TPTP Problem File: SEV666+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEV666+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - qs worst bind eqq
% Version : [Kal26] axioms : Especial.
% English :
% Refs : [CK18] Czajka L. & Kaliszyk (2018), Hammer for Coq: Automatio
% : [Kal26] Kalizyk (2026), Email to G. Sutcliffe
% Source : [Kal26]
% Names : qs.worst.bind.eqq.p [Kal26]
% Status : ContradictoryAxioms
% Rating : 0.83 v9.3.0
% Syntax : Number of formulae : 3536 (1482 unt; 0 def)
% Number of atoms : 11081 (3491 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7724 ( 179 ~; 700 |;1601 &)
% (1276 <=>;3968 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 670 ( 669 usr; 0 prp; 1-23 aty)
% Number of functors : 2208 (2208 usr;1285 con; 0-22 aty)
% Number of variables : 12069 (11454 !; 615 ?)
% SPC : FOF_CAX_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$2139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242139___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__1959___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__1105___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4))) )
| ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242139___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__1959___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__lam__1105___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$2693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242693___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) )
| ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_242693___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.bool$7955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2etrue
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_247955___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) )
| ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2efalse
& c_24__case__Coq_2eInit_2eDatatypes_2ebool_247955___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.comparison$186717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__3)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__4)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eEq
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__0) ) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eLt
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__1) ) )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eGt
& ( c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(Vv__CANONICAL__2) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$185329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24185329___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__2,Vv__CANONICAL__5) )
| ? [Vvar__1___24Anonymous__185333] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__185333)
& ? [Vvar__2___24Anonymous__185334] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__185334)
& Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__185333,Vvar__2___24Anonymous__185334)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_24185329___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__185333,c_24__fix__185366__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__185334,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$5837',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_245837___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__lam__5885___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) )
| ? [Vvar__1___24Anonymous__5841] :
( t(Vvar__1___24Anonymous__5841,Vv__CANONICAL__1)
& ? [Vvar__2___24Anonymous__5842] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__5842)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__5841,Vvar__2___24Anonymous__5842)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_245837___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__lam__6074___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1___24Anonymous__5841,Vvar__2___24Anonymous__5842) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$7499',axiom,
! [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_247606___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_247499___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__7505] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7505)
& ? [Vvar__2___24Anonymous__7506] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__7506)
& Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__7505,Vvar__2___24Anonymous__7506)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_247499___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__7505),c_24__fix__7645__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vvar__2___24Anonymous__7506)) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7521] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7521)
& ? [Vvar__2___24Anonymous__7522] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__7522)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_247606___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__7521,Vvar__2___24Anonymous__7522)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_247499___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__7521,c_24__fix__7742__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__7522,c_24__case__Coq_2eInit_2eDatatypes_2elist_247606___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__7))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$7606',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__case__Coq_2eInit_2eDatatypes_2elist_247606___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__7610] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7610)
& ? [Vvar__2___24Anonymous__7611] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__7611)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__7610,Vvar__2___24Anonymous__7611)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_247606___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1___24Anonymous__7610),c_24__fix__7645__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__7611)) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$11029',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__11030] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11030)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11030)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2411029___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__11048__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__11030,Vv__CANONICAL__2)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$186248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186248___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__186249] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__186249)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__186249)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186248___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__186249)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$186270',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__186271] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__186271)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__186271)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__186271)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$71114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__71127___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__71119] :
( t(Vvar__2___24Anonymous__71119,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__71120] :
( t(Vvar__3___24Anonymous__71120,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__71119,Vvar__3___24Anonymous__71120)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2471114___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__71119)),Vvar__3___24Anonymous__71120)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$186265',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__186266] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186266)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__186266)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__186266) )
| ? [Vvar__0___24Anonymous__186267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186267)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__186267)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__186267) ) ) ) ).
fof('$_def_$_cast_41937',axiom,
! [V0__monoid,V1__monad,V3__X,V4__V,V5__f] : c_24__cast__41937___24a5(V0__monoid,V1__monad,V3__X,V4__V,V5__f) = V5__f ).
fof('$_def_$_cast_41954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__cast__41954___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_def_$_cast_41965',axiom,
! [V0__monoid,V1__monad,V3__X,V4__V,V5__f] : c_24__cast__41965___24a5(V0__monoid,V1__monad,V3__X,V4__V,V5__f) = V5__f ).
fof('$_def_$_cast_41982',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__cast__41982___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_def_$_let_3_C_MMT_4200',axiom,
! [V0__monoid,V1__monad,V3__T] : c_24__let__3__C__MMT__4200___24a3(V0__monoid,V1__monad,V3__T) = cQuicksortComplexity_2emonads_2emon___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__T)) ).
fof('$_def_$_let_3_C_MMT_42047',axiom,
! [V0__monoid,V1__monad,V3__T] : c_24__let__3__C__MMT__42047___24a3(V0__monoid,V1__monad,V3__T) = cQuicksortComplexity_2emonads_2emon___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__T)) ).
fof('$_def_$_let_4_bind_MMT_4201',axiom,
! [V0__monoid,V1__monad,V4__A,V5__B,V6__a,V7__ab] : c_24__let__4__bind__MMT__4201___24a6(V0__monoid,V1__monad,V4__A,V5__B,V6__a,V7__ab) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V4__A),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__B),V6__a,c_24__lam__5538___24a5(V0__monoid,V1__monad,V4__A,V5__B,V7__ab)) ).
fof('$_def_$_let_4_bind_MMT_42048',axiom,
! [V0__monoid,V1__monad,V4__A,V5__B,V6__a,V7__ab] : c_24__let__4__bind__MMT__42048___24a6(V0__monoid,V1__monad,V4__A,V5__B,V6__a,V7__ab) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V4__A),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__B),V6__a,c_24__lam__42071___24a5(V0__monoid,V1__monad,V4__A,V5__B,V7__ab)) ).
fof('$_def_$_let_5_ret_MMT_4202',axiom,
! [V0__monoid,V1__monad,V5__T] : c_24__let__5__ret__MMT__4202___24a3(V0__monoid,V1__monad,V5__T) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V5__T,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T),cQuicksortComplexity_2emonads_2emon___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T)),cQuicksortComplexity_2emonads_2eret___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T)),cCoq_2eInit_2eDatatypes_2epair___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__monoid))) ).
fof('$_def_$_let_5_ret_MMT_42049',axiom,
! [V0__monoid,V1__monad,V5__T] : c_24__let__5__ret__MMT__42049___24a3(V0__monoid,V1__monad,V5__T) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V5__T,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T),cQuicksortComplexity_2emonads_2emon___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T)),cQuicksortComplexity_2emonads_2eret___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T)),cCoq_2eInit_2eDatatypes_2epair___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V5__T,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__monoid))) ).
fof('$_def_$_let_v_CANONICAL_2_2201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__let__v__CANONICAL__2__2201___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_def_$_let_v_CANONICAL_3_11576',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2] : c_24__let__v__CANONICAL__3__11576___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_def_$_let_v_CANONICAL_3_2259',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__let__v__CANONICAL__3__2259___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_def_$_let_v_CANONICAL_5_11789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3] : c_24__let__v__CANONICAL__5__11789___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_def_$_let_v_CANONICAL_5_2482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3] : c_24__let__v__CANONICAL__5__2482___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).
fof('$_def_$_let_var_6_p_69423_69426',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69422] : c_24__let__var__6__p__69423__69426___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69422) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69422) ).
fof('$_def_$_let_var_6_p_69425_69427',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69424] : c_24__let__var__6__p__69425__69427___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69424) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69424) ).
fof('$_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__185933] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__185933)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__185933)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__185934] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__185934)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__185934)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__185937] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__185937)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__185937)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__185934,Vvar__0___24Anonymous__185937) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b))) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__44323] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44323)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44323)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__42313] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__42313)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__42313) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__42361] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__42361)
& ? [Vvar__1___24Anonymous__42362] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__42362)
& ? [Vvar__2___24Anonymous__42363] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__42363)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__42361,Vvar__1___24Anonymous__42362,Vvar__2___24Anonymous__42363)
& ( ? [Vvar__0___24Anonymous__42376] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42376)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__42376)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__42376,Vvar__2___24Anonymous__42363) )
| ? [Vvar__0___24Anonymous__42377] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42377)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__42377)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__42377,Vvar__0___24Anonymous__42361) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__42362 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__186833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186833)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__186833)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__186833,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__186834] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186834)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__186834)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__186834,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__42339] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__42339)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__42339) ) ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.CompSpecT',axiom,
! [V0__A,V1__eq,V2__lt,V3__x,V4__y] : cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V0__A,V1__eq,V2__lt,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(happ(happ(V1__eq,V3__x),V4__y),happ(happ(V2__lt,V3__x),V4__y),happ(happ(V2__lt,V4__y),V3__x)) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__68] :
( t(Vvar__1___24Anonymous__68,V0__A)
& ? [Vvar__2___24Anonymous__69] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__69)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__68,Vvar__2___24Anonymous__69)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__68,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__69,V3__m)) ) ) ) ) ) ).
fof('$_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__44] :
( t(Vvar__2___24Anonymous__44,V0__A)
& ? [Vvar__3___24Anonymous__45] :
( t(Vvar__3___24Anonymous__45,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__44,Vvar__3___24Anonymous__45)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__44 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__58] :
( t(Vvar__1___24Anonymous__58,V0__A)
& ? [Vvar__2___24Anonymous__59] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__59)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__58,Vvar__2___24Anonymous__59)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__59)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__2513] :
( t(Vvar__2___24Anonymous__2513,V0__A)
& ? [Vvar__3___24Anonymous__2514] :
( t(Vvar__3___24Anonymous__2514,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__2513,Vvar__3___24Anonymous__2514)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__2514 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__77] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__77,V2__m)) ) ) ) ).
fof('$_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__22756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22756)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22756)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__22757] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22757)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22757)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__22760] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22760)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22760)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__22757,Vvar__0___24Anonymous__22760) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__22773] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22773)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22773)
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__22773,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__22773)) ) ) ) ).
fof('$_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__22794] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22794)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22794)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22794)
& ( ( Vvar__0___24Anonymous__22794 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22797] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22797)
& Vvar__0___24Anonymous__22794 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22797)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__22797)) ) ) ) ) ) ) ) ).
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__44121] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44121)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44121)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__44122] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44122)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44122)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__44125] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44125)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44125)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__44122,Vvar__0___24Anonymous__44125) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__44134] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44134)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44134)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44134)
& ( ( Vvar__0___24Anonymous__44134 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__44137] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44137)
& Vvar__0___24Anonymous__44134 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44137)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__44137) ) ) ) ) ) ) ) ).
fof('$_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__22778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22778)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22778)
& 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__22778)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22778)) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__2591] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2591)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2591)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__2594] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2594)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2594)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__2591,Vvar__0___24Anonymous__2594) ) ) ) ) ) ) ) ).
fof('$_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__44128] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44128)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44128)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__44131] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44131)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44131)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__44128,Vvar__0___24Anonymous__44131)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22765] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22765)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22765)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22768)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22768)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__22765,Vvar__0___24Anonymous__22768)) ) ) ) ) ) ) ) ).
fof('$_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__10328] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10328)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10328)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__10328,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__22771] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22771)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22771)
& 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__22771)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__22754] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22754)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22754)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__22754 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__22801,V0__a,c_24__lam__44151) ).
fof('$_def_Coq.Init.Nat.sqrt',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__10331] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10331)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10331)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__10334] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10334)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10334)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__10331,Vvar__0___24Anonymous__10334) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__22799] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22799)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22799)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__22799) ) ) ) ).
fof('$_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('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__136___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__130] :
( t(Vvar__2__x__130,V0__A)
& p(happ(V1__P,Vvar__2__x__130))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__130)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__130 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__25627___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__25621] :
( t(Vvar__2__x__25621,V0__A)
& ? [Vvar__3___24Anonymous__25622] :
( t(Vvar__3___24Anonymous__25622,happ(V1__P,Vvar__2__x__25621))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__25621,Vvar__3___24Anonymous__25622)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__25621 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__25650___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__25644] :
( t(Vvar__2__x__25644,V0__A)
& ? [Vvar__3___24Anonymous__25645] :
( t(Vvar__3___24Anonymous__25645,happ(V1__P,Vvar__2__x__25644))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__25644,Vvar__3___24Anonymous__25645)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__25645 ) ) ) ) ) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__6481] :
( t(Vvar__1___24Anonymous__6481,V0__A)
& ? [Vvar__2___24Anonymous__6482] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6482)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6481,Vvar__2___24Anonymous__6482)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__6481 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__6482) ) ) ) ) ) ) ) ).
fof('$_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__6536] :
( t(Vvar__1___24Anonymous__6536,V0__A)
& ? [Vvar__2___24Anonymous__6537] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6537)
& ( cType___24t(V0__A)
=> ( c_24__type__6542___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__6536,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6536,Vvar__2___24Anonymous__6537)
& ( ( happ(V1__f,Vvar__1___24Anonymous__6536) = 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__6536,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__6537)) )
| ( happ(V1__f,Vvar__1___24Anonymous__6536) = 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__6537) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__22616] :
( t(Vvar__1___24Anonymous__22616,V1__B)
& ? [Vvar__2___24Anonymous__22617] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__22617)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__22616,Vvar__2___24Anonymous__22617)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__22617,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__22616)) ) ) ) ) ) ) ).
fof('$_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__44076] :
( t(Vvar__1___24Anonymous__44076,V1__B)
& ? [Vvar__2___24Anonymous__44077] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__44077)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__44076,Vvar__2___24Anonymous__44077)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__44076),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__44077)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__68911] :
( t(Vvar__1___24Anonymous__68911,V0__A)
& ? [Vvar__2___24Anonymous__68912] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__68912)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__68912)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__68911,Vvar__2___24Anonymous__68912)
& ( ( Vvar__2___24Anonymous__68912 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__68911 )
| ? [Vvar__1___24Anonymous__68923] :
( t(Vvar__1___24Anonymous__68923,V0__A)
& ? [Vvar__2___24Anonymous__68924] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__68924)
& Vvar__2___24Anonymous__68912 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__68923,Vvar__2___24Anonymous__68924)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__68912,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__6515] :
( t(Vvar__1___24Anonymous__6515,V0__A)
& ? [Vvar__2___24Anonymous__6516] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6516)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6515,Vvar__2___24Anonymous__6516)
& 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__6515),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__6516)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__10231] :
( t(Vvar__1___24Anonymous__10231,V0__A)
& ? [Vvar__2___24Anonymous__10232] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10232)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10231,Vvar__2___24Anonymous__10232)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__10231 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__10234] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10234)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10234)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__10241] :
( t(Vvar__1___24Anonymous__10241,V0__A)
& ? [Vvar__2___24Anonymous__10242] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10242)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10241,Vvar__2___24Anonymous__10242)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__10234,Vvar__2___24Anonymous__10242,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_bool',axiom,
! [V0__A,V1__eqA,V2__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V0__A,V1__eqA,V2__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6542___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cCoq_2eInit_2eDatatypes_2ebool,V1__eqA,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V2__f) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__44254___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__24849___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
! [V0__U,V1__P,V2__p,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
<=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
! [V0__U,V1__p,V2__Q,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x)
<=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
! [V0__U,V1__x,V2__P] :
( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
<=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V0__U)
<=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y) ) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
! [V0__U,V1__x] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__U,V1__x)
<=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ).
fof('$_def_Coq.Logic.FinFun.Bijective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eBijective___24a3(V0__A,V1__B,V2__f)
<=> ? [V3__g] :
( c_24__type__24136___24t(V0__A,V1__B,V3__g)
& ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
& ! [V4__y] :
( t(V4__y,V1__B)
=> happ(V2__f,happ(V3__g,V4__y)) = V4__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Injective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eInjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Logic.FinFun.Surjective',axiom,
! [V0__A,V1__B,V2__f] :
( cCoq_2eLogic_2eFinFun_2eSurjective___24a3(V0__A,V1__B,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__B)
=> ? [V4__x] :
( t(V4__x,V0__A)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_Coq.Logic.FinFun.bInjective',axiom,
! [V0__n,V1__f] :
( cCoq_2eLogic_2eFinFun_2ebInjective___24a2(V0__n,V1__f)
<=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( 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('$_def_Coq.NArith.BinNat.N.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__42091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42091)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42091)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__42094] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42094)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42094)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__42091,Vvar__0___24Anonymous__42094)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__42103] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42103)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42103)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__42104] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42104)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42104)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__42107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42107)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42107)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__42104,Vvar__0___24Anonymous__42107) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__42090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42090)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42090)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__42090)) ) ) ) ).
fof('$_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__42112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42112)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42112)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__42113] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42113)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42113)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__42116] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42116)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42116)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__42113,Vvar__0___24Anonymous__42116) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__72047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72047)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72047)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__72047)
& ( ? [Vvar__0___24Anonymous__72051] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72051)
& Vvar__0___24Anonymous__72047 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__72051)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__72052] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72052)
& Vvar__0___24Anonymous__72047 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__72052)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__72047 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__186798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186798)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__186798)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__186801] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186801)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__186801)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__186798,Vvar__0___24Anonymous__186801)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.log2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__65432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65432)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65432)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65432)
& ( ? [Vvar__0___24Anonymous__65436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65436)
& Vvar__0___24Anonymous__65432 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__65436)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__65436)) )
| ? [Vvar__0___24Anonymous__65437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65437)
& Vvar__0___24Anonymous__65432 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__65437)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__65437)) )
| ( Vvar__0___24Anonymous__65432 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__42098] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42098)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42098)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__42101] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42101)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42101)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__42098,Vvar__0___24Anonymous__42101)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.NArith.BinNatDef.N.pow',axiom,
! [V0__n,V1__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
=> ( ( V1__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__105002] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105002)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105002)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__105005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105005)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__105005)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__105005,Vvar__0___24Anonymous__105002)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__104990] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104990)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__104990)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__104990) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__186803] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186803)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__186803)
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__186803)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__104991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104991)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__104991)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__104996] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104996)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104991)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104996)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__104996)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__104991,Vvar__0___24Anonymous__104996) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__104999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__104999)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__104991,Vvar__0___24Anonymous__104996) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__104999)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__104999) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__104991,Vvar__0___24Anonymous__104996) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__71940] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71940)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__71940)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__71940)) ) ) ) ).
fof('$_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__42089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42089)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42089)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__42089)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__65443] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65443)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__65443)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__65443,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__42133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42133)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__42133)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__42133) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__44538] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44538)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44538)
& ( ? [Vvar__0___24Anonymous__44542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44542)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44542)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__44537__1__add__carry___24a2(Vvar__0___24Anonymous__44538,Vvar__0___24Anonymous__44542)) )
| ? [Vvar__0___24Anonymous__44543] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44543)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44543)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__44538,Vvar__0___24Anonymous__44543)) )
| ( 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__44538)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__44544] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44544)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44544)
& ( ? [Vvar__0___24Anonymous__44548] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44548)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44548)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__44544,Vvar__0___24Anonymous__44548)) )
| ? [Vvar__0___24Anonymous__44549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44549)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44549)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__44544,Vvar__0___24Anonymous__44549)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44544) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__44550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44550)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44550)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44550)) )
| ? [Vvar__0___24Anonymous__44551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44551)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44551)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44551) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__105063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105063)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105063)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__105063),Vvar__0___24Anonymous__105063)) )
| ? [Vvar__0___24Anonymous__105064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105064)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105064)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__105064),Vvar__0___24Anonymous__105064) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__44582] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44582)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44582)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__44582,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__44583] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44583)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44583)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__44583,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__44572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44572)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44572)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__44572,V2__y))) )
| ? [Vvar__0___24Anonymous__44573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44573)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44573)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__44573,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__44599] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44599)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44599)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44599)
& ( ( Vvar__0___24Anonymous__44599 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__44602] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44602)
& Vvar__0___24Anonymous__44599 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44602)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__44599)) ) ) ) ) ) ) ) ).
fof('$_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__42310] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42310)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42310)
& 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__42310)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__105058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105058)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__105058)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105058) )
| ? [Vvar__0___24Anonymous__105059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__105059)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__105059)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__105059) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__44569] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44569)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__44569)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__44569 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__44535] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44535)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44535)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44535)) )
| ? [Vvar__0___24Anonymous__44536] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44536)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44536)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44536) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__22963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22963)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22963)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__22963) )
| ? [Vvar__0___24Anonymous__22964] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22964)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22964)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__22964)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__44222] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44222)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44222)
& 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__44222)) ) ) ) ).
