952___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8034',axiom,
! [V_24Y] :
( c_24__type__8034___24t(V_24Y)
<=> t(V_24Y,c_24__type__8034) ) ).
fof('$tdef_$_type_24044',axiom,
! [V_24Y] :
( c_24__type__24044___24t(V_24Y)
<=> t(V_24Y,c_24__type__24044) ) ).
fof('$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_8241',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8241___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8241___24a1(V_24X1)) ) ).
fof('$tdef_$_type_74896',axiom,
! [V_24Y] :
( c_24__type__74896___24t(V_24Y)
<=> t(V_24Y,c_24__type__74896) ) ).
fof('$tdef_QuicksortComplexity.nat_below.natBelow',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2enat__below_2enatBelow___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18603',axiom,
! [V_24Y] :
( c_24__type__18603___24t(V_24Y)
<=> t(V_24Y,c_24__type__18603) ) ).
fof('$tdef_$_type_1343',axiom,
! [V_24Y] :
( c_24__type__1343___24t(V_24Y)
<=> t(V_24Y,c_24__type__1343) ) ).
fof('$tdef_$_type_73738',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73738___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73738___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_380',axiom,
! [V_24Y] :
( c_24__type__380___24t(V_24Y)
<=> t(V_24Y,c_24__type__380) ) ).
fof('$tdef_$_type_75430',axiom,
! [V_24Y] :
( c_24__type__75430___24t(V_24Y)
<=> t(V_24Y,c_24__type__75430) ) ).
fof('$tdef_$_type_444',axiom,
! [V_24Y] :
( c_24__type__444___24t(V_24Y)
<=> t(V_24Y,c_24__type__444) ) ).
fof('$tdef_$_type_2302',axiom,
! [V_24Y] :
( c_24__type__2302___24t(V_24Y)
<=> t(V_24Y,c_24__type__2302) ) ).
fof('$tdef_$_type_31433',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31433___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31433___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_34942',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34942___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34942___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7705',axiom,
! [V_24Y] :
( c_24__type__7705___24t(V_24Y)
<=> t(V_24Y,c_24__type__7705) ) ).
fof('$tdef_$_type_35702',axiom,
! [V_24Y] :
( c_24__type__35702___24t(V_24Y)
<=> t(V_24Y,c_24__type__35702) ) ).
fof('$tdef_$_type_8319',axiom,
! [V_24Y] :
( c_24__type__8319___24t(V_24Y)
<=> t(V_24Y,c_24__type__8319) ) ).
fof('$tdef_$_type_290',axiom,
! [V_24Y] :
( c_24__type__290___24t(V_24Y)
<=> t(V_24Y,c_24__type__290) ) ).
fof('$tdef_$_type_70716',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__70716___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__70716___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31195',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31195___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31195___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2257',axiom,
! [V_24Y] :
( c_24__type__2257___24t(V_24Y)
<=> t(V_24Y,c_24__type__2257) ) ).
fof('$tdef_$_type_37432',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37432___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37432___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73211',axiom,
! [V_24Y] :
( c_24__type__73211___24t(V_24Y)
<=> t(V_24Y,c_24__type__73211) ) ).
fof('$tdef_$_type_57',axiom,
! [V_24Y] :
( c_24__type__57___24t(V_24Y)
<=> t(V_24Y,c_24__type__57) ) ).
fof('$tdef_$_type_4421',axiom,
! [V_24Y] :
( c_24__type__4421___24t(V_24Y)
<=> t(V_24Y,c_24__type__4421) ) ).
fof('$tdef_$_type_76834',axiom,
! [V_24Y] :
( c_24__type__76834___24t(V_24Y)
<=> t(V_24Y,c_24__type__76834) ) ).
fof('$tdef_$_type_7336',axiom,
! [V_24Y] :
( c_24__type__7336___24t(V_24Y)
<=> t(V_24Y,c_24__type__7336) ) ).
fof('$tdef_$_type_4276',axiom,
! [V_24Y] :
( c_24__type__4276___24t(V_24Y)
<=> t(V_24Y,c_24__type__4276) ) ).
fof('$tdef_$_type_38517',axiom,
! [V_24Y] :
( c_24__type__38517___24t(V_24Y)
<=> t(V_24Y,c_24__type__38517) ) ).
fof('$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('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_9004',axiom,
! [V_24Y] :
( c_24__type__9004___24t(V_24Y)
<=> t(V_24Y,c_24__type__9004) ) ).
fof('$tdef_$_type_8161',axiom,
! [V_24Y] :
( c_24__type__8161___24t(V_24Y)
<=> t(V_24Y,c_24__type__8161) ) ).
fof('$tdef_$_type_34981',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34981___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34981___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_7086',axiom,
! [V_24Y] :
( c_24__type__7086___24t(V_24Y)
<=> t(V_24Y,c_24__type__7086) ) ).
fof('$tdef_$_type_73761',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73761___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73761___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Bool.Bvector.Bvector',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eBool_2eBvector_2eBvector___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBvector_2eBvector___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39606',axiom,
! [V_24Y] :
( c_24__type__39606___24t(V_24Y)
<=> t(V_24Y,c_24__type__39606) ) ).
fof('$tdef_$_type_73912',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73912___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73912___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73480',axiom,
! [V_24Y] :
( c_24__type__73480___24t(V_24Y)
<=> t(V_24Y,c_24__type__73480) ) ).
fof('$tdef_$_type_42',axiom,
! [V_24Y] :
( c_24__type__42___24t(V_24Y)
<=> t(V_24Y,c_24__type__42) ) ).
fof('$tdef_$_type_38074',axiom,
! [V_24Y] :
( c_24__type__38074___24t(V_24Y)
<=> t(V_24Y,c_24__type__38074) ) ).
fof('$tdef_$_type_23451',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23451___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23451___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34568',axiom,
! [V_24Y] :
( c_24__type__34568___24t(V_24Y)
<=> t(V_24Y,c_24__type__34568) ) ).
fof('$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_19443',axiom,
! [V_24Y] :
( c_24__type__19443___24t(V_24Y)
<=> t(V_24Y,c_24__type__19443) ) ).