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__6754___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__186805] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__186805)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__186805) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__183988] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__183988)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__183988) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__186759] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__186759)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__186759) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__186839] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__186839)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__186839) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq = c_3d___24a1(cCoq_2eStrings_2eString_2estring) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__185004] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__185004)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__185004) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__185192] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__185192)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__185192) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Bezout',axiom,
! [V0__n,V1__m,V2__p] :
( cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p)
<=> ? [V3__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__a)
& ? [V4__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__b)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__a,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__b,V1__m)) = V2__p ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__42471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42471)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42471)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42471) )
| ? [Vvar__0___24Anonymous__42472] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42472)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42472)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42472) ) ) ) ).
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__11307] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11307)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11307)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__11311] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11311)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11311)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__11307,Vvar__0___24Anonymous__11311)) )
| ? [Vvar__0___24Anonymous__11312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11312)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11312)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__11307,Vvar__0___24Anonymous__11312) ) ) ) ) )
| ? [Vvar__0___24Anonymous__11313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11313)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11313)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__11317] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11317)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11317)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__11317,Vvar__0___24Anonymous__11313) )
| ? [Vvar__0___24Anonymous__11318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11318)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11318)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__11313,Vvar__0___24Anonymous__11318)) ) ) ) ) ) ) ) ).
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__42454] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42454)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42454)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__42455] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42455)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42455)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__42456] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42456)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42456)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__42460] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42460)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42460)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__42456,Vvar__0___24Anonymous__42460) )
| ? [Vvar__0___24Anonymous__42461] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42461)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42461)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__42462] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42462)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42462)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__42466] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42466)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__42466)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__42467] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__42467)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__42467)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__42462,Vvar__0___24Anonymous__42467)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__65540] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__65540)
& ? [Vvar__3___24Anonymous__65541] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__65541)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__65540,Vvar__3___24Anonymous__65541)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__65540 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.eqb',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__72056] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72056)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__72056)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__72057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72057)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__72057)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__72058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72058)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__72058)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__72062] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72062)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__72062)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__72058,Vvar__0___24Anonymous__72062) )
| ? [Vvar__0___24Anonymous__72063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72063)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__72063)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__72064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72064)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__72064)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__72068] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72068)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__72068)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__72069] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__72069)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__72069)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__72064,Vvar__0___24Anonymous__72069) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
| ? [Vvar__0___24Anonymous__185141] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185141)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__185141)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__185145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185145)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__185145)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__185141,Vvar__0___24Anonymous__185145)) )
| ? [Vvar__0___24Anonymous__185146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185146)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__185146)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__185141,Vvar__0___24Anonymous__185146)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__185147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185147)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__185147)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__185151] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185151)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__185151)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__185147,Vvar__0___24Anonymous__185151)) )
| ? [Vvar__0___24Anonymous__185152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185152)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__185152)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__185147,Vvar__0___24Anonymous__185152)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.log2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__65544] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65544)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65544)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__65544)
& ( ? [Vvar__0___24Anonymous__65548] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65548)
& Vvar__0___24Anonymous__65544 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__65548)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__65548)) )
| ? [Vvar__0___24Anonymous__65549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65549)
& Vvar__0___24Anonymous__65544 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__65549)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__65549)) )
| ( Vvar__0___24Anonymous__65544 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__65550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__65550)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__65550)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__105172] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__105172)
& ? [Vvar__3___24Anonymous__105173] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__105173)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__105172,Vvar__3___24Anonymous__105173)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__105173 ) ) ) ) ).
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__11326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11326)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11326)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11330)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11330)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11326,Vvar__0___24Anonymous__11330)) )
| ? [Vvar__0___24Anonymous__11331] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11331)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11331)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11326,Vvar__0___24Anonymous__11331)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__11332] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11332)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11332)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11336] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11336)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11336)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11332,Vvar__0___24Anonymous__11336)) )
| ? [Vvar__0___24Anonymous__11337] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11337)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11337)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__11332,Vvar__0___24Anonymous__11337)) ) ) ) ) ) ) ) ).
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__44701] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44701)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44701)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44701) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__11339] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11339)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11339)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__11339)) ) ) ) ).
fof('$_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__11322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11322)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11322)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11322) )
| ? [Vvar__0___24Anonymous__11323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11323)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11323)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11323) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__71959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71959)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__71959)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__71959) )
| ? [Vvar__0___24Anonymous__71960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__71960)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__71960)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__185005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185005)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__185005)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__185006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185006)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__185006)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__186858] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186858)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__186858)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__186858)) )
| ? [Vvar__0___24Anonymous__186859] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186859)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__186859)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__108191] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108191)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__108191)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__108191 )
| ? [Vvar__0___24Anonymous__108192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108192)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__108192)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b) )
| ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.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__6605] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6605)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6605)
& 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__6605,V3__fl,V4__def)) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__185692___24a1(V0__D) ).
fof('$_def_Coq.micromega.Env.jump',axiom,
! [V0__D,V1__j,V2__e,V3__x] : cCoq_2emicromega_2eEnv_2ejump___24a4(V0__D,V1__j,V2__e,V3__x) = happ(V2__e,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V3__x,V1__j)) ).
fof('$_def_Coq.micromega.Env.nth',axiom,
! [V0__D,V1__n,V2__e] : cCoq_2emicromega_2eEnv_2enth___24a3(V0__D,V1__n,V2__e) = happ(V2__e,V1__n) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__69045] :
( t(Vvar__1___24Anonymous__69045,V1__A)
& ? [Vvar__2___24Anonymous__69046] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__69046)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__69046)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__69045,Vvar__2___24Anonymous__69046)
& ( ( Vvar__2___24Anonymous__69046 = 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__69045)) ) )
| ? [Vvar__1___24Anonymous__69057] :
( t(Vvar__1___24Anonymous__69057,V1__A)
& ? [Vvar__2___24Anonymous__69058] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__69058)
& Vvar__2___24Anonymous__69046 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__69057,Vvar__2___24Anonymous__69058)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__69045))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__69046) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__186319___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__186327___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__186335___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__186343___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__68775] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__68775)
& ? [Vvar__2___24Anonymous__68776] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__68776)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__68775,Vvar__2___24Anonymous__68776)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__68775),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__68776,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__67278] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__67278)
& ? [Vvar__2__denum__67279] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__67279)
& ? [Vvar__3__condition__67280] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__67280)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__67278,Vvar__2__denum__67279,Vvar__3__condition__67280)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__67280 ) ) ) ) ) ).
fof('$_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__67269] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__67269)
& ? [Vvar__2__denum__67270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__67270)
& ? [Vvar__3__condition__67271] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__67271)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__67269,Vvar__2__denum__67270,Vvar__3__condition__67271)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__67270 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__67258] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__67258)
& ? [Vvar__2__denum__67259] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__67259)
& ? [Vvar__3__condition__67260] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__67260)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__67258,Vvar__2__denum__67259,Vvar__3__condition__67260)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__67258 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__68794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__68794)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__68794)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__68794) ) ) ) ) ).
fof('$_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__177656] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__177656)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__177656)
& 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__177656) )
| ? [Vvar__0___24Anonymous__177657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__177657)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__177657)
& 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__177657)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__8059___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
fof('$_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__23936] :
( t(Vvar__1___24Anonymous__23936,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__23936)
& 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__23936) )
| ? [Vvar__1___24Anonymous__23938] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23938)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__23938)
& 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__23938,V13__l) )
| ? [Vvar__1___24Anonymous__23940] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__23940)
& ? [Vvar__2___24Anonymous__23941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__23941)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__23940,Vvar__2___24Anonymous__23941)
& 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__23940)),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__23941)) ) )
| ? [Vvar__1___24Anonymous__23944] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__23944)
& ? [Vvar__2___24Anonymous__23945] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__23945)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__23944,Vvar__2___24Anonymous__23945)
& 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__23944)),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__23945)) ) )
| ? [Vvar__1___24Anonymous__23948] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__23948)
& ? [Vvar__2___24Anonymous__23949] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__23949)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__23948,Vvar__2___24Anonymous__23949)
& 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__23948)),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__23949)) ) )
| ? [Vvar__1___24Anonymous__23952] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__23952)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__23952)
& 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__23952)) )
| ? [Vvar__1___24Anonymous__23954] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__23954)
& ? [Vvar__2___24Anonymous__23955] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23955)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__23954,Vvar__2___24Anonymous__23955)
& 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__23954)),happ(V10__Cp__phi,Vvar__2___24Anonymous__23955)) ) ) ) ) ) ) ) ).
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__23559] :
( t(Vvar__1___24Anonymous__23559,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__23559)
& ( ? [Vvar__1___24Anonymous__23569] :
( t(Vvar__1___24Anonymous__23569,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23569)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__23559),Vvar__1___24Anonymous__23569) )
| ? [Vvar__1___24Anonymous__23571] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23571)
& ? [Vvar__2___24Anonymous__23572] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23572)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23571,Vvar__2___24Anonymous__23572)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__23575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23575)
& ? [Vvar__2___24Anonymous__23576] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23576)
& ? [Vvar__3___24Anonymous__23577] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23577)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23575,Vvar__2___24Anonymous__23576,Vvar__3___24Anonymous__23577)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__23582] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23582)
& ? [Vvar__2___24Anonymous__23583] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23583)
& ( 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__23582,Vvar__2___24Anonymous__23583)
& ( ? [Vvar__1___24Anonymous__23603] :
( t(Vvar__1___24Anonymous__23603,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23603)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__23605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23605)
& ? [Vvar__2___24Anonymous__23606] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23606)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23582)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23605)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23605,Vvar__2___24Anonymous__23606)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23582,Vvar__1___24Anonymous__23605) = 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__23583,Vvar__2___24Anonymous__23606) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__23582,Vvar__1___24Anonymous__23605) = 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__23582,Vvar__1___24Anonymous__23605) = 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__23611] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23611)
& ? [Vvar__2___24Anonymous__23612] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23612)
& ? [Vvar__3___24Anonymous__23613] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23613)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23611,Vvar__2___24Anonymous__23612,Vvar__3___24Anonymous__23613)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__23618] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23618)
& ? [Vvar__2___24Anonymous__23619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23619)
& ? [Vvar__3___24Anonymous__23620] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23620)
& ( 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__23618,Vvar__2___24Anonymous__23619,Vvar__3___24Anonymous__23620)
& ( ? [Vvar__1___24Anonymous__23653] :
( t(Vvar__1___24Anonymous__23653,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__23653)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__23655] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23655)
& ? [Vvar__2___24Anonymous__23656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__23656)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__23655,Vvar__2___24Anonymous__23656)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__23659] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23659)
& ? [Vvar__2___24Anonymous__23660] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23660)
& ? [Vvar__3___24Anonymous__23661] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__23661)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23619)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23660)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__23659,Vvar__2___24Anonymous__23660,Vvar__3___24Anonymous__23661)
& ( ( cType___24t(V0__C)
=> ( c_24__type__8059___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23618)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__23659)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__23619,Vvar__2___24Anonymous__23660) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23618,Vvar__1___24Anonymous__23659) = 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__23620,Vvar__3___24Anonymous__23661) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__23618,Vvar__1___24Anonymous__23659) = 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__23619,Vvar__2___24Anonymous__23660) = 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__23619,Vvar__2___24Anonymous__23660) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
! [V0__C,V1__c] : cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V0__C,V1__c) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__C) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__25145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25145)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25145)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__25145) ) ) ) ) ).
fof('$_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__69422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__69422)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__69422)
& 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__69423__69426___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69422)),c_24__let__var__6__p__69423__69426___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69422))) )
| ? [Vvar__0___24Anonymous__69424] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__69424)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__69424)
& 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__69425__69427___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69424)),c_24__let__var__6__p__69425__69427___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__69424)) )
| ( 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('$_def_QuicksortComplexity.arith_lems.geb',axiom,
! [V0__x,V1__y] : cQuicksortComplexity_2earith__lems_2egeb___24a2(V0__x,V1__y) = cCoq_2eInit_2eNat_2eleb___24a2(V1__y,V0__x) ).
fof('$_def_QuicksortComplexity.fix_measure_utils.MR',axiom,
! [V0__T,V1__M,V2__R,V3__m,V4__x,V5__y] :
( cQuicksortComplexity_2efix__measure__utils_2eMR___24a6(V0__T,V1__M,V2__R,V3__m,V4__x,V5__y)
<=> p(happ(happ(V2__R,happ(V3__m,V4__x)),happ(V3__m,V5__y))) ) ).
fof('$_def_QuicksortComplexity.list_utils.Partitioning',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T) = c_24__type__10497___24a1(V0__T) ).
fof('$_def_QuicksortComplexity.list_utils.addToPartitioning',axiom,
! [V0__T,V1__c,V2__l,V3__h,V4__H] : cQuicksortComplexity_2elist__utils_2eaddToPartitioning___24a5(V0__T,V1__c,V2__l,V3__h,V4__H) = cCoq_2eInit_2eSpecif_2eexist___24a4(c_24__type__34750___24a2(V0__T,V2__l),c_24__lam__34758___24a3(V0__T,V2__l,V3__h),c_24__lam__34800___24a5(V0__T,V1__c,V2__l,V3__h,V4__H),cQuicksortComplexity_2elist__utils_2epartition__oblig___24a5(V0__T,V1__c,V2__l,V3__h,V4__H)) ).
fof('$_def_QuicksortComplexity.list_utils.count',axiom,
! [V0__X,V1__p,V3__l] :
( cType___24t(V0__X)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__X)
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__6973] :
( t(Vvar__1___24Anonymous__6973,V0__X)
& ? [Vvar__2___24Anonymous__6974] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,Vvar__2___24Anonymous__6974)
& ( cType___24t(V0__X)
=> ( c_24__type__6542___24t(V0__X,V1__p)
=> ( t(Vvar__1___24Anonymous__6973,V0__X)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__X,Vvar__1___24Anonymous__6973,Vvar__2___24Anonymous__6974)
& ( ( happ(V1__p,Vvar__1___24Anonymous__6973) = cCoq_2eInit_2eDatatypes_2etrue
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__6974)) )
| ( happ(V1__p,Vvar__1___24Anonymous__6973) = cCoq_2eInit_2eDatatypes_2efalse
& cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,V3__l) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V0__X,V1__p,Vvar__2___24Anonymous__6974) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.list_utils.emp',axiom,
! [V0__T] : cQuicksortComplexity_2elist__utils_2eemp___24a1(V0__T) = cCoq_2eInit_2eSpecif_2eexist___24a4(c_24__type__10497___24a1(V0__T),c_24__lam__34849___24a1(V0__T),c_24__lam__34851___24a1(V0__T),cCoq_2eSorting_2ePermutation_2eperm__nil___24a1(V0__T)) ).
fof('$_def_QuicksortComplexity.list_utils.repeat',axiom,
! [V1__T,V2__n,V3__x] :
( cType___24t(V1__T)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T) )
| ? [Vvar__0___24Anonymous__34858] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34858)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34858)
& cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,V2__n,V3__x) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V3__x,cQuicksortComplexity_2elist__utils_2erepeat___24a3(V1__T,Vvar__0___24Anonymous__34858,V3__x)) ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.IdMonad.C',axiom,
! [V0__s] : cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(V0__s) = V0__s ).
fof('$_def_QuicksortComplexity.monads.IdMonad.M',axiom,
cQuicksortComplexity_2emonads_2eIdMonad_2eM = cQuicksortComplexity_2emonads_2eBuild__Monad___24a6(cQuicksortComplexity_2emonads_2eIdMonad_2eC,cQuicksortComplexity_2emonads_2eIdMonad_2ebind,cQuicksortComplexity_2emonads_2eIdMonad_2eret,c_24__lam__2757,c_24__lam__2759,c_24__lam__2790) ).
fof('$_def_QuicksortComplexity.monads.IdMonad.bind',axiom,
! [V0__A,V1__B,V2__x,V3__y] : cQuicksortComplexity_2emonads_2eIdMonad_2ebind___24a4(V0__A,V1__B,V2__x,V3__y) = happ(V3__y,V2__x) ).
fof('$_def_QuicksortComplexity.monads.IdMonad.id_isa_monad',axiom,
! [V0__A,V1__a] : cQuicksortComplexity_2emonads_2eIdMonad_2eid__isa__monad___24a2(V0__A,V1__a) = V1__a ).
fof('$_def_QuicksortComplexity.monads.IdMonad.ret',axiom,
! [V0__A,V1__x] : cQuicksortComplexity_2emonads_2eIdMonad_2eret___24a2(V0__A,V1__x) = V1__x ).
fof('$_def_QuicksortComplexity.monads.MonadFunctor',axiom,
! [V0__M] : cQuicksortComplexity_2emonads_2eMonadFunctor___24a1(V0__M) = cQuicksortComplexity_2emonads_2eBuild__Functor___24a4(cQuicksortComplexity_2emonads_2emon___24a1(V0__M),cQuicksortComplexity_2emonads_2ebind__map___24a1(V0__M),c_24__lam__39157___24a1(V0__M),c_24__lam__39502___24a1(V0__M)) ).
fof('$_def_QuicksortComplexity.monads.a_monad_isa_functor',axiom,
! [V0__M,V2__T,V3__x] : cQuicksortComplexity_2emonads_2ea__monad__isa__functor___24a3(V0__M,V2__T,V3__x) = V3__x ).
fof('$_def_QuicksortComplexity.monads.bind',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__517] :
( c_24__type__199___24t(Vvar__0__mon__517)
& ? [Vvar__1__bind__519] :
( c_24__type__676___24t(Vvar__0__mon__517,Vvar__1__bind__519)
& ? [Vvar__2__ret__530] :
( c_24__type__686___24t(Vvar__0__mon__517,Vvar__2__ret__530)
& ! [Vvar__var__3__a__536__541] :
( cType___24t(Vvar__var__3__a__536__541)
=> ! [Vvar__var__4__b__537__542] :
( cType___24t(Vvar__var__4__b__537__542)
=> ! [Vvar__var__5__x__539__544] :
( t(Vvar__var__5__x__539__544,Vvar__var__3__a__536__541)
=> ! [Vvar__var__6__f__540__545] :
( c_24__type__681___24t(Vvar__0__mon__517,Vvar__var__3__a__536__541,Vvar__var__4__b__537__542,Vvar__var__6__f__540__545)
=> happ(happ(happ(happ(Vvar__1__bind__519,Vvar__var__3__a__536__541),Vvar__var__4__b__537__542),happ(happ(Vvar__2__ret__530,Vvar__var__3__a__536__541),Vvar__var__5__x__539__544)),Vvar__var__6__f__540__545) = happ(Vvar__var__6__f__540__545,Vvar__var__5__x__539__544) ) ) ) )
& ! [Vvar__var__4__a__547__549] :
( cType___24t(Vvar__var__4__a__547__549)
=> ! [Vvar__var__5__f__548__550] :
( t(Vvar__var__5__f__548__550,happ(Vvar__0__mon__517,Vvar__var__4__a__547__549))
=> happ(happ(happ(happ(Vvar__1__bind__519,Vvar__var__4__a__547__549),Vvar__var__4__a__547__549),Vvar__var__5__f__548__550),happ(Vvar__2__ret__530,Vvar__var__4__a__547__549)) = Vvar__var__5__f__548__550 ) )
& ! [Vvar__var__5__a__552__561] :
( cType___24t(Vvar__var__5__a__552__561)
=> ! [Vvar__var__6__b__553__562] :
( cType___24t(Vvar__var__6__b__553__562)
=> ! [Vvar__var__7__c__555__564] :
( cType___24t(Vvar__var__7__c__555__564)
=> ! [Vvar__var__8__n__557__566] :
( t(Vvar__var__8__n__557__566,happ(Vvar__0__mon__517,Vvar__var__5__a__552__561))
=> ! [Vvar__var__9__f__558__567] :
( c_24__type__681___24t(Vvar__0__mon__517,Vvar__var__5__a__552__561,Vvar__var__6__b__553__562,Vvar__var__9__f__558__567)
=> ! [Vvar__var__10__g__559__568] :
( c_24__type__705___24t(Vvar__0__mon__517,Vvar__var__5__a__552__561,Vvar__var__6__b__553__562,Vvar__var__7__c__555__564,Vvar__var__10__g__559__568)
=> happ(happ(happ(happ(Vvar__1__bind__519,Vvar__var__6__b__553__562),Vvar__var__7__c__555__564),happ(happ(happ(happ(Vvar__1__bind__519,Vvar__var__5__a__552__561),Vvar__var__6__b__553__562),Vvar__var__8__n__557__566),Vvar__var__9__f__558__567)),Vvar__var__10__g__559__568) = happ(happ(happ(happ(Vvar__1__bind__519,Vvar__var__5__a__552__561),Vvar__var__7__c__555__564),Vvar__var__8__n__557__566),c_24__lam__730___24a7(Vvar__0__mon__517,Vvar__1__bind__519,Vvar__var__5__a__552__561,Vvar__var__6__b__553__562,Vvar__var__7__c__555__564,Vvar__var__9__f__558__567,Vvar__var__10__g__559__568)) ) ) ) ) ) )
& V0__m = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__517,Vvar__1__bind__519,Vvar__2__ret__530)
& cQuicksortComplexity_2emonads_2ebind___24a1(V0__m) = Vvar__1__bind__519 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.bind_map',axiom,
! [V0__M,V1__a,V2__b,V3__f,V4__x] : cQuicksortComplexity_2emonads_2ebind__map___24a5(V0__M,V1__a,V2__b,V3__f,V4__x) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V1__a,V2__b,V4__x,c_24__lam__39010___24a4(V0__M,V1__a,V2__b,V3__f)) ).
fof('$_def_QuicksortComplexity.monads.extMonad',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
<=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__759___24t(V0__M,V1__A,V2__B,V3__f)
=> ! [V4__g] :
( c_24__type__759___24t(V0__M,V1__A,V2__B,V4__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V1__A,cQuicksortComplexity_2emonads_2emon___24a2(V0__M,V2__B),V3__f,V4__g)
=> ! [V6__x] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__M,V1__A,V6__x)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V1__A,V2__B,V6__x,V3__f) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V1__A,V2__B,V6__x,V4__g) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.filterM',axiom,
! [V1__A,V2__M,V3__p,V4__l] :
( cType___24t(V1__A)
=> ( cQuicksortComplexity_2emonads_2eMonad___24t(V2__M)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cQuicksortComplexity_2emonads_2efilterM___24a4(V1__A,V2__M,V3__p,V4__l) = cQuicksortComplexity_2emonads_2eret___24a3(V2__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)) )
| ? [Vvar__1___24Anonymous__2649] :
( t(Vvar__1___24Anonymous__2649,V1__A)
& ? [Vvar__2___24Anonymous__2650] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2650)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2649,Vvar__2___24Anonymous__2650)
& cQuicksortComplexity_2emonads_2efilterM___24a4(V1__A,V2__M,V3__p,V4__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V2__M,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__A),happ(V3__p,Vvar__1___24Anonymous__2649),c_24__lam__2678___24a5(V1__A,V2__M,V3__p,Vvar__1___24Anonymous__2649,Vvar__2___24Anonymous__2650)) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.foldlM',axiom,
! [V1__A,V2__B,V3__M,V4__f,V5__x,V6__l] :
( cType___24t(V1__A)
=> ( cType___24t(V2__B)
=> ( cQuicksortComplexity_2emonads_2eMonad___24t(V3__M)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__B,V6__l)
=> ( ( V6__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__B)
& cQuicksortComplexity_2emonads_2efoldlM___24a6(V1__A,V2__B,V3__M,V4__f,V5__x,V6__l) = cQuicksortComplexity_2emonads_2eret___24a3(V3__M,V1__A,V5__x) )
| ? [Vvar__1___24Anonymous__39679] :
( t(Vvar__1___24Anonymous__39679,V2__B)
& ? [Vvar__2___24Anonymous__39680] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__B,Vvar__2___24Anonymous__39680)
& V6__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__B,Vvar__1___24Anonymous__39679,Vvar__2___24Anonymous__39680)
& cQuicksortComplexity_2emonads_2efoldlM___24a6(V1__A,V2__B,V3__M,V4__f,V5__x,V6__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V3__M,V1__A,V1__A,happ(happ(V4__f,V5__x),Vvar__1___24Anonymous__39679),c_24__lam__39695___24a5(V1__A,V2__B,V3__M,V4__f,Vvar__2___24Anonymous__39680)) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.foldrM',axiom,
! [V1__A,V2__B,V3__M,V4__f,V5__x,V6__l] :
( cType___24t(V1__A)
=> ( cType___24t(V2__B)
=> ( cQuicksortComplexity_2emonads_2eMonad___24t(V3__M)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V2__B,V6__l)
=> ( ( V6__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V2__B)
& cQuicksortComplexity_2emonads_2efoldrM___24a6(V1__A,V2__B,V3__M,V4__f,V5__x,V6__l) = cQuicksortComplexity_2emonads_2eret___24a3(V3__M,V1__A,V5__x) )
| ? [Vvar__1___24Anonymous__7849] :
( t(Vvar__1___24Anonymous__7849,V2__B)
& ? [Vvar__2___24Anonymous__7850] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V2__B,Vvar__2___24Anonymous__7850)
& V6__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V2__B,Vvar__1___24Anonymous__7849,Vvar__2___24Anonymous__7850)
& cQuicksortComplexity_2emonads_2efoldrM___24a6(V1__A,V2__B,V3__M,V4__f,V5__x,V6__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V3__M,V1__A,V1__A,cQuicksortComplexity_2emonads_2efoldrM___24a6(V1__A,V2__B,V3__M,V4__f,V5__x,Vvar__2___24Anonymous__7850),c_24__lam__7865___24a5(V1__A,V2__B,V3__M,V4__f,Vvar__1___24Anonymous__7849)) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.func',axiom,
! [V0__f] :
( cQuicksortComplexity_2emonads_2eFunctor___24t(V0__f)
=> ? [Vvar__0__func__38806] :
( c_24__type__199___24t(Vvar__0__func__38806)
& ? [Vvar__1__func__map__38808] :
( c_24__type__38897___24t(Vvar__0__func__38806,Vvar__1__func__map__38808)
& ! [Vvar__var__2__X__38820__38823] :
( cType___24t(Vvar__var__2__X__38820__38823)
=> happ(happ(happ(Vvar__1__func__map__38808,Vvar__var__2__X__38820__38823),Vvar__var__2__X__38820__38823),c_24__lam__38903___24a2(Vvar__0__func__38806,Vvar__var__2__X__38820__38823)) = c_24__lam__38906___24a2(Vvar__0__func__38806,Vvar__var__2__X__38820__38823) )
& ! [Vvar__var__3__a__38827__38835] :
( cType___24t(Vvar__var__3__a__38827__38835)
=> ! [Vvar__var__4__b__38828__38836] :
( cType___24t(Vvar__var__4__b__38828__38836)
=> ! [Vvar__var__5__c__38829__38837] :
( cType___24t(Vvar__var__5__c__38829__38837)
=> ! [Vvar__var__6__x__38834__38842] :
( t(Vvar__var__6__x__38834__38842,happ(Vvar__0__func__38806,Vvar__var__3__a__38827__38835))
=> ! [Vvar__var__7__f__38832__38840] :
( c_24__type__38914___24t(Vvar__0__func__38806,Vvar__var__3__a__38827__38835,Vvar__var__4__b__38828__38836,Vvar__var__5__c__38829__38837,Vvar__var__7__f__38832__38840)
=> ! [Vvar__var__8__g__38833__38841] :
( c_24__type__38920___24t(Vvar__0__func__38806,Vvar__var__3__a__38827__38835,Vvar__var__4__b__38828__38836,Vvar__var__5__c__38829__38837,Vvar__var__8__g__38833__38841)
=> happ(happ(happ(happ(Vvar__1__func__map__38808,Vvar__var__3__a__38827__38835),Vvar__var__5__c__38829__38837),cCoq_2eProgram_2eBasics_2ecompose___24a5(Vvar__var__3__a__38827__38835,Vvar__var__4__b__38828__38836,Vvar__var__5__c__38829__38837,Vvar__var__7__f__38832__38840,Vvar__var__8__g__38833__38841)),Vvar__var__6__x__38834__38842) = happ(happ(happ(happ(Vvar__1__func__map__38808,Vvar__var__4__b__38828__38836),Vvar__var__5__c__38829__38837),Vvar__var__7__f__38832__38840),happ(happ(happ(happ(Vvar__1__func__map__38808,Vvar__var__3__a__38827__38835),Vvar__var__4__b__38828__38836),Vvar__var__8__g__38833__38841),Vvar__var__6__x__38834__38842)) ) ) ) ) ) )
& V0__f = cQuicksortComplexity_2emonads_2eBuild__Functor___24a2(Vvar__0__func__38806,Vvar__1__func__map__38808)
& cQuicksortComplexity_2emonads_2efunc___24a1(V0__f) = Vvar__0__func__38806 ) ) ) ).
fof('$_def_QuicksortComplexity.monads.lift',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(V0__m)
=> ? [Vvar__0__transMonad__39842] :
( c_24__type__39762___24t(Vvar__0__transMonad__39842)
& ? [Vvar__1__lift__39845] :
( c_24__type__39870___24t(Vvar__0__transMonad__39842,Vvar__1__lift__39845)
& V0__m = cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(Vvar__0__transMonad__39842,Vvar__1__lift__39845)
& cQuicksortComplexity_2emonads_2elift___24a1(V0__m) = Vvar__1__lift__39845 ) ) ) ).
fof('$_def_QuicksortComplexity.monads.liftM',axiom,
! [V0__A,V1__B,V2__f,V3__M,V4__x] : cQuicksortComplexity_2emonads_2eliftM___24a5(V0__A,V1__B,V2__f,V3__M,V4__x) = cQuicksortComplexity_2emonads_2ebind___24a5(V3__M,V0__A,V1__B,V4__x,c_24__lam__7828___24a4(V0__A,V1__B,V2__f,V3__M)) ).
fof('$_def_QuicksortComplexity.monads.liftM2',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__M,V5__x,V6__y] : cQuicksortComplexity_2emonads_2eliftM2___24a7(V0__A,V1__B,V2__C,V3__f,V4__M,V5__x,V6__y) = cQuicksortComplexity_2emonads_2ebind___24a5(V4__M,V0__A,V2__C,V5__x,c_24__lam__39622___24a6(V0__A,V1__B,V2__C,V3__f,V4__M,V6__y)) ).