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_$_type_69977',axiom,
! [V_24Y] :
( c_24__type__69977___24t(V_24Y)
<=> t(V_24Y,c_24__type__69977) ) ).
fof('$tdef_$_type_38399',axiom,
! [V_24Y] :
( c_24__type__38399___24t(V_24Y)
<=> t(V_24Y,c_24__type__38399) ) ).
fof('$tdef_$_type_31239',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31239___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31239___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10',axiom,
! [V_24Y] :
( c_24__type__10___24t(V_24Y)
<=> t(V_24Y,c_24__type__10) ) ).
fof('$tdef_$_type_7083',axiom,
! [V_24Y] :
( c_24__type__7083___24t(V_24Y)
<=> t(V_24Y,c_24__type__7083) ) ).
fof('$tdef_$_type_54495',axiom,
! [V_24Y] :
( c_24__type__54495___24t(V_24Y)
<=> t(V_24Y,c_24__type__54495) ) ).
fof('$tdef_$_type_38796',axiom,
! [V_24Y] :
( c_24__type__38796___24t(V_24Y)
<=> t(V_24Y,c_24__type__38796) ) ).
fof('$tdef_$_type_24071',axiom,
! [V_24Y] :
( c_24__type__24071___24t(V_24Y)
<=> t(V_24Y,c_24__type__24071) ) ).
fof('$tdef_$_type_8143',axiom,
! [V_24Y] :
( c_24__type__8143___24t(V_24Y)
<=> t(V_24Y,c_24__type__8143) ) ).
fof('$tdef_$_type_73390',axiom,
! [V_24Y] :
( c_24__type__73390___24t(V_24Y)
<=> t(V_24Y,c_24__type__73390) ) ).
fof('$tdef_$_type_7075',axiom,
! [V_24Y] :
( c_24__type__7075___24t(V_24Y)
<=> t(V_24Y,c_24__type__7075) ) ).
fof('$tdef_$_type_34672',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34672___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34672___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_324',axiom,
! [V_24Y] :
( c_24__type__324___24t(V_24Y)
<=> t(V_24Y,c_24__type__324) ) ).
fof('$tdef_$_type_75510',axiom,
! [V_24Y] :
( c_24__type__75510___24t(V_24Y)
<=> t(V_24Y,c_24__type__75510) ) ).
fof('$tdef_$_type_2262',axiom,
! [V_24Y] :
( c_24__type__2262___24t(V_24Y)
<=> t(V_24Y,c_24__type__2262) ) ).
fof('$tdef_$_type_9009',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9009___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9009___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20973',axiom,
! [V_24Y] :
( c_24__type__20973___24t(V_24Y)
<=> t(V_24Y,c_24__type__20973) ) ).
fof('$tdef_$_type_22112',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__22112___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__22112___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_70814',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__70814___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__70814___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8136',axiom,
! [V_24Y] :
( c_24__type__8136___24t(V_24Y)
<=> t(V_24Y,c_24__type__8136) ) ).
fof('$tdef_$_type_46775',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__46775___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__46775___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34889',axiom,
! [V_24Y] :
( c_24__type__34889___24t(V_24Y)
<=> t(V_24Y,c_24__type__34889) ) ).
fof('$tdef_$_type_34147',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34147___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34147___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_30356',axiom,
! [V_24Y] :
( c_24__type__30356___24t(V_24Y)
<=> t(V_24Y,c_24__type__30356) ) ).
fof('$tdef_$_type_50003',axiom,
! [V_24Y] :
( c_24__type__50003___24t(V_24Y)
<=> t(V_24Y,c_24__type__50003) ) ).
fof('$tdef_$_type_1172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__1172___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__1172___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15059',axiom,
! [V_24Y] :
( c_24__type__15059___24t(V_24Y)
<=> t(V_24Y,c_24__type__15059) ) ).
fof('$tdef_QuicksortComplexity.arith_lems.R_ceil_log2_S',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32804',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__32804___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__32804___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_669',axiom,
! [V_24Y] :
( c_24__type__669___24t(V_24Y)
<=> t(V_24Y,c_24__type__669) ) ).
fof('$tdef_$_type_21078',axiom,
! [V_24Y] :
( c_24__type__21078___24t(V_24Y)
<=> t(V_24Y,c_24__type__21078) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_QuicksortComplexity.util.decision',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2eutil_2edecision___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2eutil_2edecision___24a1(V_24X1)) ) ).
fof('$tdef_$_type_50047',axiom,
! [V_24Y] :
( c_24__type__50047___24t(V_24Y)
<=> t(V_24Y,c_24__type__50047) ) ).
fof('$tdef_$_type_1277',axiom,
! [V_24Y] :
( c_24__type__1277___24t(V_24Y)
<=> t(V_24Y,c_24__type__1277) ) ).
fof('$tdef_$_type_27948',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__27948___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__27948___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_23642',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__23642___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__23642___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73141',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73141___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73141___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30677',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__30677___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__30677___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38662',axiom,
! [V_24Y] :
( c_24__type__38662___24t(V_24Y)
<=> t(V_24Y,c_24__type__38662) ) ).
fof('$tdef_$_type_38905',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38905___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38905___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38667',axiom,
! [V_24Y] :
( c_24__type__38667___24t(V_24Y)
<=> t(V_24Y,c_24__type__38667) ) ).
fof('$tdef_$_type_26910',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__26910___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__26910___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_9242',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__9242___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__9242___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37748',axiom,
! [V_24Y] :
( c_24__type__37748___24t(V_24Y)
<=> t(V_24Y,c_24__type__37748) ) ).
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_$_type_7907',axiom,
! [V_24Y] :
( c_24__type__7907___24t(V_24Y)
<=> t(V_24Y,c_24__type__7907) ) ).
fof('$tdef_$_type_20388',axiom,
! [V_24Y] :
( c_24__type__20388___24t(V_24Y)
<=> t(V_24Y,c_24__type__20388) ) ).
fof('$tdef_$_type_158',axiom,
! [V_24Y] :
( c_24__type__158___24t(V_24Y)
<=> t(V_24Y,c_24__type__158) ) ).
fof('$tdef_$_type_76776',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__76776___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__76776___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74370',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__74370___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__74370___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73926',axiom,
! [V_24Y] :
( c_24__type__73926___24t(V_24Y)
<=> t(V_24Y,c_24__type__73926) ) ).
fof('$tdef_$_type_22657',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22657___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22657___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20449',axiom,
! [V_24Y] :
( c_24__type__20449___24t(V_24Y)
<=> t(V_24Y,c_24__type__20449) ) ).
fof('$tdef_$_type_26218',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26218___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26218___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_22446',axiom,
! [V_24Y] :
( c_24__type__22446___24t(V_24Y)
<=> t(V_24Y,c_24__type__22446) ) ).
fof('$tdef_$_type_20012',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__20012___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__20012___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1083',axiom,
! [V_24Y] :
( c_24__type__1083___24t(V_24Y)
<=> t(V_24Y,c_24__type__1083) ) ).
fof('$tdef_$_type_2174',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2174___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2174___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_76788',axiom,
! [V_24Y] :
( c_24__type__76788___24t(V_24Y)
<=> t(V_24Y,c_24__type__76788) ) ).