fof('$_def_QuicksortComplexity.monads.mon',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__291] :
( c_24__type__199___24t(Vvar__0__mon__291)
& ? [Vvar__1__bind__293] :
( c_24__type__450___24t(Vvar__0__mon__291,Vvar__1__bind__293)
& ? [Vvar__2__ret__304] :
( c_24__type__460___24t(Vvar__0__mon__291,Vvar__2__ret__304)
& ! [Vvar__var__3__a__310__315] :
( cType___24t(Vvar__var__3__a__310__315)
=> ! [Vvar__var__4__b__311__316] :
( cType___24t(Vvar__var__4__b__311__316)
=> ! [Vvar__var__5__x__313__318] :
( t(Vvar__var__5__x__313__318,Vvar__var__3__a__310__315)
=> ! [Vvar__var__6__f__314__319] :
( c_24__type__455___24t(Vvar__0__mon__291,Vvar__var__3__a__310__315,Vvar__var__4__b__311__316,Vvar__var__6__f__314__319)
=> happ(happ(happ(happ(Vvar__1__bind__293,Vvar__var__3__a__310__315),Vvar__var__4__b__311__316),happ(happ(Vvar__2__ret__304,Vvar__var__3__a__310__315),Vvar__var__5__x__313__318)),Vvar__var__6__f__314__319) = happ(Vvar__var__6__f__314__319,Vvar__var__5__x__313__318) ) ) ) )
& ! [Vvar__var__4__a__321__323] :
( cType___24t(Vvar__var__4__a__321__323)
=> ! [Vvar__var__5__f__322__324] :
( t(Vvar__var__5__f__322__324,happ(Vvar__0__mon__291,Vvar__var__4__a__321__323))
=> happ(happ(happ(happ(Vvar__1__bind__293,Vvar__var__4__a__321__323),Vvar__var__4__a__321__323),Vvar__var__5__f__322__324),happ(Vvar__2__ret__304,Vvar__var__4__a__321__323)) = Vvar__var__5__f__322__324 ) )
& ! [Vvar__var__5__a__326__335] :
( cType___24t(Vvar__var__5__a__326__335)
=> ! [Vvar__var__6__b__327__336] :
( cType___24t(Vvar__var__6__b__327__336)
=> ! [Vvar__var__7__c__329__338] :
( cType___24t(Vvar__var__7__c__329__338)
=> ! [Vvar__var__8__n__331__340] :
( t(Vvar__var__8__n__331__340,happ(Vvar__0__mon__291,Vvar__var__5__a__326__335))
=> ! [Vvar__var__9__f__332__341] :
( c_24__type__455___24t(Vvar__0__mon__291,Vvar__var__5__a__326__335,Vvar__var__6__b__327__336,Vvar__var__9__f__332__341)
=> ! [Vvar__var__10__g__333__342] :
( c_24__type__479___24t(Vvar__0__mon__291,Vvar__var__5__a__326__335,Vvar__var__6__b__327__336,Vvar__var__7__c__329__338,Vvar__var__10__g__333__342)
=> happ(happ(happ(happ(Vvar__1__bind__293,Vvar__var__6__b__327__336),Vvar__var__7__c__329__338),happ(happ(happ(happ(Vvar__1__bind__293,Vvar__var__5__a__326__335),Vvar__var__6__b__327__336),Vvar__var__8__n__331__340),Vvar__var__9__f__332__341)),Vvar__var__10__g__333__342) = happ(happ(happ(happ(Vvar__1__bind__293,Vvar__var__5__a__326__335),Vvar__var__7__c__329__338),Vvar__var__8__n__331__340),c_24__lam__504___24a7(Vvar__0__mon__291,Vvar__1__bind__293,Vvar__var__5__a__326__335,Vvar__var__6__b__327__336,Vvar__var__7__c__329__338,Vvar__var__9__f__332__341,Vvar__var__10__g__333__342)) ) ) ) ) ) )
& V0__m = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__291,Vvar__1__bind__293,Vvar__2__ret__304)
& cQuicksortComplexity_2emonads_2emon___24a1(V0__m) = Vvar__0__mon__291 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.ret',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ? [Vvar__0__mon__761] :
( c_24__type__199___24t(Vvar__0__mon__761)
& ? [Vvar__1__bind__763] :
( c_24__type__920___24t(Vvar__0__mon__761,Vvar__1__bind__763)
& ? [Vvar__2__ret__774] :
( c_24__type__930___24t(Vvar__0__mon__761,Vvar__2__ret__774)
& ! [Vvar__var__3__a__780__785] :
( cType___24t(Vvar__var__3__a__780__785)
=> ! [Vvar__var__4__b__781__786] :
( cType___24t(Vvar__var__4__b__781__786)
=> ! [Vvar__var__5__x__783__788] :
( t(Vvar__var__5__x__783__788,Vvar__var__3__a__780__785)
=> ! [Vvar__var__6__f__784__789] :
( c_24__type__925___24t(Vvar__0__mon__761,Vvar__var__3__a__780__785,Vvar__var__4__b__781__786,Vvar__var__6__f__784__789)
=> happ(happ(happ(happ(Vvar__1__bind__763,Vvar__var__3__a__780__785),Vvar__var__4__b__781__786),happ(happ(Vvar__2__ret__774,Vvar__var__3__a__780__785),Vvar__var__5__x__783__788)),Vvar__var__6__f__784__789) = happ(Vvar__var__6__f__784__789,Vvar__var__5__x__783__788) ) ) ) )
& ! [Vvar__var__4__a__791__793] :
( cType___24t(Vvar__var__4__a__791__793)
=> ! [Vvar__var__5__f__792__794] :
( t(Vvar__var__5__f__792__794,happ(Vvar__0__mon__761,Vvar__var__4__a__791__793))
=> happ(happ(happ(happ(Vvar__1__bind__763,Vvar__var__4__a__791__793),Vvar__var__4__a__791__793),Vvar__var__5__f__792__794),happ(Vvar__2__ret__774,Vvar__var__4__a__791__793)) = Vvar__var__5__f__792__794 ) )
& ! [Vvar__var__5__a__796__805] :
( cType___24t(Vvar__var__5__a__796__805)
=> ! [Vvar__var__6__b__797__806] :
( cType___24t(Vvar__var__6__b__797__806)
=> ! [Vvar__var__7__c__799__808] :
( cType___24t(Vvar__var__7__c__799__808)
=> ! [Vvar__var__8__n__801__810] :
( t(Vvar__var__8__n__801__810,happ(Vvar__0__mon__761,Vvar__var__5__a__796__805))
=> ! [Vvar__var__9__f__802__811] :
( c_24__type__925___24t(Vvar__0__mon__761,Vvar__var__5__a__796__805,Vvar__var__6__b__797__806,Vvar__var__9__f__802__811)
=> ! [Vvar__var__10__g__803__812] :
( c_24__type__949___24t(Vvar__0__mon__761,Vvar__var__5__a__796__805,Vvar__var__6__b__797__806,Vvar__var__7__c__799__808,Vvar__var__10__g__803__812)
=> happ(happ(happ(happ(Vvar__1__bind__763,Vvar__var__6__b__797__806),Vvar__var__7__c__799__808),happ(happ(happ(happ(Vvar__1__bind__763,Vvar__var__5__a__796__805),Vvar__var__6__b__797__806),Vvar__var__8__n__801__810),Vvar__var__9__f__802__811)),Vvar__var__10__g__803__812) = happ(happ(happ(happ(Vvar__1__bind__763,Vvar__var__5__a__796__805),Vvar__var__7__c__799__808),Vvar__var__8__n__801__810),c_24__lam__974___24a7(Vvar__0__mon__761,Vvar__1__bind__763,Vvar__var__5__a__796__805,Vvar__var__6__b__797__806,Vvar__var__7__c__799__808,Vvar__var__9__f__802__811,Vvar__var__10__g__803__812)) ) ) ) ) ) )
& V0__m = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__761,Vvar__1__bind__763,Vvar__2__ret__774)
& cQuicksortComplexity_2emonads_2eret___24a1(V0__m) = Vvar__2__ret__774 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monads.transMonad',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(V0__m)
=> ? [Vvar__0__transMonad__39807] :
( c_24__type__39762___24t(Vvar__0__transMonad__39807)
& ? [Vvar__1__lift__39810] :
( c_24__type__39835___24t(Vvar__0__transMonad__39807,Vvar__1__lift__39810)
& V0__m = cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(Vvar__0__transMonad__39807,Vvar__1__lift__39810)
& cQuicksortComplexity_2emonads_2etransMonad___24a1(V0__m) = Vvar__0__transMonad__39807 ) ) ) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.M',axiom,
! [V0__monoid,V1__monad] : cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad) = cQuicksortComplexity_2emonads_2eBuild__Monad___24a6(c_24__let__3__C__MMT__4200___24a2(V0__monoid,V1__monad),c_24__let__4__bind__MMT__4201___24a2(V0__monoid,V1__monad),c_24__let__5__ret__MMT__4202___24a2(V0__monoid,V1__monad),c_24__lam__4357___24a2(V0__monoid,V1__monad),c_24__lam__4461___24a2(V0__monoid,V1__monad),c_24__lam__5521___24a2(V0__monoid,V1__monad)) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.lift',axiom,
! [V0__monoid,V1__monad] : cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2elift___24a2(V0__monoid,V1__monad) = c_24__lam__42055___24a2(V0__monoid,V1__monad) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.NatAddMonoid',axiom,
cQuicksortComplexity_2emonoid__monad__trans_2eNatAddMonoid = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a6(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eNat_2eadd,c_24__lam__1062,c_24__lam__1063,c_24__lam__1069) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.SimplyProfiled',axiom,
cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled = cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a3(cQuicksortComplexity_2emonoid__monad__trans_2eNatAddMonoid,cQuicksortComplexity_2emonads_2eIdMonad_2eM,cQuicksortComplexity_2emonads_2eIdMonad_2eext) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.cost',axiom,
! [V0__X] : cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a1(V0__X) = cCoq_2eInit_2eDatatypes_2efst___24a2(cCoq_2eInit_2eDatatypes_2enat,V0__X) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.monoid_mult',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ? [Vvar__0__monoid__type__39996] :
( cType___24t(Vvar__0__monoid__type__39996)
& ? [Vvar__1__monoid__zero__39997] :
( t(Vvar__1__monoid__zero__39997,Vvar__0__monoid__type__39996)
& ? [Vvar__2__monoid__mult__39998] :
( c_24__type__1053___24t(Vvar__0__monoid__type__39996,Vvar__2__monoid__mult__39998)
& ! [Vvar__var__3__x__40004__40005] :
( t(Vvar__var__3__x__40004__40005,Vvar__0__monoid__type__39996)
=> happ(happ(Vvar__2__monoid__mult__39998,Vvar__1__monoid__zero__39997),Vvar__var__3__x__40004__40005) = Vvar__var__3__x__40004__40005 )
& ! [Vvar__var__4__x__40007__40008] :
( t(Vvar__var__4__x__40007__40008,Vvar__0__monoid__type__39996)
=> happ(happ(Vvar__2__monoid__mult__39998,Vvar__var__4__x__40007__40008),Vvar__1__monoid__zero__39997) = Vvar__var__4__x__40007__40008 )
& ! [Vvar__var__5__x__40010__40013] :
( t(Vvar__var__5__x__40010__40013,Vvar__0__monoid__type__39996)
=> ! [Vvar__var__6__y__40011__40014] :
( t(Vvar__var__6__y__40011__40014,Vvar__0__monoid__type__39996)
=> ! [Vvar__var__7__z__40012__40015] :
( t(Vvar__var__7__z__40012__40015,Vvar__0__monoid__type__39996)
=> happ(happ(Vvar__2__monoid__mult__39998,happ(happ(Vvar__2__monoid__mult__39998,Vvar__var__5__x__40010__40013),Vvar__var__6__y__40011__40014)),Vvar__var__7__z__40012__40015) = happ(happ(Vvar__2__monoid__mult__39998,Vvar__var__5__x__40010__40013),happ(happ(Vvar__2__monoid__mult__39998,Vvar__var__6__y__40011__40014),Vvar__var__7__z__40012__40015)) ) ) )
& V0__m = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__39996,Vvar__1__monoid__zero__39997,Vvar__2__monoid__mult__39998)
& cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a1(V0__m) = Vvar__2__monoid__mult__39998 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.monoid_type',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ? [Vvar__0__monoid__type__989] :
( cType___24t(Vvar__0__monoid__type__989)
& ? [Vvar__1__monoid__zero__990] :
( t(Vvar__1__monoid__zero__990,Vvar__0__monoid__type__989)
& ? [Vvar__2__monoid__mult__991] :
( c_24__type__1053___24t(Vvar__0__monoid__type__989,Vvar__2__monoid__mult__991)
& ! [Vvar__var__3__x__997__998] :
( t(Vvar__var__3__x__997__998,Vvar__0__monoid__type__989)
=> happ(happ(Vvar__2__monoid__mult__991,Vvar__1__monoid__zero__990),Vvar__var__3__x__997__998) = Vvar__var__3__x__997__998 )
& ! [Vvar__var__4__x__1000__1001] :
( t(Vvar__var__4__x__1000__1001,Vvar__0__monoid__type__989)
=> happ(happ(Vvar__2__monoid__mult__991,Vvar__var__4__x__1000__1001),Vvar__1__monoid__zero__990) = Vvar__var__4__x__1000__1001 )
& ! [Vvar__var__5__x__1003__1006] :
( t(Vvar__var__5__x__1003__1006,Vvar__0__monoid__type__989)
=> ! [Vvar__var__6__y__1004__1007] :
( t(Vvar__var__6__y__1004__1007,Vvar__0__monoid__type__989)
=> ! [Vvar__var__7__z__1005__1008] :
( t(Vvar__var__7__z__1005__1008,Vvar__0__monoid__type__989)
=> happ(happ(Vvar__2__monoid__mult__991,happ(happ(Vvar__2__monoid__mult__991,Vvar__var__5__x__1003__1006),Vvar__var__6__y__1004__1007)),Vvar__var__7__z__1005__1008) = happ(happ(Vvar__2__monoid__mult__991,Vvar__var__5__x__1003__1006),happ(happ(Vvar__2__monoid__mult__991,Vvar__var__6__y__1004__1007),Vvar__var__7__z__1005__1008)) ) ) )
& V0__m = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__989,Vvar__1__monoid__zero__990,Vvar__2__monoid__mult__991)
& cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__m) = Vvar__0__monoid__type__989 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.monoid_zero',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ? [Vvar__0__monoid__type__39925] :
( cType___24t(Vvar__0__monoid__type__39925)
& ? [Vvar__1__monoid__zero__39926] :
( t(Vvar__1__monoid__zero__39926,Vvar__0__monoid__type__39925)
& ? [Vvar__2__monoid__mult__39927] :
( c_24__type__1053___24t(Vvar__0__monoid__type__39925,Vvar__2__monoid__mult__39927)
& ! [Vvar__var__3__x__39933__39934] :
( t(Vvar__var__3__x__39933__39934,Vvar__0__monoid__type__39925)
=> happ(happ(Vvar__2__monoid__mult__39927,Vvar__1__monoid__zero__39926),Vvar__var__3__x__39933__39934) = Vvar__var__3__x__39933__39934 )
& ! [Vvar__var__4__x__39936__39937] :
( t(Vvar__var__4__x__39936__39937,Vvar__0__monoid__type__39925)
=> happ(happ(Vvar__2__monoid__mult__39927,Vvar__var__4__x__39936__39937),Vvar__1__monoid__zero__39926) = Vvar__var__4__x__39936__39937 )
& ! [Vvar__var__5__x__39939__39942] :
( t(Vvar__var__5__x__39939__39942,Vvar__0__monoid__type__39925)
=> ! [Vvar__var__6__y__39940__39943] :
( t(Vvar__var__6__y__39940__39943,Vvar__0__monoid__type__39925)
=> ! [Vvar__var__7__z__39941__39944] :
( t(Vvar__var__7__z__39941__39944,Vvar__0__monoid__type__39925)
=> happ(happ(Vvar__2__monoid__mult__39927,happ(happ(Vvar__2__monoid__mult__39927,Vvar__var__5__x__39939__39942),Vvar__var__6__y__39940__39943)),Vvar__var__7__z__39941__39944) = happ(happ(Vvar__2__monoid__mult__39927,Vvar__var__5__x__39939__39942),happ(happ(Vvar__2__monoid__mult__39927,Vvar__var__6__y__39940__39943),Vvar__var__7__z__39941__39944)) ) ) )
& V0__m = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__39925,Vvar__1__monoid__zero__39926,Vvar__2__monoid__mult__39927)
& cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__m) = Vvar__1__monoid__zero__39926 ) ) ) ) ).
fof('$_def_QuicksortComplexity.monoid_monad_trans.result',axiom,
! [V0__X] : cQuicksortComplexity_2emonoid__monad__trans_2eresult___24a1(V0__X) = cCoq_2eInit_2eDatatypes_2esnd___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(cQuicksortComplexity_2emonoid__monad__trans_2eNatAddMonoid),V0__X) ).
fof('$_def_QuicksortComplexity.nat_below.Snb',axiom,
! [V0__n,V1__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__nb)
=> ? [Vvar__0__v__40085] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__40085)
& ? [Vvar__1__p__40086] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__40086)
& V1__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__40085,Vvar__1__p__40086)
& cQuicksortComplexity_2enat__below_2eSnb___24a2(V0__n,V1__nb) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__v__40085),Vvar__1__p__40086) ) ) ) ) ).
fof('$_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('$_def_QuicksortComplexity.nat_below.nb_val',axiom,
! [V0__n,V1__nb] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(V0__n,V1__nb)
=> ? [Vvar__0__v__40074] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__40074)
& ? [Vvar__1__p__40075] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__40075)
& V1__nb = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__40074,Vvar__1__p__40075)
& cQuicksortComplexity_2enat__below_2enb__val___24a2(V0__n,V1__nb) = Vvar__0__v__40074 ) ) ) ) ).
fof('$_def_QuicksortComplexity.ne_list.from_vec',axiom,
! [V1__A,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2ene__list_2efrom__vec___24a2(V1__A,V2__n) = c_24__lam__11082___24a1(V1__A) )
| ? [Vvar__0___24Anonymous__11079] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11079)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11079)
& cQuicksortComplexity_2ene__list_2efrom__vec___24a2(V1__A,V2__n) = c_24__lam__11085___24a2(V1__A,Vvar__0___24Anonymous__11079) ) ) ) ).
fof('$_def_QuicksortComplexity.ne_list.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cQuicksortComplexity_2ene__list_2eL___24t(V0__A,V4__l)
=> ( ? [Vvar__1___24Anonymous__40136] :
( t(Vvar__1___24Anonymous__40136,V0__A)
& V4__l = cQuicksortComplexity_2ene__list_2eone___24a2(V0__A,Vvar__1___24Anonymous__40136)
& cQuicksortComplexity_2ene__list_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cQuicksortComplexity_2ene__list_2eone___24a2(V1__B,happ(V2__f,Vvar__1___24Anonymous__40136)) )
| ? [Vvar__1___24Anonymous__40138] :
( t(Vvar__1___24Anonymous__40138,V0__A)
& ? [Vvar__2___24Anonymous__40139] :
( cQuicksortComplexity_2ene__list_2eL___24t(V0__A,Vvar__2___24Anonymous__40139)
& V4__l = cQuicksortComplexity_2ene__list_2econs___24a3(V0__A,Vvar__1___24Anonymous__40138,Vvar__2___24Anonymous__40139)
& cQuicksortComplexity_2ene__list_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cQuicksortComplexity_2ene__list_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__40138),cQuicksortComplexity_2ene__list_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__40139)) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.body',axiom,
! [V0__M,V1__T,V2__le,V3__l,V4__qs0] : cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a5(V0__M,V1__T,V2__le,V3__l,V4__qs0) = c_24__case__Coq_2eInit_2eDatatypes_2elist_245837___24a6(V0__M,V1__T,V2__le,V3__l,V4__qs0,cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),V3__l)) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.filter',axiom,
! [V0__M,V1__T,V2__c,V3__l] : cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter___24a4(V0__M,V1__T,V2__c,V3__l) = cCoq_2eInit_2eDatatypes_2elist__rec___24a5(V1__T,c_24__lam__1102___24a2(V0__M,V1__T),cQuicksortComplexity_2emonads_2eret___24a3(V0__M,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__1108___24a2(V0__M,V1__T)),cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__1108___24a2(V0__M,V1__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T))),c_24__lam__1444___24a3(V0__M,V1__T,V2__c),V3__l) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.fold_filter',axiom,
! [V0__M,V1__T,V2__c] : cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter___24a3(V0__M,V1__T,V2__c) = cQuicksortComplexity_2emonads_2efoldrM___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),V1__T,V0__M,c_24__lam__7988___24a3(V0__M,V1__T,V2__c),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T)) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.gt',axiom,
! [V0__M,V1__T,V2__le,V3__x,V4__y] : cQuicksortComplexity_2eqs__definitions_2emon__det_2egt___24a5(V0__M,V1__T,V2__le,V3__x,V4__y) = cQuicksortComplexity_2emonads_2eliftM___24a5(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2enegb,V0__M,happ(happ(V2__le,V3__x),V4__y)) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.qs',axiom,
! [V0__M,V1__T,V2__le] : cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a3(V0__M,V1__T,V2__le) = cCoq_2eProgram_2eWf_2eFix__sub___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__2258___24a2(V0__M,V1__T)),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__3___24a1(V1__T),c_24__lam__2258___24a2(V0__M,V1__T),c_24__lam__2481___24a3(V0__M,V1__T,V2__le)) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det.simple_filter',axiom,
! [V0__M,V1__T,V3__c,V4__l] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ( cType___24t(V1__T)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T)
& cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter___24a4(V0__M,V1__T,V3__c,V4__l) = cQuicksortComplexity_2emonads_2eret___24a3(V0__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2enil___24a1(V1__T)) )
| ? [Vvar__1___24Anonymous__7914] :
( t(Vvar__1___24Anonymous__7914,V1__T)
& ? [Vvar__2___24Anonymous__7915] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,Vvar__2___24Anonymous__7915)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,Vvar__1___24Anonymous__7914,Vvar__2___24Anonymous__7915)
& cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter___24a4(V0__M,V1__T,V3__c,V4__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter___24a4(V0__M,V1__T,V3__c,Vvar__2___24Anonymous__7915),c_24__lam__7940___24a4(V0__M,V1__T,V3__c,Vvar__1___24Anonymous__7914)) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det_partition.partition',axiom,
! [V0__T,V1__M,V2__cmp,V4__pivot,V5__l] :
( cType___24t(V0__T)
=> ( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)
& cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition___24a5(V0__T,V1__M,V2__cmp,V4__pivot,V5__l) = cQuicksortComplexity_2emonads_2eret___24a3(V1__M,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11370___24a2(V0__T,V1__M)),cQuicksortComplexity_2elist__utils_2eemp___24a1(V0__T)) )
| ? [Vvar__1___24Anonymous__11351] :
( t(Vvar__1___24Anonymous__11351,V0__T)
& ? [Vvar__2___24Anonymous__11352] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2___24Anonymous__11352)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,Vvar__1___24Anonymous__11351,Vvar__2___24Anonymous__11352)
& cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition___24a5(V0__T,V1__M,V2__cmp,V4__pivot,V5__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__M,cCoq_2eInit_2eDatatypes_2ecomparison,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11375___24a4(V0__T,V1__M,Vvar__1___24Anonymous__11351,Vvar__2___24Anonymous__11352)),happ(happ(V2__cmp,Vvar__1___24Anonymous__11351),V4__pivot),c_24__lam__11422___24a6(V0__T,V1__M,V2__cmp,V4__pivot,Vvar__1___24Anonymous__11351,Vvar__2___24Anonymous__11352)) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_det_partition.qs',axiom,
! [V0__T,V1__M,V2__cmp] : cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs___24a3(V0__T,V1__M,V2__cmp) = cCoq_2eProgram_2eWf_2eFix__sub___24a5(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__11575___24a2(V0__T,V1__M)),cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs__obligation__3___24a1(V0__T),c_24__lam__11575___24a2(V0__T,V1__M),c_24__lam__11788___24a3(V0__T,V1__M,V2__cmp)) ).
fof('$_def_QuicksortComplexity.qs_definitions.mon_nondet.partition',axiom,
! [V0__T,V1__M,V2__cmp,V4__pivot,V5__l] :
( cType___24t(V0__T)
=> ( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__T)
& cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition___24a5(V0__T,V1__M,V2__cmp,V4__pivot,V5__l) = cQuicksortComplexity_2emonads_2eret___24a3(V1__M,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11370___24a2(V0__T,V1__M)),cQuicksortComplexity_2elist__utils_2eemp___24a1(V0__T)) )
| ? [Vvar__1___24Anonymous__11812] :
( t(Vvar__1___24Anonymous__11812,V0__T)
& ? [Vvar__2___24Anonymous__11813] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,Vvar__2___24Anonymous__11813)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,Vvar__1___24Anonymous__11812,Vvar__2___24Anonymous__11813)
& cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition___24a5(V0__T,V1__M,V2__cmp,V4__pivot,V5__l) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__M,cCoq_2eInit_2eDatatypes_2ecomparison,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11375___24a4(V0__T,V1__M,Vvar__1___24Anonymous__11812,Vvar__2___24Anonymous__11813)),happ(happ(V2__cmp,Vvar__1___24Anonymous__11812),V4__pivot),c_24__lam__11881___24a6(V0__T,V1__M,V2__cmp,V4__pivot,Vvar__1___24Anonymous__11812,Vvar__2___24Anonymous__11813)) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.qs_definitions.nonmonadic.gt',axiom,
! [V0__T,V1__le,V2__x,V3__y] : cQuicksortComplexity_2eqs__definitions_2enonmonadic_2egt___24a4(V0__T,V1__le,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__le,V2__x),V3__y)) ).
fof('$_def_QuicksortComplexity.sort_order.Ec',axiom,
! [V0__e] :
( cQuicksortComplexity_2esort__order_2eE___24t(V0__e)
=> ? [Vvar__0__Ec__40240] :
( cType___24t(Vvar__0__Ec__40240)
& ? [Vvar__1__Ecmp__40241] :
( c_24__type__40214___24t(Vvar__0__Ec__40240,Vvar__1__Ecmp__40241)
& ! [Vvar__var__2__x__40247__40249] :
( t(Vvar__var__2__x__40247__40249,Vvar__0__Ec__40240)
=> ! [Vvar__var__3__y__40248__40250] :
( t(Vvar__var__3__y__40248__40250,Vvar__0__Ec__40240)
=> happ(happ(Vvar__1__Ecmp__40241,Vvar__var__2__x__40247__40249),Vvar__var__3__y__40248__40250) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vvar__1__Ecmp__40241,Vvar__var__3__y__40248__40250),Vvar__var__2__x__40247__40249)) ) )
& ! [Vvar__var__3__x__40252__40258] :
( t(Vvar__var__3__x__40252__40258,Vvar__0__Ec__40240)
=> ! [Vvar__var__4__y__40253__40259] :
( t(Vvar__var__4__y__40253__40259,Vvar__0__Ec__40240)
=> ! [Vvar__var__5__z__40255__40261] :
( t(Vvar__var__5__z__40255__40261,Vvar__0__Ec__40240)
=> ! [Vvar__var__6__c__40254__40260] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__6__c__40254__40260)
=> ( happ(happ(Vvar__1__Ecmp__40241,Vvar__var__3__x__40252__40258),Vvar__var__4__y__40253__40259) = Vvar__var__6__c__40254__40260
=> ( happ(happ(Vvar__1__Ecmp__40241,Vvar__var__4__y__40253__40259),Vvar__var__5__z__40255__40261) = Vvar__var__6__c__40254__40260
=> happ(happ(Vvar__1__Ecmp__40241,Vvar__var__3__x__40252__40258),Vvar__var__5__z__40255__40261) = Vvar__var__6__c__40254__40260 ) ) ) ) ) )
& ! [Vvar__var__4__x__40265__40271] :
( t(Vvar__var__4__x__40265__40271,Vvar__0__Ec__40240)
=> ! [Vvar__var__5__y__40266__40272] :
( t(Vvar__var__5__y__40266__40272,Vvar__0__Ec__40240)
=> ! [Vvar__var__6__z__40267__40273] :
( t(Vvar__var__6__z__40267__40273,Vvar__0__Ec__40240)
=> ! [Vvar__var__7__c__40268__40274] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__7__c__40268__40274)
=> ( happ(happ(Vvar__1__Ecmp__40241,Vvar__var__4__x__40265__40271),Vvar__var__5__y__40266__40272) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vvar__1__Ecmp__40241,Vvar__var__5__y__40266__40272),Vvar__var__6__z__40267__40273) = Vvar__var__7__c__40268__40274
=> happ(happ(Vvar__1__Ecmp__40241,Vvar__var__4__x__40265__40271),Vvar__var__6__z__40267__40273) = Vvar__var__7__c__40268__40274 ) ) ) ) ) )
& V0__e = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__40240,Vvar__1__Ecmp__40241)
& cQuicksortComplexity_2esort__order_2eEc___24a1(V0__e) = Vvar__0__Ec__40240 ) ) ) ).
fof('$_def_QuicksortComplexity.util.ext_eq',axiom,
! [V0__A,V1__B,V2__f,V3__g] :
( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__f,V3__g)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) ) ) ).
fof('$_def_QuicksortComplexity.util.id',axiom,
! [V0__X,V1__x] : cQuicksortComplexity_2eutil_2eid___24a2(V0__X,V1__x) = V1__x ).
fof('$_def_QuicksortComplexity.vec.from_list',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__11111] :
( t(Vvar__1___24Anonymous__11111,V1__A)
& ? [Vvar__2___24Anonymous__11112] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__11112)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__11111,Vvar__2___24Anonymous__11112)
& cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,V2__l) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1___24Anonymous__11111,cCoq_2eInit_2eDatatypes_2elength___24a2(V1__A,Vvar__2___24Anonymous__11112),cQuicksortComplexity_2evec_2efrom__list___24a2(V1__A,Vvar__2___24Anonymous__11112)) ) ) ) ) ) ).
fof('$_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__44382] :
( t(Vvar__1__h__44382,V1__X)
& ? [Vvar__2__n__44383] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__44383)
& ? [Vvar__3___24Anonymous__44384] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__44383,Vvar__3___24Anonymous__44384)
& V5__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__44382,Vvar__2__n__44383,Vvar__3___24Anonymous__44384)
& 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__44382),Vvar__2__n__44383,cQuicksortComplexity_2evec_2emap___24a5(V1__X,V2__Y,V3__f,Vvar__2__n__44383,Vvar__3___24Anonymous__44384)) ) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.nats',axiom,
! [V1__x,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cQuicksortComplexity_2evec_2enats___24a2(V1__x,V2__n) = cCoq_2eVectors_2eVectorDef_2enil___24a1(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__11196] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11196)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11196)
& cQuicksortComplexity_2evec_2enats___24a2(V1__x,V2__n) = cQuicksortComplexity_2evec_2emap___24a5(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,Vvar__0___24Anonymous__11196))),cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11196))),c_24__lam__11200___24a2(V1__x,Vvar__0___24Anonymous__11196),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11196),cCoq_2eVectors_2eVectorDef_2econs___24a4(cQuicksortComplexity_2enat__below_2enatBelow___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__x,Vvar__0___24Anonymous__11196))),cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(V1__x,Vvar__0___24Anonymous__11196),Vvar__0___24Anonymous__11196,cQuicksortComplexity_2evec_2enats___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__x),Vvar__0___24Anonymous__11196))) ) ) ) ).
fof('$_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__11133___24a2(V1__X,V2__n) )
| ? [Vvar__1__h__11122] :
( t(Vvar__1__h__11122,V1__X)
& ? [Vvar__2__n__11123] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__11123)
& ? [Vvar__3___24Anonymous__11124] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__11123,Vvar__3___24Anonymous__11124)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__11122,Vvar__2__n__11123,Vvar__3___24Anonymous__11124)
& cQuicksortComplexity_2evec_2enth___24a3(V1__X,V2__n,V3__v) = c_24__lam__11139___24a5(V1__X,V2__n,Vvar__1__h__11122,Vvar__2__n__11123,Vvar__3___24Anonymous__11124) ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.remove',axiom,
! [V0__T,V1__n,V2__v,V3__nb] : cQuicksortComplexity_2evec_2eremove___24a4(V0__T,V1__n,V2__v,V3__nb) = cQuicksortComplexity_2evec_2enatBelow__rect__S___24a6(c_24__lam__11160___24a2(V0__T,V1__n),c_24__lam__11167___24a2(V0__T,V1__n),c_24__lam__11186___24a2(V0__T,V1__n),V1__n,V3__nb,V2__v) ).
fof('$_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__44366] :
( t(Vvar__1__h__44366,V1__A)
& ? [Vvar__2__n__44367] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__44367)
& ? [Vvar__3___24Anonymous__44368] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__44367,Vvar__3___24Anonymous__44368)
& V2__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__44366,Vvar__2__n__44367,Vvar__3___24Anonymous__44368)
& cQuicksortComplexity_2evec_2etail___24a3(V0__n,V1__A,V2__v) = Vvar__3___24Anonymous__44368 ) ) ) ) ) ) ) ).
fof('$_def_QuicksortComplexity.vec.to_list',axiom,
! [V1__X,V2__n,V3__v] :
( cType___24t(V1__X)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,V2__n,V3__v)
=> ( ( V3__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__X)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__X) )
| ? [Vvar__1__h__11096] :
( t(Vvar__1__h__11096,V1__X)
& ? [Vvar__2__n__11097] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__11097)
& ? [Vvar__3___24Anonymous__11098] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V1__X,Vvar__2__n__11097,Vvar__3___24Anonymous__11098)
& V3__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__X,Vvar__1__h__11096,Vvar__2__n__11097,Vvar__3___24Anonymous__11098)
& cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,V2__n,V3__v) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__X,Vvar__1__h__11096,cQuicksortComplexity_2evec_2eto__list___24a3(V1__X,Vvar__2__n__11097,Vvar__3___24Anonymous__11098)) ) ) ) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__43962,Vvar__1___24Anonymous__43963,Vvar__0__P__43964,Vvar__1___24Anonymous__43965] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__43962) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__43964) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__42318,Vvar__1___24Anonymous__42319,Vvar__2___24Anonymous__42320] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__42318,Vvar__1___24Anonymous__42319,Vvar__2___24Anonymous__42320) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__176851,Vvar__1__Plt__176852,Vvar__2__Pgt__176853,Vvar__3___24Anonymous__176854,Vvar__0__Peq__176855,Vvar__1__Plt__176856,Vvar__2__Pgt__176857,Vvar__3___24Anonymous__176858] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__176851,Vvar__1__Plt__176852,Vvar__2__Pgt__176853) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__176855,Vvar__1__Plt__176856,Vvar__2__Pgt__176857) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__9] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__6463,Vvar__1___24Anonymous__6464,Vvar__0__A__6465] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__6463,Vvar__1___24Anonymous__6464) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__6465) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__21042,Vvar__1__B__21043,Vvar__2___24Anonymous__21044,Vvar__0__A__21045,Vvar__1__B__21046,Vvar__2___24Anonymous__21047] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21042,Vvar__1__B__21043,Vvar__2___24Anonymous__21044) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21045,Vvar__1__B__21046,Vvar__2___24Anonymous__21047) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__2527,Vvar__0__A__2528,Vvar__1___24Anonymous__2529,Vvar__2___24Anonymous__2530] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2527) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2528,Vvar__1___24Anonymous__2529,Vvar__2___24Anonymous__2530) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__10412,Vvar__1__B__10413,Vvar__2___24Anonymous__10414,Vvar__0__A__10415,Vvar__1__B__10416,Vvar__2___24Anonymous__10417] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10412,Vvar__1__B__10413,Vvar__2___24Anonymous__10414) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10415,Vvar__1__B__10416) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__28523,Vvar__1__B__28524,Vvar__2___24Anonymous__28525,Vvar__0__A__28526,Vvar__1__B__28527,Vvar__2___24Anonymous__28528] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28523,Vvar__1__B__28524) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28526,Vvar__1__B__28527) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13620] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13620) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__10163] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10163) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__10151,Vvar__0___24Anonymous__10152] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10151) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10152) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__107999] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__107999) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__186288,Vvar__1___24Anonymous__186289,Vvar__0__x__186290,Vvar__1__n__186291,Vvar__2___24Anonymous__186292] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__186288) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__186290,Vvar__1__n__186291) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__44314,Vvar__1___24Anonymous__44315] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44314,Vvar__1___24Anonymous__44315) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__178015,Vvar__1__lt__178016,Vvar__2__eq__178017,Vvar__3__x__178018,Vvar__4__y__178019,Vvar__5___24Anonymous__178020,Vvar__0__X__178021,Vvar__1__lt__178022,Vvar__2__eq__178023,Vvar__3__x__178024,Vvar__4__y__178025,Vvar__5___24Anonymous__178026] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__178015,Vvar__1__lt__178016,Vvar__2__eq__178017,Vvar__3__x__178018,Vvar__4__y__178019) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__178021,Vvar__1__lt__178022,Vvar__2__eq__178023,Vvar__3__x__178024,Vvar__4__y__178025) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__21163,Vvar__0__n__21164,Vvar__1___24Anonymous__21165] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21163) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21164,Vvar__1___24Anonymous__21165) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__10451,Vvar__0__A__10452,Vvar__1__h__10453,Vvar__2__n__10454,Vvar__3___24Anonymous__10455] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10451) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10452,Vvar__1__h__10453,Vvar__2__n__10454,Vvar__3___24Anonymous__10455) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__185831,Vvar__1___24Anonymous__185832,Vvar__0__C__185833,Vvar__1___24Anonymous__185834] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__185831,Vvar__1___24Anonymous__185832) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__185833,Vvar__1___24Anonymous__185834) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__65639,Vvar__1___24Anonymous__65640,Vvar__0__C__65641,Vvar__1___24Anonymous__65642,Vvar__2___24Anonymous__65643] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__65639,Vvar__1___24Anonymous__65640) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__65641,Vvar__1___24Anonymous__65642,Vvar__2___24Anonymous__65643) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__185912,Vvar__1___24Anonymous__185913] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__185912,Vvar__1___24Anonymous__185913) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__69181,Vvar__1___24Anonymous__69182,Vvar__0__C__69183,Vvar__1___24Anonymous__69184] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__69181,Vvar__1___24Anonymous__69182) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__69183,Vvar__1___24Anonymous__69184) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__71684,Vvar__1__TX__71685,Vvar__2__AA__71686,Vvar__3__AF__71687,Vvar__0__TA__71688,Vvar__1__TX__71689,Vvar__2__AA__71690,Vvar__3__AF__71691] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__71684,Vvar__1__TX__71685,Vvar__2__AA__71686,Vvar__3__AF__71687) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__71688,Vvar__1__TX__71689,Vvar__2__AA__71690,Vvar__3__AF__71691) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__186656,Vvar__0__A__186657,Vvar__1___24Anonymous__186658] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__186656) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__186657,Vvar__1___24Anonymous__186658) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__66905,Vvar__0__C__66906] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__66905) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__66906) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__23889,Vvar__0__C__23890] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__23889) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__23890) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__23533,Vvar__1___24Anonymous__23534,Vvar__0__C__23535,Vvar__1___24Anonymous__23536,Vvar__2___24Anonymous__23537] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23533,Vvar__1___24Anonymous__23534) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23535,Vvar__1___24Anonymous__23536,Vvar__2___24Anonymous__23537) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__23699,Vvar__1___24Anonymous__23700] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__23699,Vvar__1___24Anonymous__23700) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__107822,Vvar__1__req__107823,Vvar__2__reqb__107824,Vvar__3___24Anonymous__107825] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__107822,Vvar__1__req__107823,Vvar__2__reqb__107824) ).