fof('$tdef_$_type_38433',axiom,
! [V_24Y] :
( c_24__type__38433___24t(V_24Y)
<=> t(V_24Y,c_24__type__38433) ) ).
fof('$tdef_$_type_22500',axiom,
! [V_24Y] :
( c_24__type__22500___24t(V_24Y)
<=> t(V_24Y,c_24__type__22500) ) ).
fof('$tdef_$_type_10895',axiom,
! [V_24Y] :
( c_24__type__10895___24t(V_24Y)
<=> t(V_24Y,c_24__type__10895) ) ).
fof('$tdef_$_type_962',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__962___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__962___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20371',axiom,
! [V_24Y] :
( c_24__type__20371___24t(V_24Y)
<=> t(V_24Y,c_24__type__20371) ) ).
fof('$tdef_$_type_7312',axiom,
! [V_24Y] :
( c_24__type__7312___24t(V_24Y)
<=> t(V_24Y,c_24__type__7312) ) ).
fof('$tdef_$_type_30154',axiom,
! [V_24Y] :
( c_24__type__30154___24t(V_24Y)
<=> t(V_24Y,c_24__type__30154) ) ).
fof('$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_$_type_75470',axiom,
! [V_24Y] :
( c_24__type__75470___24t(V_24Y)
<=> t(V_24Y,c_24__type__75470) ) ).
fof('$tdef_$_type_20',axiom,
! [V_24Y] :
( c_24__type__20___24t(V_24Y)
<=> t(V_24Y,c_24__type__20) ) ).
fof('$tdef_$_type_1843',axiom,
! [V_24Y] :
( c_24__type__1843___24t(V_24Y)
<=> t(V_24Y,c_24__type__1843) ) ).
fof('$tdef_$_type_31970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31970___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31970___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_21762',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21762___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21762___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35067',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35067___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35067___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8308',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8308___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8308___24a1(V_24X1)) ) ).
fof('$tdef_$_type_74137',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__74137___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__74137___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_287',axiom,
! [V_24Y] :
( c_24__type__287___24t(V_24Y)
<=> t(V_24Y,c_24__type__287) ) ).
fof('$tdef_$_type_34114',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34114___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34114___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_74436',axiom,
! [V_24Y] :
( c_24__type__74436___24t(V_24Y)
<=> t(V_24Y,c_24__type__74436) ) ).
fof('$tdef_$_type_7284',axiom,
! [V_24Y] :
( c_24__type__7284___24t(V_24Y)
<=> t(V_24Y,c_24__type__7284) ) ).
fof('$tdef_$_type_18586',axiom,
! [V_24Y] :
( c_24__type__18586___24t(V_24Y)
<=> t(V_24Y,c_24__type__18586) ) ).
fof('$tdef_$_type_19839',axiom,
! [V_24X1,V_24Y] :
( c_24__type__19839___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__19839___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39021',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__39021___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__39021___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34817',axiom,
! [V_24Y] :
( c_24__type__34817___24t(V_24Y)
<=> t(V_24Y,c_24__type__34817) ) ).
fof('$tdef_$_type_10892',axiom,
! [V_24Y] :
( c_24__type__10892___24t(V_24Y)
<=> t(V_24Y,c_24__type__10892) ) ).
fof('$tdef_$_type_7338',axiom,
! [V_24Y] :
( c_24__type__7338___24t(V_24Y)
<=> t(V_24Y,c_24__type__7338) ) ).
fof('$tdef_$_type_21937',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21937___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21937___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_434',axiom,
! [V_24Y] :
( c_24__type__434___24t(V_24Y)
<=> t(V_24Y,c_24__type__434) ) ).
fof('$tdef_$_type_2221',axiom,
! [V_24Y] :
( c_24__type__2221___24t(V_24Y)
<=> t(V_24Y,c_24__type__2221) ) ).
fof('$tdef_$_type_60134',axiom,
! [V_24Y] :
( c_24__type__60134___24t(V_24Y)
<=> t(V_24Y,c_24__type__60134) ) ).
fof('$tdef_$_type_2198',axiom,
! [V_24Y] :
( c_24__type__2198___24t(V_24Y)
<=> t(V_24Y,c_24__type__2198) ) ).
fof('$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_15070',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15070___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15070___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10880',axiom,
! [V_24Y] :
( c_24__type__10880___24t(V_24Y)
<=> t(V_24Y,c_24__type__10880) ) ).
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_$_type_20040',axiom,
! [V_24Y] :
( c_24__type__20040___24t(V_24Y)
<=> t(V_24Y,c_24__type__20040) ) ).
fof('$tdef_$_type_73311',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73311___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73311___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_1014',axiom,
! [V_24Y] :
( c_24__type__1014___24t(V_24Y)
<=> t(V_24Y,c_24__type__1014) ) ).
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_$_type_59575',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__59575___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__59575___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9024',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9024___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9024___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38461',axiom,
! [V_24Y] :
( c_24__type__38461___24t(V_24Y)
<=> t(V_24Y,c_24__type__38461) ) ).
fof('$tdef_$_type_7927',axiom,
! [V_24Y] :
( c_24__type__7927___24t(V_24Y)
<=> t(V_24Y,c_24__type__7927) ) ).
fof('$tdef_$_type_74359',axiom,
! [V_24Y] :
( c_24__type__74359___24t(V_24Y)
<=> t(V_24Y,c_24__type__74359) ) ).
fof('$tdef_$_type_33230',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__33230___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__33230___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_59811',axiom,
! [V_24Y] :
( c_24__type__59811___24t(V_24Y)
<=> t(V_24Y,c_24__type__59811) ) ).
fof('$tdef_$_type_37455',axiom,
! [V_24Y] :
( c_24__type__37455___24t(V_24Y)
<=> t(V_24Y,c_24__type__37455) ) ).
fof('$tdef_$_type_73051',axiom,
! [V_24Y] :
( c_24__type__73051___24t(V_24Y)
<=> t(V_24Y,c_24__type__73051) ) ).
fof('$tdef_$_type_38017',axiom,
! [V_24Y] :
( c_24__type__38017___24t(V_24Y)
<=> t(V_24Y,c_24__type__38017) ) ).