fof('$_discrim_QuicksortComplexity.arith_lems.R_ceil_log2_S_0$QuicksortComplexity.arith_lems.R_ceil_log2_S_1',axiom,
! [Vvar__0__n__31167,Vvar__1___24Anonymous__31168,Vvar__0__n__31169,Vvar__1____x__31170,Vvar__2___24Anonymous__31171,Vvar__3____res__31172,Vvar__4___24Anonymous__31173] : cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__31167) != cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__31169,Vvar__1____x__31170,Vvar__3____res__31172,Vvar__4___24Anonymous__31173) ).
fof('$_discrim_QuicksortComplexity.arith_lems.R_floor_log2_S_0$QuicksortComplexity.arith_lems.R_floor_log2_S_1',axiom,
! [Vvar__0__n__33297,Vvar__1___24Anonymous__33298,Vvar__0__n__33299,Vvar__1__n_27__33300,Vvar__2___24Anonymous__33301,Vvar__3____res__33302,Vvar__4___24Anonymous__33303] : cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__33297) != cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__33299,Vvar__1__n_27__33300,Vvar__3____res__33302,Vvar__4___24Anonymous__33303) ).
fof('$_discrim_QuicksortComplexity.ne_list.one$QuicksortComplexity.ne_list.cons',axiom,
! [Vvar__0__T__11063,Vvar__1___24Anonymous__11064,Vvar__0__T__11065,Vvar__1___24Anonymous__11066,Vvar__2___24Anonymous__11067] : cQuicksortComplexity_2ene__list_2eone___24a2(Vvar__0__T__11063,Vvar__1___24Anonymous__11064) != cQuicksortComplexity_2ene__list_2econs___24a3(Vvar__0__T__11065,Vvar__1___24Anonymous__11066,Vvar__2___24Anonymous__11067) ).
fof('$_discrim_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_0$QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_1',axiom,
! [Vvar__0__l__185374,Vvar__1___24Anonymous__185375,Vvar__0__l__185376,Vvar__1__pivot__185377,Vvar__2__t__185378,Vvar__3___24Anonymous__185379,Vvar__4____res0__185380,Vvar__5___24Anonymous__185381,Vvar__6____res__185382,Vvar__7___24Anonymous__185383] : cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0___24a1(Vvar__0__l__185374) != cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1___24a7(Vvar__0__l__185376,Vvar__1__pivot__185377,Vvar__2__t__185378,Vvar__4____res0__185380,Vvar__5___24Anonymous__185381,Vvar__6____res__185382,Vvar__7___24Anonymous__185383) ).
fof('$_fix_11048_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__11048__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__0___24Anonymous__11049] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11049)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11049)
& c_24__fix__11048__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__11048__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__11049,Vv__CANONICAL__2)) ) ) ) ).
fof('$_fix_12068_v_CANONICAL_3',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__12068__v__CANONICAL__3___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__12072] :
( t(Vvar__1___24Anonymous__12072,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__12073] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__12073)
& Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__12072,Vvar__2___24Anonymous__12073)
& c_24__fix__12068__v__CANONICAL__3___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__12068__v__CANONICAL__3___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__12073)) ) ) ) ) ) ).
fof('$_fix_185366_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& c_24__fix__185366__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
| ? [Vvar__1___24Anonymous__185370] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__185370)
& ? [Vvar__2___24Anonymous__185371] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2___24Anonymous__185371)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__185370,Vvar__2___24Anonymous__185371)
& c_24__fix__185366__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__185370,c_24__fix__185366__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__185371,Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_fix_44537_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__44552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44552)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44552)
& ( ? [Vvar__0___24Anonymous__44556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44556)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44556)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__44537__1__add__carry___24a2(Vvar__0___24Anonymous__44552,Vvar__0___24Anonymous__44556)) )
| ? [Vvar__0___24Anonymous__44557] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44557)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44557)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__44537__1__add__carry___24a2(Vvar__0___24Anonymous__44552,Vvar__0___24Anonymous__44557)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44552)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__44558] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44558)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44558)
& ( ? [Vvar__0___24Anonymous__44562] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44562)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44562)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__44537__1__add__carry___24a2(Vvar__0___24Anonymous__44558,Vvar__0___24Anonymous__44562)) )
| ? [Vvar__0___24Anonymous__44563] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44563)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44563)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__44558,Vvar__0___24Anonymous__44563)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44558)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__44564] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44564)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44564)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44564)) )
| ? [Vvar__0___24Anonymous__44565] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44565)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44565)
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__44565)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__44537__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_fix_7645_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__7645__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__7649] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7649)
& ? [Vvar__2___24Anonymous__7650] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__7650)
& Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__7649,Vvar__2___24Anonymous__7650)
& c_24__fix__7645__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__7649),c_24__fix__7645__v__CANONICAL__2___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2___24Anonymous__7650)) ) ) ) ) ) ).
fof('$_fix_7742_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0))
& c_24__fix__7742__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__7746] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__1___24Anonymous__7746)
& ? [Vvar__2___24Anonymous__7747] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__2___24Anonymous__7747)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__7746,Vvar__2___24Anonymous__7747)
& c_24__fix__7742__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),Vvar__1___24Anonymous__7746,c_24__fix__7742__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__7747,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__43970,Vvar__0__P__43971,Vvar__1___24Anonymous__43972,Vvar__1___24Anonymous__43973] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__43970) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__43971)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__43970 = Vvar__0__P__43971 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__43966,Vvar__0__P__43967,Vvar__1___24Anonymous__43968,Vvar__1___24Anonymous__43969] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__43966) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__43967)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__43966 = Vvar__0__P__43967 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__42321,Vvar__0___24Anonymous__42322,Vvar__1___24Anonymous__42323,Vvar__1___24Anonymous__42324,Vvar__2___24Anonymous__42325,Vvar__2___24Anonymous__42326] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__42321,Vvar__1___24Anonymous__42323,Vvar__2___24Anonymous__42325) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__42322,Vvar__1___24Anonymous__42324,Vvar__2___24Anonymous__42326)
=> ( Vvar__2___24Anonymous__42325 = Vvar__2___24Anonymous__42326
& Vvar__1___24Anonymous__42323 = Vvar__1___24Anonymous__42324
& Vvar__0___24Anonymous__42321 = Vvar__0___24Anonymous__42322 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__176859,Vvar__0__Peq__176860,Vvar__1__Plt__176861,Vvar__1__Plt__176862,Vvar__2__Pgt__176863,Vvar__2__Pgt__176864,Vvar__3___24Anonymous__176865,Vvar__3___24Anonymous__176866] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__176859,Vvar__1__Plt__176861,Vvar__2__Pgt__176863) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__176860,Vvar__1__Plt__176862,Vvar__2__Pgt__176864)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__176863 = Vvar__2__Pgt__176864
& Vvar__1__Plt__176861 = Vvar__1__Plt__176862
& Vvar__0__Peq__176859 = Vvar__0__Peq__176860 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__176875,Vvar__0__Peq__176876,Vvar__1__Plt__176877,Vvar__1__Plt__176878,Vvar__2__Pgt__176879,Vvar__2__Pgt__176880,Vvar__3___24Anonymous__176881,Vvar__3___24Anonymous__176882] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__176875,Vvar__1__Plt__176877,Vvar__2__Pgt__176879) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__176876,Vvar__1__Plt__176878,Vvar__2__Pgt__176880)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__176879 = Vvar__2__Pgt__176880
& Vvar__1__Plt__176877 = Vvar__1__Plt__176878
& Vvar__0__Peq__176875 = Vvar__0__Peq__176876 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__176867,Vvar__0__Peq__176868,Vvar__1__Plt__176869,Vvar__1__Plt__176870,Vvar__2__Pgt__176871,Vvar__2__Pgt__176872,Vvar__3___24Anonymous__176873,Vvar__3___24Anonymous__176874] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__176867,Vvar__1__Plt__176869,Vvar__2__Pgt__176871) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__176868,Vvar__1__Plt__176870,Vvar__2__Pgt__176872)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__176871 = Vvar__2__Pgt__176872
& Vvar__1__Plt__176869 = Vvar__1__Plt__176870
& Vvar__0__Peq__176867 = Vvar__0__Peq__176868 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__6470,Vvar__0__A__6471] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__6470) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__6471)
=> Vvar__0__A__6470 = Vvar__0__A__6471 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__6466,Vvar__0__A__6467,Vvar__1___24Anonymous__6468,Vvar__1___24Anonymous__6469] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__6466,Vvar__1___24Anonymous__6468) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__6467,Vvar__1___24Anonymous__6469)
=> ( Vvar__1___24Anonymous__6468 = Vvar__1___24Anonymous__6469
& Vvar__0__A__6466 = Vvar__0__A__6467 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__2533,Vvar__0__A__2534,Vvar__1___24Anonymous__2535,Vvar__1___24Anonymous__2536,Vvar__2___24Anonymous__2537,Vvar__2___24Anonymous__2538] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2533,Vvar__1___24Anonymous__2535,Vvar__2___24Anonymous__2537) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2534,Vvar__1___24Anonymous__2536,Vvar__2___24Anonymous__2538)
=> ( Vvar__2___24Anonymous__2537 = Vvar__2___24Anonymous__2538
& Vvar__1___24Anonymous__2535 = Vvar__1___24Anonymous__2536
& Vvar__0__A__2533 = Vvar__0__A__2534 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__21048,Vvar__0__A__21049,Vvar__1__B__21050,Vvar__1__B__21051,Vvar__2___24Anonymous__21052,Vvar__2___24Anonymous__21053] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21048,Vvar__1__B__21050,Vvar__2___24Anonymous__21052) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21049,Vvar__1__B__21051,Vvar__2___24Anonymous__21053)
=> ( Vvar__2___24Anonymous__21052 = Vvar__2___24Anonymous__21053
& Vvar__1__B__21050 = Vvar__1__B__21051
& Vvar__0__A__21048 = Vvar__0__A__21049 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__21054,Vvar__0__A__21055,Vvar__1__B__21056,Vvar__1__B__21057,Vvar__2___24Anonymous__21058,Vvar__2___24Anonymous__21059] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21054,Vvar__1__B__21056,Vvar__2___24Anonymous__21058) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21055,Vvar__1__B__21057,Vvar__2___24Anonymous__21059)
=> ( Vvar__2___24Anonymous__21058 = Vvar__2___24Anonymous__21059
& Vvar__1__B__21056 = Vvar__1__B__21057
& Vvar__0__A__21054 = Vvar__0__A__21055 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__2531,Vvar__0__A__2532] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2531) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2532)
=> Vvar__0__A__2531 = Vvar__0__A__2532 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__24,Vvar__0__A__25,Vvar__1__B__26,Vvar__1__B__27,Vvar__2___24Anonymous__28,Vvar__2___24Anonymous__29,Vvar__3___24Anonymous__30,Vvar__3___24Anonymous__31] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__24,Vvar__1__B__26,Vvar__2___24Anonymous__28,Vvar__3___24Anonymous__30) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__25,Vvar__1__B__27,Vvar__2___24Anonymous__29,Vvar__3___24Anonymous__31)
=> ( Vvar__3___24Anonymous__30 = Vvar__3___24Anonymous__31
& Vvar__2___24Anonymous__28 = Vvar__2___24Anonymous__29
& Vvar__1__B__26 = Vvar__1__B__27
& Vvar__0__A__24 = Vvar__0__A__25 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__104,Vvar__0__A__105,Vvar__1__P__106,Vvar__1__P__107,Vvar__2__x__108,Vvar__2__x__109,Vvar__3___24Anonymous__110,Vvar__3___24Anonymous__111] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__104,Vvar__1__P__106,Vvar__2__x__108) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__105,Vvar__1__P__107,Vvar__2__x__109)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__108 = Vvar__2__x__109
& Vvar__1__P__106 = Vvar__1__P__107
& Vvar__0__A__104 = Vvar__0__A__105 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__25444,Vvar__0__A__25445,Vvar__1__P__25446,Vvar__1__P__25447,Vvar__2__Q__25448,Vvar__2__Q__25449,Vvar__3__x__25450,Vvar__3__x__25451,Vvar__4___24Anonymous__25452,Vvar__4___24Anonymous__25453,Vvar__5___24Anonymous__25454,Vvar__5___24Anonymous__25455] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__25444,Vvar__1__P__25446,Vvar__2__Q__25448,Vvar__3__x__25450) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__25445,Vvar__1__P__25447,Vvar__2__Q__25449,Vvar__3__x__25451)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__25450 = Vvar__3__x__25451
& Vvar__2__Q__25448 = Vvar__2__Q__25449
& Vvar__1__P__25446 = Vvar__1__P__25447
& Vvar__0__A__25444 = Vvar__0__A__25445 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__10382,Vvar__0__A__10383,Vvar__1__P__10384,Vvar__1__P__10385,Vvar__2__x__10386,Vvar__2__x__10387,Vvar__3___24Anonymous__10388,Vvar__3___24Anonymous__10389] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10382,Vvar__1__P__10384,Vvar__2__x__10386,Vvar__3___24Anonymous__10388) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10383,Vvar__1__P__10385,Vvar__2__x__10387,Vvar__3___24Anonymous__10389)
=> ( Vvar__3___24Anonymous__10388 = Vvar__3___24Anonymous__10389
& Vvar__2__x__10386 = Vvar__2__x__10387
& Vvar__1__P__10384 = Vvar__1__P__10385
& Vvar__0__A__10382 = Vvar__0__A__10383 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__55257,Vvar__0__A__55258,Vvar__1__P__55259,Vvar__1__P__55260,Vvar__2__Q__55261,Vvar__2__Q__55262,Vvar__3__x__55263,Vvar__3__x__55264,Vvar__4___24Anonymous__55265,Vvar__4___24Anonymous__55266,Vvar__5___24Anonymous__55267,Vvar__5___24Anonymous__55268] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__55257,Vvar__1__P__55259,Vvar__2__Q__55261,Vvar__3__x__55263,Vvar__4___24Anonymous__55265,Vvar__5___24Anonymous__55267) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__55258,Vvar__1__P__55260,Vvar__2__Q__55262,Vvar__3__x__55264,Vvar__4___24Anonymous__55266,Vvar__5___24Anonymous__55268)
=> ( Vvar__5___24Anonymous__55267 = Vvar__5___24Anonymous__55268
& Vvar__4___24Anonymous__55265 = Vvar__4___24Anonymous__55266
& Vvar__3__x__55263 = Vvar__3__x__55264
& Vvar__2__Q__55261 = Vvar__2__Q__55262
& Vvar__1__P__55259 = Vvar__1__P__55260
& Vvar__0__A__55257 = Vvar__0__A__55258 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__10418,Vvar__0__A__10419,Vvar__1__B__10420,Vvar__1__B__10421,Vvar__2___24Anonymous__10422,Vvar__2___24Anonymous__10423] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10418,Vvar__1__B__10420,Vvar__2___24Anonymous__10422) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10419,Vvar__1__B__10421,Vvar__2___24Anonymous__10423)
=> ( Vvar__2___24Anonymous__10422 = Vvar__2___24Anonymous__10423
& Vvar__1__B__10420 = Vvar__1__B__10421
& Vvar__0__A__10418 = Vvar__0__A__10419 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__10424,Vvar__0__A__10425,Vvar__1__B__10426,Vvar__1__B__10427,Vvar__2___24Anonymous__10428,Vvar__2___24Anonymous__10429] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10424,Vvar__1__B__10426) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10425,Vvar__1__B__10427)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__10426 = Vvar__1__B__10427
& Vvar__0__A__10424 = Vvar__0__A__10425 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__28529,Vvar__0__A__28530,Vvar__1__B__28531,Vvar__1__B__28532,Vvar__2___24Anonymous__28533,Vvar__2___24Anonymous__28534] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28529,Vvar__1__B__28531) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28530,Vvar__1__B__28532)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__28531 = Vvar__1__B__28532
& Vvar__0__A__28529 = Vvar__0__A__28530 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__28535,Vvar__0__A__28536,Vvar__1__B__28537,Vvar__1__B__28538,Vvar__2___24Anonymous__28539,Vvar__2___24Anonymous__28540] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28535,Vvar__1__B__28537) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28536,Vvar__1__B__28538)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__28537 = Vvar__1__B__28538