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_$_type_59966',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__59966___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__59966___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_1028',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1028___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1028___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73158',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73158___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73158___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_56222',axiom,
! [V_24Y] :
( c_24__type__56222___24t(V_24Y)
<=> t(V_24Y,c_24__type__56222) ) ).
fof('$tdef_$_type_1960',axiom,
! [V_24Y] :
( c_24__type__1960___24t(V_24Y)
<=> t(V_24Y,c_24__type__1960) ) ).
fof('$tdef_$_type_15153',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15153___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15153___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22800',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22800___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22800___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8305',axiom,
! [V_24Y] :
( c_24__type__8305___24t(V_24Y)
<=> t(V_24Y,c_24__type__8305) ) ).
fof('$tdef_$_type_75300',axiom,
! [V_24Y] :
( c_24__type__75300___24t(V_24Y)
<=> t(V_24Y,c_24__type__75300) ) ).
fof('$tdef_$_type_60178',axiom,
! [V_24Y] :
( c_24__type__60178___24t(V_24Y)
<=> t(V_24Y,c_24__type__60178) ) ).
fof('$tdef_$_type_31571',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31571___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31571___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_73790',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73790___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73790___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_73721',axiom,
! [V_24Y] :
( c_24__type__73721___24t(V_24Y)
<=> t(V_24Y,c_24__type__73721) ) ).
fof('$tdef_$_type_70883',axiom,
! [V_24Y] :
( c_24__type__70883___24t(V_24Y)
<=> t(V_24Y,c_24__type__70883) ) ).
fof('$tdef_$_type_31403',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31403___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31403___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_73483',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73483___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73483___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21145',axiom,
! [V_24X1,V_24Y] :
( c_24__type__21145___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__21145___24a1(V_24X1)) ) ).
fof('$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_9577',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9577___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9577___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15075',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15075___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15075___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8796',axiom,
! [V_24Y] :
( c_24__type__8796___24t(V_24Y)
<=> t(V_24Y,c_24__type__8796) ) ).
fof('$tdef_$_type_24053',axiom,
! [V_24Y] :
( c_24__type__24053___24t(V_24Y)
<=> t(V_24Y,c_24__type__24053) ) ).
fof('$tdef_$_type_1180',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1180___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1180___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73188',axiom,
! [V_24Y] :
( c_24__type__73188___24t(V_24Y)
<=> t(V_24Y,c_24__type__73188) ) ).
fof('$tdef_$_type_12512',axiom,
! [V_24Y] :
( c_24__type__12512___24t(V_24Y)
<=> t(V_24Y,c_24__type__12512) ) ).
fof('$tdef_$_type_76843',axiom,
! [V_24Y] :
( c_24__type__76843___24t(V_24Y)
<=> t(V_24Y,c_24__type__76843) ) ).
fof('$tdef_$_type_22572',axiom,
! [V_24Y] :
( c_24__type__22572___24t(V_24Y)
<=> t(V_24Y,c_24__type__22572) ) ).
fof('$tdef_$_type_8',axiom,
! [V_24Y] :
( c_24__type__8___24t(V_24Y)
<=> t(V_24Y,c_24__type__8) ) ).
fof('$tdef_$_type_33851',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__33851___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__33851___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_30426',axiom,
! [V_24Y] :
( c_24__type__30426___24t(V_24Y)
<=> t(V_24Y,c_24__type__30426) ) ).
fof('$tdef_$_type_24149',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24149___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_73833',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73833___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73833___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15099',axiom,
! [V_24Y] :
( c_24__type__15099___24t(V_24Y)
<=> t(V_24Y,c_24__type__15099) ) ).
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_$_type_70859',axiom,
! [V_24Y] :
( c_24__type__70859___24t(V_24Y)
<=> t(V_24Y,c_24__type__70859) ) ).
fof('$tdef_$_type_1044',axiom,
! [V_24Y] :
( c_24__type__1044___24t(V_24Y)
<=> t(V_24Y,c_24__type__1044) ) ).
fof('$tdef_$_type_9614',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__9614___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__9614___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_21576',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21576___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21576___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73456',axiom,
! [V_24Y] :
( c_24__type__73456___24t(V_24Y)
<=> t(V_24Y,c_24__type__73456) ) ).
fof('$tdef_$_type_39568',axiom,
! [V_24Y] :
( c_24__type__39568___24t(V_24Y)
<=> t(V_24Y,c_24__type__39568) ) ).
fof('$tdef_$_type_15146',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__15146___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__15146___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_24047',axiom,
! [V_24Y] :
( c_24__type__24047___24t(V_24Y)
<=> t(V_24Y,c_24__type__24047) ) ).
fof('$tdef_$_type_1280',axiom,
! [V_24Y] :
( c_24__type__1280___24t(V_24Y)
<=> t(V_24Y,c_24__type__1280) ) ).
fof('$tdef_$_type_73851',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73851___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73851___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_75315',axiom,
! [V_24Y] :
( c_24__type__75315___24t(V_24Y)
<=> t(V_24Y,c_24__type__75315) ) ).
fof('$tdef_$_type_28963',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__28963___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__28963___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_34392',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34392___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34392___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_59900',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__59900___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__59900___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2297',axiom,
! [V_24Y] :
( c_24__type__2297___24t(V_24Y)
<=> t(V_24Y,c_24__type__2297) ) ).
fof('$tdef_$_type_74668',axiom,
! [V_24Y] :
( c_24__type__74668___24t(V_24Y)
<=> t(V_24Y,c_24__type__74668) ) ).
fof('$tdef_$_type_19937',axiom,
! [V_24X1,V_24Y] :
( c_24__type__19937___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__19937___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73477',axiom,
! [V_24Y] :
( c_24__type__73477___24t(V_24Y)
<=> t(V_24Y,c_24__type__73477) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_34560',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34560___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34560___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8216',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8216___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8216___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34752',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34752___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34752___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_73438',axiom,
! [V_24Y] :
( c_24__type__73438___24t(V_24Y)
<=> t(V_24Y,c_24__type__73438) ) ).
fof('$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_19829',axiom,
! [V_24X1,V_24Y] :
( c_24__type__19829___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__19829___24a1(V_24X1)) ) ).
fof('$tdef_$_type_75905',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75905___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75905___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73359',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73359___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73359___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1940',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1940___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1940___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9456',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9456___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9456___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_15170',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15170___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15170___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_75054',axiom,
! [V_24Y] :
( c_24__type__75054___24t(V_24Y)
<=> t(V_24Y,c_24__type__75054) ) ).
fof('$tdef_$_type_1100',axiom,
! [V_24Y] :
( c_24__type__1100___24t(V_24Y)
<=> t(V_24Y,c_24__type__1100) ) ).
fof('$tdef_$_type_31131',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31131___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31131___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__30803___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__30803___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_19980',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__19980___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__19980___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_356',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__356___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__356___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_20294',axiom,
! [V_24Y] :
( c_24__type__20294___24t(V_24Y)
<=> t(V_24Y,c_24__type__20294) ) ).
fof('$tdef_$_type_73418',axiom,
! [V_24Y] :
( c_24__type__73418___24t(V_24Y)
<=> t(V_24Y,c_24__type__73418) ) ).
fof('$tdef_$_type_22505',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22505___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22505___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20147',axiom,
! [V_24Y] :
( c_24__type__20147___24t(V_24Y)
<=> t(V_24Y,c_24__type__20147) ) ).
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_$_type_34292',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34292___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34292___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_59497',axiom,
! [V_24Y] :
( c_24__type__59497___24t(V_24Y)
<=> t(V_24Y,c_24__type__59497) ) ).
fof('$tdef_$_type_38321',axiom,
! [V_24Y] :
( c_24__type__38321___24t(V_24Y)
<=> t(V_24Y,c_24__type__38321) ) ).
fof('$tdef_$_type_31463',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31463___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31463___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_73054',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73054___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73054___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24247',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24247___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24247___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_76096',axiom,
! [V_24Y] :
( c_24__type__76096___24t(V_24Y)
<=> t(V_24Y,c_24__type__76096) ) ).
fof('$tdef_$_type_23844',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23844___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23844___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1047',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1047___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1047___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20259',axiom,
! [V_24Y] :
( c_24__type__20259___24t(V_24Y)
<=> t(V_24Y,c_24__type__20259) ) ).
fof('$tdef_$_type_35706',axiom,
! [V_24Y] :
( c_24__type__35706___24t(V_24Y)
<=> t(V_24Y,c_24__type__35706) ) ).
fof('$tdef_$_type_29955',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__29955___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__29955___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_635',axiom,
! [V_24Y] :
( c_24__type__635___24t(V_24Y)
<=> t(V_24Y,c_24__type__635) ) ).
fof('$tdef_$_type_21142',axiom,
! [V_24Y] :
( c_24__type__21142___24t(V_24Y)
<=> t(V_24Y,c_24__type__21142) ) ).
fof('$tdef_$_type_56805',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56805___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56805___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35744',axiom,
! [V_24Y] :
( c_24__type__35744___24t(V_24Y)
<=> t(V_24Y,c_24__type__35744) ) ).
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_$_type_7286',axiom,
! [V_24Y] :
( c_24__type__7286___24t(V_24Y)
<=> t(V_24Y,c_24__type__7286) ) ).
fof('$tdef_$_type_9317',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__9317___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__9317___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2181',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2181___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2181___24a1(V_24X1)) ) ).
fof('$tdef_$_type_74860',axiom,
! [V_24Y] :
( c_24__type__74860___24t(V_24Y)
<=> t(V_24Y,c_24__type__74860) ) ).
fof('$tdef_$_type_73347',axiom,
! [V_24Y] :
( c_24__type__73347___24t(V_24Y)
<=> t(V_24Y,c_24__type__73347) ) ).
fof('$tdef_$_type_1921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1921___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22765',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__22765___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__22765___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7341',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7341___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7341___24a1(V_24X1)) ) ).
fof('$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_2314',axiom,
! [V_24Y] :
( c_24__type__2314___24t(V_24Y)
<=> t(V_24Y,c_24__type__2314) ) ).
fof('$tdef_$_type_30857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__30857___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__30857___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_37427',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__37427___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__37427___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22590',axiom,
! [V_24Y] :
( c_24__type__22590___24t(V_24Y)
<=> t(V_24Y,c_24__type__22590) ) ).
fof('$tdef_$_type_75477',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__75477___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__75477___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38884',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38884___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38884___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19781',axiom,
! [V_24Y] :
( c_24__type__19781___24t(V_24Y)
<=> t(V_24Y,c_24__type__19781) ) ).
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_$_type_399',axiom,
! [V_24Y] :
( c_24__type__399___24t(V_24Y)
<=> t(V_24Y,c_24__type__399) ) ).
fof('$tdef_$_type_7890',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7890___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7890___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_417',axiom,
! [V_24Y] :
( c_24__type__417___24t(V_24Y)
<=> t(V_24Y,c_24__type__417) ) ).
fof('$tdef_$_type_10686',axiom,
! [V_24Y] :
( c_24__type__10686___24t(V_24Y)
<=> t(V_24Y,c_24__type__10686) ) ).
fof('$tdef_$_type_9571',axiom,
! [V_24Y] :
( c_24__type__9571___24t(V_24Y)
<=> t(V_24Y,c_24__type__9571) ) ).
fof('$tdef_$_type_73828',axiom,
! [V_24Y] :
( c_24__type__73828___24t(V_24Y)
<=> t(V_24Y,c_24__type__73828) ) ).
fof('$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_73396',axiom,
! [V_24Y] :
( c_24__type__73396___24t(V_24Y)
<=> t(V_24Y,c_24__type__73396) ) ).
fof('$tdef_$_type_31221',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31221___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31221___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1254',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1254___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1254___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34434',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34434___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34434___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30740',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__30740___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__30740___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2215',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2215___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2215___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_75815',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__75815___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__75815___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_76814',axiom,
! [V_24Y] :
( c_24__type__76814___24t(V_24Y)
<=> t(V_24Y,c_24__type__76814) ) ).
fof('$tdef_$_type_73388',axiom,
! [V_24Y] :
( c_24__type__73388___24t(V_24Y)
<=> t(V_24Y,c_24__type__73388) ) ).
fof('$tdef_$_type_21669',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__21669___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__21669___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35016',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35016___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35016___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_2178',axiom,
! [V_24Y] :
( c_24__type__2178___24t(V_24Y)
<=> t(V_24Y,c_24__type__2178) ) ).
fof('$tdef_$_type_15203',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15203___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15203___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1',axiom,
! [V_24Y] :
( c_24__type__1___24t(V_24Y)
<=> t(V_24Y,c_24__type__1) ) ).
fof('$tdef_$_type_77134',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__77134___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__77134___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34046',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__34046___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__34046___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1206',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1206___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1206___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_35071',axiom,
! [V_24Y] :
( c_24__type__35071___24t(V_24Y)
<=> t(V_24Y,c_24__type__35071) ) ).
fof('$tdef_$_type_10689',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10689___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10689___24a1(V_24X1)) ) ).