& Vvar__0__A__28535 = Vvar__0__A__28536 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__13621,Vvar__0___24Anonymous__13622] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13621) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13622)
=> Vvar__0___24Anonymous__13621 = Vvar__0___24Anonymous__13622 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__10166,Vvar__0___24Anonymous__10167] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10166) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10167)
=> Vvar__0___24Anonymous__10166 = Vvar__0___24Anonymous__10167 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__10164,Vvar__0___24Anonymous__10165] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10164) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10165)
=> Vvar__0___24Anonymous__10164 = Vvar__0___24Anonymous__10165 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__10153,Vvar__0___24Anonymous__10154] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10153) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10154)
=> Vvar__0___24Anonymous__10153 = Vvar__0___24Anonymous__10154 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__10155,Vvar__0___24Anonymous__10156] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10155) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10156)
=> Vvar__0___24Anonymous__10155 = Vvar__0___24Anonymous__10156 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__108000,Vvar__0___24Anonymous__108001] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__108000) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__108001)
=> Vvar__0___24Anonymous__108000 = Vvar__0___24Anonymous__108001 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__46842,Vvar__0__Qnum__46843,Vvar__1__Qden__46844,Vvar__1__Qden__46845] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__46842,Vvar__1__Qden__46844) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__46843,Vvar__1__Qden__46845)
=> ( Vvar__1__Qden__46844 = Vvar__1__Qden__46845
& Vvar__0__Qnum__46842 = Vvar__0__Qnum__46843 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__186069,Vvar__0__nonzero__186070,Vvar__1__cond__nonzero__186071,Vvar__1__cond__nonzero__186072] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__186069) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__186070)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__186069 = Vvar__0__nonzero__186070 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__186303,Vvar__0__x__186304,Vvar__1__n__186305,Vvar__1__n__186306,Vvar__2___24Anonymous__186307,Vvar__2___24Anonymous__186308] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__186303,Vvar__1__n__186305) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__186304,Vvar__1__n__186306)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__186305 = Vvar__1__n__186306
& Vvar__0__x__186303 = Vvar__0__x__186304 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__186293,Vvar__0__x__186294,Vvar__1___24Anonymous__186295,Vvar__1___24Anonymous__186296] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__186293) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__186294)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__186293 = Vvar__0__x__186294 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__186297,Vvar__0__x__186298,Vvar__1__n__186299,Vvar__1__n__186300,Vvar__2___24Anonymous__186301,Vvar__2___24Anonymous__186302] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__186297,Vvar__1__n__186299) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__186298,Vvar__1__n__186300)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__186299 = Vvar__1__n__186300
& Vvar__0__x__186297 = Vvar__0__x__186298 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__13524,Vvar__0___24Anonymous__13525,Vvar__1___24Anonymous__13526,Vvar__1___24Anonymous__13527,Vvar__2___24Anonymous__13528,Vvar__2___24Anonymous__13529,Vvar__3___24Anonymous__13530,Vvar__3___24Anonymous__13531,Vvar__4___24Anonymous__13532,Vvar__4___24Anonymous__13533,Vvar__5___24Anonymous__13534,Vvar__5___24Anonymous__13535,Vvar__6___24Anonymous__13536,Vvar__6___24Anonymous__13537,Vvar__7___24Anonymous__13538,Vvar__7___24Anonymous__13539] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13524,Vvar__1___24Anonymous__13526,Vvar__2___24Anonymous__13528,Vvar__3___24Anonymous__13530,Vvar__4___24Anonymous__13532,Vvar__5___24Anonymous__13534,Vvar__6___24Anonymous__13536,Vvar__7___24Anonymous__13538) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13525,Vvar__1___24Anonymous__13527,Vvar__2___24Anonymous__13529,Vvar__3___24Anonymous__13531,Vvar__4___24Anonymous__13533,Vvar__5___24Anonymous__13535,Vvar__6___24Anonymous__13537,Vvar__7___24Anonymous__13539)
=> ( Vvar__7___24Anonymous__13538 = Vvar__7___24Anonymous__13539
& Vvar__6___24Anonymous__13536 = Vvar__6___24Anonymous__13537
& Vvar__5___24Anonymous__13534 = Vvar__5___24Anonymous__13535
& Vvar__4___24Anonymous__13532 = Vvar__4___24Anonymous__13533
& Vvar__3___24Anonymous__13530 = Vvar__3___24Anonymous__13531
& Vvar__2___24Anonymous__13528 = Vvar__2___24Anonymous__13529
& Vvar__1___24Anonymous__13526 = Vvar__1___24Anonymous__13527
& Vvar__0___24Anonymous__13524 = Vvar__0___24Anonymous__13525 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__44316,Vvar__0___24Anonymous__44317,Vvar__1___24Anonymous__44318,Vvar__1___24Anonymous__44319] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44316,Vvar__1___24Anonymous__44318) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44317,Vvar__1___24Anonymous__44319)
=> ( Vvar__1___24Anonymous__44318 = Vvar__1___24Anonymous__44319
& Vvar__0___24Anonymous__44316 = Vvar__0___24Anonymous__44317 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__178039,Vvar__0__X__178040,Vvar__1__lt__178041,Vvar__1__lt__178042,Vvar__2__eq__178043,Vvar__2__eq__178044,Vvar__3__x__178045,Vvar__3__x__178046,Vvar__4__y__178047,Vvar__4__y__178048,Vvar__5___24Anonymous__178049,Vvar__5___24Anonymous__178050] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__178039,Vvar__1__lt__178041,Vvar__2__eq__178043,Vvar__3__x__178045,Vvar__4__y__178047) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__178040,Vvar__1__lt__178042,Vvar__2__eq__178044,Vvar__3__x__178046,Vvar__4__y__178048)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__178047 = Vvar__4__y__178048
& Vvar__3__x__178045 = Vvar__3__x__178046
& Vvar__2__eq__178043 = Vvar__2__eq__178044
& Vvar__1__lt__178041 = Vvar__1__lt__178042
& Vvar__0__X__178039 = Vvar__0__X__178040 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__178051,Vvar__0__X__178052,Vvar__1__lt__178053,Vvar__1__lt__178054,Vvar__2__eq__178055,Vvar__2__eq__178056,Vvar__3__x__178057,Vvar__3__x__178058,Vvar__4__y__178059,Vvar__4__y__178060,Vvar__5___24Anonymous__178061,Vvar__5___24Anonymous__178062] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__178051,Vvar__1__lt__178053,Vvar__2__eq__178055,Vvar__3__x__178057,Vvar__4__y__178059) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__178052,Vvar__1__lt__178054,Vvar__2__eq__178056,Vvar__3__x__178058,Vvar__4__y__178060)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__178059 = Vvar__4__y__178060
& Vvar__3__x__178057 = Vvar__3__x__178058
& Vvar__2__eq__178055 = Vvar__2__eq__178056
& Vvar__1__lt__178053 = Vvar__1__lt__178054
& Vvar__0__X__178051 = Vvar__0__X__178052 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__178027,Vvar__0__X__178028,Vvar__1__lt__178029,Vvar__1__lt__178030,Vvar__2__eq__178031,Vvar__2__eq__178032,Vvar__3__x__178033,Vvar__3__x__178034,Vvar__4__y__178035,Vvar__4__y__178036,Vvar__5___24Anonymous__178037,Vvar__5___24Anonymous__178038] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__178027,Vvar__1__lt__178029,Vvar__2__eq__178031,Vvar__3__x__178033,Vvar__4__y__178035) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__178028,Vvar__1__lt__178030,Vvar__2__eq__178032,Vvar__3__x__178034,Vvar__4__y__178036)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__178035 = Vvar__4__y__178036
& Vvar__3__x__178033 = Vvar__3__x__178034
& Vvar__2__eq__178031 = Vvar__2__eq__178032
& Vvar__1__lt__178029 = Vvar__1__lt__178030
& Vvar__0__X__178027 = Vvar__0__X__178028 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__21166,Vvar__0__n__21167] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21166) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21167)
=> Vvar__0__n__21166 = Vvar__0__n__21167 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__21168,Vvar__0__n__21169,Vvar__1___24Anonymous__21170,Vvar__1___24Anonymous__21171] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21168,Vvar__1___24Anonymous__21170) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21169,Vvar__1___24Anonymous__21171)
=> ( Vvar__1___24Anonymous__21170 = Vvar__1___24Anonymous__21171
& Vvar__0__n__21168 = Vvar__0__n__21169 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__10458,Vvar__0__A__10459,Vvar__1__h__10460,Vvar__1__h__10461,Vvar__2__n__10462,Vvar__2__n__10463,Vvar__3___24Anonymous__10464,Vvar__3___24Anonymous__10465] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10458,Vvar__1__h__10460,Vvar__2__n__10462,Vvar__3___24Anonymous__10464) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10459,Vvar__1__h__10461,Vvar__2__n__10463,Vvar__3___24Anonymous__10465)
=> ( Vvar__3___24Anonymous__10464 = Vvar__3___24Anonymous__10465
& Vvar__2__n__10462 = Vvar__2__n__10463
& Vvar__1__h__10460 = Vvar__1__h__10461
& Vvar__0__A__10458 = Vvar__0__A__10459 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__10456,Vvar__0__A__10457] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10456) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10457)
=> Vvar__0__A__10456 = Vvar__0__A__10457 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__183725,Vvar__0__a__183726,Vvar__1__b__183727,Vvar__1__b__183728,Vvar__2__u__183729,Vvar__2__u__183730,Vvar__3__v__183731,Vvar__3__v__183732,Vvar__4__d__183733,Vvar__4__d__183734,Vvar__5___24Anonymous__183735,Vvar__5___24Anonymous__183736,Vvar__6___24Anonymous__183737,Vvar__6___24Anonymous__183738] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__183725,Vvar__1__b__183727,Vvar__2__u__183729,Vvar__3__v__183731,Vvar__4__d__183733) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__183726,Vvar__1__b__183728,Vvar__2__u__183730,Vvar__3__v__183732,Vvar__4__d__183734)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__183733 = Vvar__4__d__183734
& Vvar__3__v__183731 = Vvar__3__v__183732
& Vvar__2__u__183729 = Vvar__2__u__183730
& Vvar__1__b__183727 = Vvar__1__b__183728
& Vvar__0__a__183725 = Vvar__0__a__183726 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__183795,Vvar__0__x__183796,Vvar__1__p__183797,Vvar__1__p__183798,Vvar__2__q__183799,Vvar__2__q__183800,Vvar__3__r__183801,Vvar__3__r__183802,Vvar__4___24Anonymous__183803,Vvar__4___24Anonymous__183804,Vvar__5___24Anonymous__183805,Vvar__5___24Anonymous__183806,Vvar__6___24Anonymous__183807,Vvar__6___24Anonymous__183808] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__183795,Vvar__1__p__183797,Vvar__2__q__183799,Vvar__3__r__183801) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__183796,Vvar__1__p__183798,Vvar__2__q__183800,Vvar__3__r__183802)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__183801 = Vvar__3__r__183802
& Vvar__2__q__183799 = Vvar__2__q__183800
& Vvar__1__p__183797 = Vvar__1__p__183798
& Vvar__0__x__183795 = Vvar__0__x__183796 ) ) ).
fof('$_inj_Coq.funind.Recdef.cmt',axiom,
! [Vvar__0__m__6630,Vvar__0__m__6631,Vvar__1__n__6632,Vvar__1__n__6633,Vvar__2__v__6634,Vvar__2__v__6635,Vvar__3___24Anonymous__6636,Vvar__3___24Anonymous__6637,Vvar__4___24Anonymous__6638,Vvar__4___24Anonymous__6639] :
( cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__6630,Vvar__1__n__6632,Vvar__2__v__6634) = cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__6631,Vvar__1__n__6633,Vvar__2__v__6635)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__v__6634 = Vvar__2__v__6635
& Vvar__1__n__6632 = Vvar__1__n__6633
& Vvar__0__m__6630 = Vvar__0__m__6631 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__185839,Vvar__0__C__185840,Vvar__1___24Anonymous__185841,Vvar__1___24Anonymous__185842] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__185839,Vvar__1___24Anonymous__185841) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__185840,Vvar__1___24Anonymous__185842)
=> ( Vvar__1___24Anonymous__185841 = Vvar__1___24Anonymous__185842
& Vvar__0__C__185839 = Vvar__0__C__185840 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__185843,Vvar__0__C__185844,Vvar__1___24Anonymous__185845,Vvar__1___24Anonymous__185846,Vvar__2___24Anonymous__185847,Vvar__2___24Anonymous__185848] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__185843,Vvar__1___24Anonymous__185845,Vvar__2___24Anonymous__185847) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__185844,Vvar__1___24Anonymous__185846,Vvar__2___24Anonymous__185848)
=> ( Vvar__2___24Anonymous__185847 = Vvar__2___24Anonymous__185848
& Vvar__1___24Anonymous__185845 = Vvar__1___24Anonymous__185846
& Vvar__0__C__185843 = Vvar__0__C__185844 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__185835,Vvar__0__C__185836,Vvar__1___24Anonymous__185837,Vvar__1___24Anonymous__185838] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__185835,Vvar__1___24Anonymous__185837) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__185836,Vvar__1___24Anonymous__185838)
=> ( Vvar__1___24Anonymous__185837 = Vvar__1___24Anonymous__185838
& Vvar__0__C__185835 = Vvar__0__C__185836 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__185855,Vvar__0__C__185856,Vvar__1___24Anonymous__185857,Vvar__1___24Anonymous__185858,Vvar__2___24Anonymous__185859,Vvar__2___24Anonymous__185860] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__185855,Vvar__1___24Anonymous__185857,Vvar__2___24Anonymous__185859) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__185856,Vvar__1___24Anonymous__185858,Vvar__2___24Anonymous__185860)
=> ( Vvar__2___24Anonymous__185859 = Vvar__2___24Anonymous__185860
& Vvar__1___24Anonymous__185857 = Vvar__1___24Anonymous__185858
& Vvar__0__C__185855 = Vvar__0__C__185856 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__185861,Vvar__0__C__185862,Vvar__1___24Anonymous__185863,Vvar__1___24Anonymous__185864] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__185861,Vvar__1___24Anonymous__185863) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__185862,Vvar__1___24Anonymous__185864)
=> ( Vvar__1___24Anonymous__185863 = Vvar__1___24Anonymous__185864
& Vvar__0__C__185861 = Vvar__0__C__185862 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__185865,Vvar__0__C__185866,Vvar__1___24Anonymous__185867,Vvar__1___24Anonymous__185868,Vvar__2___24Anonymous__185869,Vvar__2___24Anonymous__185870] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__185865,Vvar__1___24Anonymous__185867,Vvar__2___24Anonymous__185869) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__185866,Vvar__1___24Anonymous__185868,Vvar__2___24Anonymous__185870)
=> ( Vvar__2___24Anonymous__185869 = Vvar__2___24Anonymous__185870
& Vvar__1___24Anonymous__185867 = Vvar__1___24Anonymous__185868
& Vvar__0__C__185865 = Vvar__0__C__185866 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__185849,Vvar__0__C__185850,Vvar__1___24Anonymous__185851,Vvar__1___24Anonymous__185852,Vvar__2___24Anonymous__185853,Vvar__2___24Anonymous__185854] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__185849,Vvar__1___24Anonymous__185851,Vvar__2___24Anonymous__185853) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__185850,Vvar__1___24Anonymous__185852,Vvar__2___24Anonymous__185854)
=> ( Vvar__2___24Anonymous__185853 = Vvar__2___24Anonymous__185854
& Vvar__1___24Anonymous__185851 = Vvar__1___24Anonymous__185852
& Vvar__0__C__185849 = Vvar__0__C__185850 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__65654,Vvar__0__C__65655,Vvar__1___24Anonymous__65656,Vvar__1___24Anonymous__65657,Vvar__2___24Anonymous__65658,Vvar__2___24Anonymous__65659,Vvar__3___24Anonymous__65660,Vvar__3___24Anonymous__65661] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__65654,Vvar__1___24Anonymous__65656,Vvar__2___24Anonymous__65658,Vvar__3___24Anonymous__65660) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__65655,Vvar__1___24Anonymous__65657,Vvar__2___24Anonymous__65659,Vvar__3___24Anonymous__65661)
=> ( Vvar__3___24Anonymous__65660 = Vvar__3___24Anonymous__65661
& Vvar__2___24Anonymous__65658 = Vvar__2___24Anonymous__65659
& Vvar__1___24Anonymous__65656 = Vvar__1___24Anonymous__65657
& Vvar__0__C__65654 = Vvar__0__C__65655 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__65644,Vvar__0__C__65645,Vvar__1___24Anonymous__65646,Vvar__1___24Anonymous__65647] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__65644,Vvar__1___24Anonymous__65646) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__65645,Vvar__1___24Anonymous__65647)
=> ( Vvar__1___24Anonymous__65646 = Vvar__1___24Anonymous__65647
& Vvar__0__C__65644 = Vvar__0__C__65645 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__65648,Vvar__0__C__65649,Vvar__1___24Anonymous__65650,Vvar__1___24Anonymous__65651,Vvar__2___24Anonymous__65652,Vvar__2___24Anonymous__65653] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__65648,Vvar__1___24Anonymous__65650,Vvar__2___24Anonymous__65652) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__65649,Vvar__1___24Anonymous__65651,Vvar__2___24Anonymous__65653)
=> ( Vvar__2___24Anonymous__65652 = Vvar__2___24Anonymous__65653
& Vvar__1___24Anonymous__65650 = Vvar__1___24Anonymous__65651
& Vvar__0__C__65648 = Vvar__0__C__65649 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__185918,Vvar__0___24Anonymous__185919,Vvar__1___24Anonymous__185920,Vvar__1___24Anonymous__185921] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__185918,Vvar__1___24Anonymous__185920) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__185919,Vvar__1___24Anonymous__185921)
=> ( Vvar__1___24Anonymous__185920 = Vvar__1___24Anonymous__185921