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_$_type_32396',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__32396___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__32396___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_29609',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__29609___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__29609___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32591',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__32591___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__32591___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.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_7910',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7910___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7910___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15181',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__15181___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__15181___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7846',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__7846___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__7846___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34796',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34796___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34796___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_22694',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22694___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22694___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_384',axiom,
! [V_24Y] :
( c_24__type__384___24t(V_24Y)
<=> t(V_24Y,c_24__type__384) ) ).
fof('$tdef_$_type_38054',axiom,
! [V_24Y] :
( c_24__type__38054___24t(V_24Y)
<=> t(V_24Y,c_24__type__38054) ) ).
fof('$tdef_$_type_3134',axiom,
! [V_24Y] :
( c_24__type__3134___24t(V_24Y)
<=> t(V_24Y,c_24__type__3134) ) ).
fof('$tdef_$_type_7961',axiom,
! [V_24Y] :
( c_24__type__7961___24t(V_24Y)
<=> t(V_24Y,c_24__type__7961) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_21088',axiom,
! [V_24Y] :
( c_24__type__21088___24t(V_24Y)
<=> t(V_24Y,c_24__type__21088) ) ).
fof('$tdef_$_type_23350',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23350___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23350___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_22468',axiom,
! [V_24Y] :
( c_24__type__22468___24t(V_24Y)
<=> t(V_24Y,c_24__type__22468) ) ).
fof('$tdef_$_type_8542',axiom,
! [V_24Y] :
( c_24__type__8542___24t(V_24Y)
<=> t(V_24Y,c_24__type__8542) ) ).
fof('$tdef_$_type_8254',axiom,
! [V_24Y] :
( c_24__type__8254___24t(V_24Y)
<=> t(V_24Y,c_24__type__8254) ) ).
fof('$tdef_$_type_22019',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__22019___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__22019___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23541',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__23541___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__23541___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7825',axiom,
! [V_24Y] :
( c_24__type__7825___24t(V_24Y)
<=> t(V_24Y,c_24__type__7825) ) ).
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_$_type_34484',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__34484___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__34484___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_59870',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__59870___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__59870___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_$_type_74680',axiom,
! [V_24Y] :
( c_24__type__74680___24t(V_24Y)
<=> t(V_24Y,c_24__type__74680) ) ).
fof('$tdef_$_type_35683',axiom,
! [V_24Y] :
( c_24__type__35683___24t(V_24Y)
<=> t(V_24Y,c_24__type__35683) ) ).
fof('$tdef_$_type_34851',axiom,
! [V_24Y] :
( c_24__type__34851___24t(V_24Y)
<=> t(V_24Y,c_24__type__34851) ) ).
fof('$tdef_$_type_7769',axiom,
! [V_24Y] :
( c_24__type__7769___24t(V_24Y)
<=> t(V_24Y,c_24__type__7769) ) ).
fof('$tdef_$_type_23743',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23743___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23743___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73048',axiom,
! [V_24Y] :
( c_24__type__73048___24t(V_24Y)
<=> t(V_24Y,c_24__type__73048) ) ).
fof('$tdef_$_type_70602',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__70602___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__70602___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_70785',axiom,
! [V_24Y] :
( c_24__type__70785___24t(V_24Y)
<=> t(V_24Y,c_24__type__70785) ) ).
fof('$tdef_$_type_8007',axiom,
! [V_24Y] :
( c_24__type__8007___24t(V_24Y)
<=> t(V_24Y,c_24__type__8007) ) ).
fof('$tdef_$_type_35815',axiom,
! [V_24Y] :
( c_24__type__35815___24t(V_24Y)
<=> t(V_24Y,c_24__type__35815) ) ).
fof('$tdef_$_type_271',axiom,
! [V_24X1,V_24Y] :
( c_24__type__271___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__271___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22621',axiom,
! [V_24Y] :
( c_24__type__22621___24t(V_24Y)
<=> t(V_24Y,c_24__type__22621) ) ).
fof('$tdef_$_type_1355',axiom,
! [V_24Y] :
( c_24__type__1355___24t(V_24Y)
<=> t(V_24Y,c_24__type__1355) ) ).
fof('$tdef_$_type_7267',axiom,
! [V_24Y] :
( c_24__type__7267___24t(V_24Y)
<=> t(V_24Y,c_24__type__7267) ) ).
fof('$tdef_$_type_15187',axiom,
! [V_24Y] :
( c_24__type__15187___24t(V_24Y)
<=> t(V_24Y,c_24__type__15187) ) ).
fof('$tdef_$_type_33638',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__33638___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__33638___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_8191',axiom,
! [V_24Y] :
( c_24__type__8191___24t(V_24Y)
<=> t(V_24Y,c_24__type__8191) ) ).
fof('$tdef_$_type_75625',axiom,
! [V_24Y] :
( c_24__type__75625___24t(V_24Y)
<=> t(V_24Y,c_24__type__75625) ) ).
fof('$tdef_$_type_20962',axiom,
! [V_24Y] :
( c_24__type__20962___24t(V_24Y)
<=> t(V_24Y,c_24__type__20962) ) ).
fof('$tdef_$_type_77116',axiom,
! [V_24Y] :
( c_24__type__77116___24t(V_24Y)
<=> t(V_24Y,c_24__type__77116) ) ).
fof('$tdef_$_type_31520',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31520___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31520___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_83',axiom,
! [V_24Y] :
( c_24__type__83___24t(V_24Y)
<=> t(V_24Y,c_24__type__83) ) ).
fof('$tdef_$_type_30373',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30373___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30373___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7296',axiom,
! [V_24Y] :
( c_24__type__7296___24t(V_24Y)
<=> t(V_24Y,c_24__type__7296) ) ).
fof('$tdef_$_type_74877',axiom,
! [V_24Y] :
( c_24__type__74877___24t(V_24Y)
<=> t(V_24Y,c_24__type__74877) ) ).
fof('$tdef_$_type_684',axiom,
! [V_24Y] :
( c_24__type__684___24t(V_24Y)
<=> t(V_24Y,c_24__type__684) ) ).
fof('$tdef_$_type_30920',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__30920___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__30920___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_35196',axiom,
! [V_24Y] :
( c_24__type__35196___24t(V_24Y)
<=> t(V_24Y,c_24__type__35196) ) ).
fof('$tdef_$_type_30382',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30382___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30382___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_70790',axiom,
! [V_24X1,V_24Y] :
( c_24__type__70790___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__70790___24a1(V_24X1)) ) ).
fof('$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_694',axiom,
! [V_24Y] :
( c_24__type__694___24t(V_24Y)
<=> t(V_24Y,c_24__type__694) ) ).
fof('$tdef_$_type_73322',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__73322___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__73322___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_716',axiom,
! [V_24X1,V_24Y] :
( c_24__type__716___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__716___24a1(V_24X1)) ) ).
fof('$tdef_$_type_59567',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__59567___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__59567___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_76797',axiom,
! [V_24Y] :
( c_24__type__76797___24t(V_24Y)
<=> t(V_24Y,c_24__type__76797) ) ).
fof('$tdef_$_type_70796',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__70796___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__70796___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_654',axiom,
! [V_24Y] :
( c_24__type__654___24t(V_24Y)
<=> t(V_24Y,c_24__type__654) ) ).
fof('$tdef_$_type_74078',axiom,
! [V_24Y] :
( c_24__type__74078___24t(V_24Y)
<=> t(V_24Y,c_24__type__74078) ) ).
fof('$tdef_$_type_73458',axiom,
! [V_24Y] :
( c_24__type__73458___24t(V_24Y)
<=> t(V_24Y,c_24__type__73458) ) ).
fof('$tdef_$_type_25895',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__25895___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__25895___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_73996',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73996___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73996___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1274',axiom,
! [V_24Y] :
( c_24__type__1274___24t(V_24Y)
<=> t(V_24Y,c_24__type__1274) ) ).
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_$_type_301',axiom,
! [V_24Y] :
( c_24__type__301___24t(V_24Y)
<=> t(V_24Y,c_24__type__301) ) ).
fof('$tdef_$_type_74915',axiom,
! [V_24Y] :
( c_24__type__74915___24t(V_24Y)
<=> t(V_24Y,c_24__type__74915) ) ).
fof('$tdef_$_type_38293',axiom,
! [V_24Y] :
( c_24__type__38293___24t(V_24Y)
<=> t(V_24Y,c_24__type__38293) ) ).
fof('$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_2234',axiom,
! [V_24Y] :
( c_24__type__2234___24t(V_24Y)
<=> t(V_24Y,c_24__type__2234) ) ).
fof('$tdef_$_type_35051',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35051___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35051___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32183',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__32183___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__32183___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_1846',axiom,
! [V_24Y] :
( c_24__type__1846___24t(V_24Y)
<=> t(V_24Y,c_24__type__1846) ) ).
fof('$tdef_$_type_4273',axiom,
! [V_24Y] :
( c_24__type__4273___24t(V_24Y)
<=> t(V_24Y,c_24__type__4273) ) ).
fof('$tdef_$_type_22803',axiom,
! [V_24Y] :
( c_24__type__22803___24t(V_24Y)
<=> t(V_24Y,c_24__type__22803) ) ).
fof('$tdef_$_type_70412',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__70412___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__70412___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39011',axiom,
! [V_24Y] :
( c_24__type__39011___24t(V_24Y)
<=> t(V_24Y,c_24__type__39011) ) ).
fof('$tdef_$_type_34133',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34133___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34133___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_28271',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__28271___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__28271___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_18558',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18558___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18558___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.funind.Recdef.max_type',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2efunind_2eRecdef_2emax__type___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2efunind_2eRecdef_2emax__type___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_50008',axiom,
! [V_24Y] :
( c_24__type__50008___24t(V_24Y)
<=> t(V_24Y,c_24__type__50008) ) ).
fof('$tdef_$_type_85',axiom,
! [V_24Y] :
( c_24__type__85___24t(V_24Y)
<=> t(V_24Y,c_24__type__85) ) ).
fof('$tdef_$_type_31177',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31177___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31177___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1017',axiom,
! [V_24Y] :
( c_24__type__1017___24t(V_24Y)
<=> t(V_24Y,c_24__type__1017) ) ).
fof('$tdef_$_type_74645',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__74645___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__74645___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7711',axiom,
! [V_24Y] :
( c_24__type__7711___24t(V_24Y)
<=> t(V_24Y,c_24__type__7711) ) ).
fof('$tdef_$_type_35658',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35658___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35658___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7324',axiom,
! [V_24Y] :
( c_24__type__7324___24t(V_24Y)
<=> t(V_24Y,c_24__type__7324) ) ).
fof('$tdef_$_type_20070',axiom,
! [V_24Y] :
( c_24__type__20070___24t(V_24Y)
<=> t(V_24Y,c_24__type__20070) ) ).
fof('$tdef_$_type_21844',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__21844___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__21844___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$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_15081',axiom,
! [V_24Y] :
( c_24__type__15081___24t(V_24Y)
<=> t(V_24Y,c_24__type__15081) ) ).
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_$_type_73062',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73062___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73062___24a1(V_24X1)) ) ).
fof('$tdef_$_type_20386',axiom,
! [V_24Y] :
( c_24__type__20386___24t(V_24Y)
<=> t(V_24Y,c_24__type__20386) ) ).
fof('$tdef_$_type_30400',axiom,
! [V_24Y] :
( c_24__type__30400___24t(V_24Y)
<=> t(V_24Y,c_24__type__30400) ) ).
fof('$tdef_$_type_71654',axiom,
! [V_24Y] :
( c_24__type__71654___24t(V_24Y)
<=> t(V_24Y,c_24__type__71654) ) ).
fof('$tdef_$_type_640',axiom,
! [V_24Y] :
( c_24__type__640___24t(V_24Y)
<=> t(V_24Y,c_24__type__640) ) ).
fof('$tdef_$_type_7077',axiom,
! [V_24Y] :
( c_24__type__7077___24t(V_24Y)
<=> t(V_24Y,c_24__type__7077) ) ).
fof('$tdef_$_type_30132',axiom,
! [V_24Y] :
( c_24__type__30132___24t(V_24Y)
<=> t(V_24Y,c_24__type__30132) ) ).
fof('$tdef_$_type_1111',axiom,
! [V_24Y] :
( c_24__type__1111___24t(V_24Y)
<=> t(V_24Y,c_24__type__1111) ) ).
fof('$tdef_$_type_1052',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1052___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1052___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_73488',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73488___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73488___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3148',axiom,
! [V_24Y] :
( c_24__type__3148___24t(V_24Y)
<=> t(V_24Y,c_24__type__3148) ) ).
fof('$tdef_QuicksortComplexity.arith_lems.R_floor_log2_S',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1020',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1020___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1020___24a1(V_24X1)) ) ).
fof('$tdef_$_type_73371',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__73371___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__73371___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_453',axiom,
! [V_24Y] :
( c_24__type__453___24t(V_24Y)
<=> t(V_24Y,c_24__type__453) ) ).
fof('$tdef_$_type_28617',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__28617___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__28617___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('$tdef_indices.contents.Index',axiom,
! [V_24Y] :
( cindices_2econtents_2eIndex___24t(V_24Y)
<=> t(V_24Y,cindices_2econtents_2eIndex) ) ).
fof('$tdef_$_type_73137',axiom,
! [V_24Y] :
( c_24__type__73137___24t(V_24Y)
<=> t(V_24Y,c_24__type__73137) ) ).
fof('$tdef_$_type_50013',axiom,
! [V_24Y] :
( c_24__type__50013___24t(V_24Y)
<=> t(V_24Y,c_24__type__50013) ) ).
fof('$tdef_$_type_73744',axiom,
! [V_24Y] :
( c_24__type__73744___24t(V_24Y)
<=> t(V_24Y,c_24__type__73744) ) ).
fof('$tdef_$_type_73929',axiom,
! [V_24X1,V_24Y] :
( c_24__type__73929___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__73929___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9467',axiom,
! [V_24Y] :
( c_24__type__9467___24t(V_24Y)
<=> t(V_24Y,c_24__type__9467) ) ).
fof('$tdef_$_type_19971',axiom,
! [V_24Y] :
( c_24__type__19971___24t(V_24Y)
<=> t(V_24Y,c_24__type__19971) ) ).
fof('$tdef_$_type_77157',axiom,
! [V_24Y] :
( c_24__type__77157___24t(V_24Y)
<=> t(V_24Y,c_24__type__77157) ) ).
fof('$tdef_$_type_73399',axiom,
! [V_24Y] :
( c_24__type__73399___24t(V_24Y)
<=> t(V_24Y,c_24__type__73399) ) ).
fof('$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('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3112',axiom,
! [V_24Y] :
( c_24__type__3112___24t(V_24Y)
<=> t(V_24Y,c_24__type__3112) ) ).
fof('$tdef_$_type_76794',axiom,
! [V_24X1,V_24Y] :
( c_24__type__76794___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__76794___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8237',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8237___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8237___24a1(V_24X1)) ) ).
fof('$tdef_$_type_72983',axiom,
! [V_24Y] :
( c_24__type__72983___24t(V_24Y)
<=> t(V_24Y,c_24__type__72983) ) ).
fof('$tdef_$_type_31108',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31108___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31108___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_442',axiom,
! [V_24Y] :
( c_24__type__442___24t(V_24Y)
<=> t(V_24Y,c_24__type__442) ) ).
fof('$tdef_$_type_1242',axiom,
! [V_24Y] :
( c_24__type__1242___24t(V_24Y)
<=> t(V_24Y,c_24__type__1242) ) ).
fof('$tdef_$_type_50051',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__50051___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__50051___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22650',axiom,
! [V_24Y] :
( c_24__type__22650___24t(V_24Y)
<=> t(V_24Y,c_24__type__22650) ) ).
fof('$tdef_$_type_21359',axiom,
! [V_24Y] :
( c_24__type__21359___24t(V_24Y)
<=> t(V_24Y,c_24__type__21359) ) ).
fof('$tdef_$_type_33443',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__33443___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__33443___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_30145',axiom,
! [V_24Y] :
( c_24__type__30145___24t(V_24Y)
<=> t(V_24Y,c_24__type__30145) ) ).
fof('$tdef_$_type_20400',axiom,
! [V_24Y] :
( c_24__type__20400___24t(V_24Y)
<=> t(V_24Y,c_24__type__20400) ) ).
fof('$tdef_$_type_60022',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__60022___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__60022___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_26564',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26564___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26564___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_73404',axiom,
! [V_24Y] :
( c_24__type__73404___24t(V_24Y)
<=> t(V_24Y,c_24__type__73404) ) ).
fof('$tdef_$_type_23249',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23249___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23249___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_73023',axiom,
! [V_24Y] :
( c_24__type__73023___24t(V_24Y)
<=> t(V_24Y,c_24__type__73023) ) ).
fof('$tdef_QuicksortComplexity.sort_order.E',axiom,
! [V_24Y] :
( cQuicksortComplexity_2esort__order_2eE___24t(V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2esort__order_2eE) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_38898',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38898___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38898___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2690',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2690___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2690___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__31154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__31154___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_75031',axiom,
! [V_24Y] :
( c_24__type__75031___24t(V_24Y)
<=> t(V_24Y,c_24__type__75031) ) ).
fof('$tdef_$_type_8531',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8531___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8531___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2274',axiom,
! [V_24Y] :
( c_24__type__2274___24t(V_24Y)
<=> t(V_24Y,c_24__type__2274) ) ).
fof('$tdef_$_type_2157',axiom,
! [V_24Y] :
( c_24__type__2157___24t(V_24Y)
<=> t(V_24Y,c_24__type__2157) ) ).
fof('$tdef_$_type_77018',axiom,
! [V_24Y] :
( c_24__type__77018___24t(V_24Y)
<=> t(V_24Y,c_24__type__77018) ) ).
fof('$tdef_$_type_78',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__78___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__78___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31349',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31349___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31349___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_25549',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__25549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__25549___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_37460',axiom,
! [V_24Y] :
( c_24__type__37460___24t(V_24Y)
<=> t(V_24Y,c_24__type__37460) ) ).
fof('$tdef_$_type_35741',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35741___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35741___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22521',axiom,
! [V_24Y] :
( c_24__type__22521___24t(V_24Y)
<=> t(V_24Y,c_24__type__22521) ) ).
fof('$tdef_$_type_74091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__74091___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__74091___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_49369',axiom,
! [V_24Y] :
( c_24__type__49369___24t(V_24Y)
<=> t(V_24Y,c_24__type__49369) ) ).
fof('$tdef_$_type_74411',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__74411___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__74411___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__31544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__31544___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_1271',axiom,
! [V_24Y] :
( c_24__type__1271___24t(V_24Y)
<=> t(V_24Y,c_24__type__1271) ) ).
fof('$tdef_$_type_62438',axiom,
! [V_24Y] :
( c_24__type__62438___24t(V_24Y)
<=> t(V_24Y,c_24__type__62438) ) ).
fof('$tdef_$_type_75639',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__75639___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__75639___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24041',axiom,
! [V_24Y] :
( c_24__type__24041___24t(V_24Y)
<=> t(V_24Y,c_24__type__24041) ) ).
fof('$tdef_$_type_7883',axiom,
! [V_24Y] :
( c_24__type__7883___24t(V_24Y)
<=> t(V_24Y,c_24__type__7883) ) ).
fof('$tdef_$_type_24097',axiom,
! [V_24Y] :
( c_24__type__24097___24t(V_24Y)
<=> t(V_24Y,c_24__type__24097) ) ).
fof('$tdef_$_type_7791',axiom,
! [V_24Y] :
( c_24__type__7791___24t(V_24Y)
<=> t(V_24Y,c_24__type__7791) ) ).
fof('_HAMMER_GOAL',conjecture,
( cindices_2econtents_2eIndexSeq___24a2(cb,cQuicksortComplexity_2evec_2eto__list___24a3(cindices_2econtents_2eIndex,cn,cv))
=> cQuicksortComplexity_2evec_2ePermutation___24a4(cCoq_2eInit_2eDatatypes_2enat,cn,cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col)),cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2enat__below_2enb__val___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cQuicksortComplexity_2esort__order_2eEc___24a1(cT),col)),cn,cv),cQuicksortComplexity_2evec_2enb__nats___24a2(cb,cn)) ) ).
%------------------------------------------------------------------------------