& Vvar__0___24Anonymous__185918 = Vvar__0___24Anonymous__185919 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__185914,Vvar__0___24Anonymous__185915,Vvar__1___24Anonymous__185916,Vvar__1___24Anonymous__185917] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__185914,Vvar__1___24Anonymous__185916) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__185915,Vvar__1___24Anonymous__185917)
=> ( Vvar__1___24Anonymous__185916 = Vvar__1___24Anonymous__185917
& Vvar__0___24Anonymous__185914 = Vvar__0___24Anonymous__185915 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__186214,Vvar__0__r__186215] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__186214) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__186215)
=> Vvar__0__r__186214 = Vvar__0__r__186215 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__186202,Vvar__0__r1__186203,Vvar__1__r2__186204,Vvar__1__r2__186205] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__186202,Vvar__1__r2__186204) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__186203,Vvar__1__r2__186205)
=> ( Vvar__1__r2__186204 = Vvar__1__r2__186205
& Vvar__0__r1__186202 = Vvar__0__r1__186203 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__186206,Vvar__0__r1__186207,Vvar__1__r2__186208,Vvar__1__r2__186209] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__186206,Vvar__1__r2__186208) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__186207,Vvar__1__r2__186209)
=> ( Vvar__1__r2__186208 = Vvar__1__r2__186209
& Vvar__0__r1__186206 = Vvar__0__r1__186207 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__186216,Vvar__0__r__186217] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__186216) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__186217)
=> Vvar__0__r__186216 = Vvar__0__r__186217 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__186198,Vvar__0__r1__186199,Vvar__1__r2__186200,Vvar__1__r2__186201] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__186198,Vvar__1__r2__186200) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__186199,Vvar__1__r2__186201)
=> ( Vvar__1__r2__186200 = Vvar__1__r2__186201
& Vvar__0__r1__186198 = Vvar__0__r1__186199 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__186210,Vvar__0__r1__186211,Vvar__1__z__186212,Vvar__1__z__186213] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__186210,Vvar__1__z__186212) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__186211,Vvar__1__z__186213)
=> ( Vvar__1__z__186212 = Vvar__1__z__186213
& Vvar__0__r1__186210 = Vvar__0__r1__186211 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__186194,Vvar__0__r__186195] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__186194) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__186195)
=> Vvar__0__r__186194 = Vvar__0__r__186195 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__186196,Vvar__0__r__186197] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__186196) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__186197)
=> Vvar__0__r__186196 = Vvar__0__r__186197 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__69223,Vvar__0__T__69224,Vvar__1__Flhs__69225,Vvar__1__Flhs__69226,Vvar__2__Fop__69227,Vvar__2__Fop__69228,Vvar__3__Frhs__69229,Vvar__3__Frhs__69230] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__69223,Vvar__1__Flhs__69225,Vvar__2__Fop__69227,Vvar__3__Frhs__69229) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__69224,Vvar__1__Flhs__69226,Vvar__2__Fop__69228,Vvar__3__Frhs__69230)
=> ( Vvar__3__Frhs__69229 = Vvar__3__Frhs__69230
& Vvar__2__Fop__69227 = Vvar__2__Fop__69228
& Vvar__1__Flhs__69225 = Vvar__1__Flhs__69226
& Vvar__0__T__69223 = Vvar__0__T__69224 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__69205,Vvar__0__C__69206,Vvar__1___24Anonymous__69207,Vvar__1___24Anonymous__69208,Vvar__2___24Anonymous__69209,Vvar__2___24Anonymous__69210] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__69205,Vvar__1___24Anonymous__69207,Vvar__2___24Anonymous__69209) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__69206,Vvar__1___24Anonymous__69208,Vvar__2___24Anonymous__69210)
=> ( Vvar__2___24Anonymous__69209 = Vvar__2___24Anonymous__69210
& Vvar__1___24Anonymous__69207 = Vvar__1___24Anonymous__69208
& Vvar__0__C__69205 = Vvar__0__C__69206 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__69211,Vvar__0__C__69212,Vvar__1___24Anonymous__69213,Vvar__1___24Anonymous__69214] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__69211,Vvar__1___24Anonymous__69213) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__69212,Vvar__1___24Anonymous__69214)
=> ( Vvar__1___24Anonymous__69213 = Vvar__1___24Anonymous__69214
& Vvar__0__C__69211 = Vvar__0__C__69212 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__69185,Vvar__0__C__69186,Vvar__1___24Anonymous__69187,Vvar__1___24Anonymous__69188] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__69185,Vvar__1___24Anonymous__69187) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__69186,Vvar__1___24Anonymous__69188)
=> ( Vvar__1___24Anonymous__69187 = Vvar__1___24Anonymous__69188
& Vvar__0__C__69185 = Vvar__0__C__69186 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__69193,Vvar__0__C__69194,Vvar__1___24Anonymous__69195,Vvar__1___24Anonymous__69196,Vvar__2___24Anonymous__69197,Vvar__2___24Anonymous__69198] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__69193,Vvar__1___24Anonymous__69195,Vvar__2___24Anonymous__69197) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__69194,Vvar__1___24Anonymous__69196,Vvar__2___24Anonymous__69198)
=> ( Vvar__2___24Anonymous__69197 = Vvar__2___24Anonymous__69198
& Vvar__1___24Anonymous__69195 = Vvar__1___24Anonymous__69196
& Vvar__0__C__69193 = Vvar__0__C__69194 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__69199,Vvar__0__C__69200,Vvar__1___24Anonymous__69201,Vvar__1___24Anonymous__69202,Vvar__2___24Anonymous__69203,Vvar__2___24Anonymous__69204] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__69199,Vvar__1___24Anonymous__69201,Vvar__2___24Anonymous__69203) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__69200,Vvar__1___24Anonymous__69202,Vvar__2___24Anonymous__69204)
=> ( Vvar__2___24Anonymous__69203 = Vvar__2___24Anonymous__69204
& Vvar__1___24Anonymous__69201 = Vvar__1___24Anonymous__69202
& Vvar__0__C__69199 = Vvar__0__C__69200 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__69189,Vvar__0__C__69190,Vvar__1___24Anonymous__69191,Vvar__1___24Anonymous__69192] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__69189,Vvar__1___24Anonymous__69191) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__69190,Vvar__1___24Anonymous__69192)
=> ( Vvar__1___24Anonymous__69191 = Vvar__1___24Anonymous__69192
& Vvar__0__C__69189 = Vvar__0__C__69190 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__69215,Vvar__0__C__69216] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__69215) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__69216)
=> Vvar__0__C__69215 = Vvar__0__C__69216 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__71718,Vvar__0__TA__71719,Vvar__1__TX__71720,Vvar__1__TX__71721,Vvar__2__AA__71722,Vvar__2__AA__71723,Vvar__3__AF__71724,Vvar__3__AF__71725,Vvar__4___24Anonymous__71726,Vvar__4___24Anonymous__71727,Vvar__5___24Anonymous__71728,Vvar__5___24Anonymous__71729] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__71718,Vvar__1__TX__71720,Vvar__2__AA__71722,Vvar__3__AF__71724,Vvar__4___24Anonymous__71726,Vvar__5___24Anonymous__71728) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__71719,Vvar__1__TX__71721,Vvar__2__AA__71723,Vvar__3__AF__71725,Vvar__4___24Anonymous__71727,Vvar__5___24Anonymous__71729)
=> ( Vvar__5___24Anonymous__71728 = Vvar__5___24Anonymous__71729
& Vvar__4___24Anonymous__71726 = Vvar__4___24Anonymous__71727
& Vvar__3__AF__71724 = Vvar__3__AF__71725
& Vvar__2__AA__71722 = Vvar__2__AA__71723
& Vvar__1__TX__71720 = Vvar__1__TX__71721
& Vvar__0__TA__71718 = Vvar__0__TA__71719 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__71730,Vvar__0__TA__71731,Vvar__1__TX__71732,Vvar__1__TX__71733,Vvar__2__AA__71734,Vvar__2__AA__71735,Vvar__3__AF__71736,Vvar__3__AF__71737,Vvar__4___24Anonymous__71738,Vvar__4___24Anonymous__71739,Vvar__5___24Anonymous__71740,Vvar__5___24Anonymous__71741] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__71730,Vvar__1__TX__71732,Vvar__2__AA__71734,Vvar__3__AF__71736,Vvar__4___24Anonymous__71738,Vvar__5___24Anonymous__71740) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__71731,Vvar__1__TX__71733,Vvar__2__AA__71735,Vvar__3__AF__71737,Vvar__4___24Anonymous__71739,Vvar__5___24Anonymous__71741)
=> ( Vvar__5___24Anonymous__71740 = Vvar__5___24Anonymous__71741
& Vvar__4___24Anonymous__71738 = Vvar__4___24Anonymous__71739
& Vvar__3__AF__71736 = Vvar__3__AF__71737
& Vvar__2__AA__71734 = Vvar__2__AA__71735
& Vvar__1__TX__71732 = Vvar__1__TX__71733
& Vvar__0__TA__71730 = Vvar__0__TA__71731 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__71742,Vvar__0__TA__71743,Vvar__1__TX__71744,Vvar__1__TX__71745,Vvar__2__AA__71746,Vvar__2__AA__71747,Vvar__3__AF__71748,Vvar__3__AF__71749,Vvar__4___24Anonymous__71750,Vvar__4___24Anonymous__71751,Vvar__5___24Anonymous__71752,Vvar__5___24Anonymous__71753] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__71742,Vvar__1__TX__71744,Vvar__2__AA__71746,Vvar__3__AF__71748,Vvar__4___24Anonymous__71750,Vvar__5___24Anonymous__71752) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__71743,Vvar__1__TX__71745,Vvar__2__AA__71747,Vvar__3__AF__71749,Vvar__4___24Anonymous__71751,Vvar__5___24Anonymous__71753)
=> ( Vvar__5___24Anonymous__71752 = Vvar__5___24Anonymous__71753
& Vvar__4___24Anonymous__71750 = Vvar__4___24Anonymous__71751
& Vvar__3__AF__71748 = Vvar__3__AF__71749
& Vvar__2__AA__71746 = Vvar__2__AA__71747
& Vvar__1__TX__71744 = Vvar__1__TX__71745
& Vvar__0__TA__71742 = Vvar__0__TA__71743 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__71700,Vvar__0__TA__71701,Vvar__1__TX__71702,Vvar__1__TX__71703,Vvar__2__AA__71704,Vvar__2__AA__71705,Vvar__3__AF__71706,Vvar__3__AF__71707] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__71700,Vvar__1__TX__71702,Vvar__2__AA__71704,Vvar__3__AF__71706) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__71701,Vvar__1__TX__71703,Vvar__2__AA__71705,Vvar__3__AF__71707)
=> ( Vvar__3__AF__71706 = Vvar__3__AF__71707
& Vvar__2__AA__71704 = Vvar__2__AA__71705
& Vvar__1__TX__71702 = Vvar__1__TX__71703
& Vvar__0__TA__71700 = Vvar__0__TA__71701 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__71764,Vvar__0__TA__71765,Vvar__1__TX__71766,Vvar__1__TX__71767,Vvar__2__AA__71768,Vvar__2__AA__71769,Vvar__3__AF__71770,Vvar__3__AF__71771,Vvar__4___24Anonymous__71772,Vvar__4___24Anonymous__71773,Vvar__5___24Anonymous__71774,Vvar__5___24Anonymous__71775,Vvar__6___24Anonymous__71776,Vvar__6___24Anonymous__71777] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__71764,Vvar__1__TX__71766,Vvar__2__AA__71768,Vvar__3__AF__71770,Vvar__4___24Anonymous__71772,Vvar__5___24Anonymous__71774,Vvar__6___24Anonymous__71776) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__71765,Vvar__1__TX__71767,Vvar__2__AA__71769,Vvar__3__AF__71771,Vvar__4___24Anonymous__71773,Vvar__5___24Anonymous__71775,Vvar__6___24Anonymous__71777)
=> ( Vvar__6___24Anonymous__71776 = Vvar__6___24Anonymous__71777
& Vvar__5___24Anonymous__71774 = Vvar__5___24Anonymous__71775
& Vvar__4___24Anonymous__71772 = Vvar__4___24Anonymous__71773
& Vvar__3__AF__71770 = Vvar__3__AF__71771
& Vvar__2__AA__71768 = Vvar__2__AA__71769
& Vvar__1__TX__71766 = Vvar__1__TX__71767
& Vvar__0__TA__71764 = Vvar__0__TA__71765 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__71754,Vvar__0__TA__71755,Vvar__1__TX__71756,Vvar__1__TX__71757,Vvar__2__AA__71758,Vvar__2__AA__71759,Vvar__3__AF__71760,Vvar__3__AF__71761,Vvar__4___24Anonymous__71762,Vvar__4___24Anonymous__71763] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__71754,Vvar__1__TX__71756,Vvar__2__AA__71758,Vvar__3__AF__71760,Vvar__4___24Anonymous__71762) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__71755,Vvar__1__TX__71757,Vvar__2__AA__71759,Vvar__3__AF__71761,Vvar__4___24Anonymous__71763)
=> ( Vvar__4___24Anonymous__71762 = Vvar__4___24Anonymous__71763
& Vvar__3__AF__71760 = Vvar__3__AF__71761
& Vvar__2__AA__71758 = Vvar__2__AA__71759
& Vvar__1__TX__71756 = Vvar__1__TX__71757
& Vvar__0__TA__71754 = Vvar__0__TA__71755 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__71692,Vvar__0__TA__71693,Vvar__1__TX__71694,Vvar__1__TX__71695,Vvar__2__AA__71696,Vvar__2__AA__71697,Vvar__3__AF__71698,Vvar__3__AF__71699] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__71692,Vvar__1__TX__71694,Vvar__2__AA__71696,Vvar__3__AF__71698) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__71693,Vvar__1__TX__71695,Vvar__2__AA__71697,Vvar__3__AF__71699)
=> ( Vvar__3__AF__71698 = Vvar__3__AF__71699
& Vvar__2__AA__71696 = Vvar__2__AA__71697
& Vvar__1__TX__71694 = Vvar__1__TX__71695
& Vvar__0__TA__71692 = Vvar__0__TA__71693 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__71708,Vvar__0__TA__71709,Vvar__1__TX__71710,Vvar__1__TX__71711,Vvar__2__AA__71712,Vvar__2__AA__71713,Vvar__3__AF__71714,Vvar__3__AF__71715,Vvar__4___24Anonymous__71716,Vvar__4___24Anonymous__71717] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__71708,Vvar__1__TX__71710,Vvar__2__AA__71712,Vvar__3__AF__71714,Vvar__4___24Anonymous__71716) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__71709,Vvar__1__TX__71711,Vvar__2__AA__71713,Vvar__3__AF__71715,Vvar__4___24Anonymous__71717)
=> ( Vvar__4___24Anonymous__71716 = Vvar__4___24Anonymous__71717
& Vvar__3__AF__71714 = Vvar__3__AF__71715
& Vvar__2__AA__71712 = Vvar__2__AA__71713
& Vvar__1__TX__71710 = Vvar__1__TX__71711
& Vvar__0__TA__71708 = Vvar__0__TA__71709 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__186665,Vvar__0__A__186666,Vvar__1___24Anonymous__186667,Vvar__1___24Anonymous__186668,Vvar__2___24Anonymous__186669,Vvar__2___24Anonymous__186670,Vvar__3___24Anonymous__186671,Vvar__3___24Anonymous__186672] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__186665,Vvar__1___24Anonymous__186667,Vvar__2___24Anonymous__186669,Vvar__3___24Anonymous__186671) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__186666,Vvar__1___24Anonymous__186668,Vvar__2___24Anonymous__186670,Vvar__3___24Anonymous__186672)
=> ( Vvar__3___24Anonymous__186671 = Vvar__3___24Anonymous__186672
& Vvar__2___24Anonymous__186669 = Vvar__2___24Anonymous__186670
& Vvar__1___24Anonymous__186667 = Vvar__1___24Anonymous__186668
& Vvar__0__A__186665 = Vvar__0__A__186666 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__186661,Vvar__0__A__186662,Vvar__1___24Anonymous__186663,Vvar__1___24Anonymous__186664] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__186661,Vvar__1___24Anonymous__186663) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__186662,Vvar__1___24Anonymous__186664)
=> ( Vvar__1___24Anonymous__186663 = Vvar__1___24Anonymous__186664
& Vvar__0__A__186661 = Vvar__0__A__186662 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__186659,Vvar__0__A__186660] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__186659) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__186660)
=> Vvar__0__A__186659 = Vvar__0__A__186660 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__66909,Vvar__0__C__66910] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__66909) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__66910)
=> Vvar__0__C__66909 = Vvar__0__C__66910 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__66907,Vvar__0__C__66908] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__66907) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__66908)
=> Vvar__0__C__66907 = Vvar__0__C__66908 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__66915,Vvar__0__C__66916,Vvar__1___24Anonymous__66917,Vvar__1___24Anonymous__66918] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__66915,Vvar__1___24Anonymous__66917) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__66916,Vvar__1___24Anonymous__66918)
=> ( Vvar__1___24Anonymous__66917 = Vvar__1___24Anonymous__66918
& Vvar__0__C__66915 = Vvar__0__C__66916 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__66919,Vvar__0__C__66920,Vvar__1___24Anonymous__66921,Vvar__1___24Anonymous__66922,Vvar__2___24Anonymous__66923,Vvar__2___24Anonymous__66924] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__66919,Vvar__1___24Anonymous__66921,Vvar__2___24Anonymous__66923) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__66920,Vvar__1___24Anonymous__66922,Vvar__2___24Anonymous__66924)
=> ( Vvar__2___24Anonymous__66923 = Vvar__2___24Anonymous__66924
& Vvar__1___24Anonymous__66921 = Vvar__1___24Anonymous__66922
& Vvar__0__C__66919 = Vvar__0__C__66920 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__66911,Vvar__0__C__66912,Vvar__1___24Anonymous__66913,Vvar__1___24Anonymous__66914] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__66911,Vvar__1___24Anonymous__66913) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__66912,Vvar__1___24Anonymous__66914)
=> ( Vvar__1___24Anonymous__66913 = Vvar__1___24Anonymous__66914
& Vvar__0__C__66911 = Vvar__0__C__66912 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__66945,Vvar__0__C__66946,Vvar__1___24Anonymous__66947,Vvar__1___24Anonymous__66948,Vvar__2___24Anonymous__66949,Vvar__2___24Anonymous__66950] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__66945,Vvar__1___24Anonymous__66947,Vvar__2___24Anonymous__66949) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__66946,Vvar__1___24Anonymous__66948,Vvar__2___24Anonymous__66950)
=> ( Vvar__2___24Anonymous__66949 = Vvar__2___24Anonymous__66950
& Vvar__1___24Anonymous__66947 = Vvar__1___24Anonymous__66948
& Vvar__0__C__66945 = Vvar__0__C__66946 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__66941,Vvar__0__C__66942,Vvar__1___24Anonymous__66943,Vvar__1___24Anonymous__66944] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__66941,Vvar__1___24Anonymous__66943) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__66942,Vvar__1___24Anonymous__66944)
=> ( Vvar__1___24Anonymous__66943 = Vvar__1___24Anonymous__66944
& Vvar__0__C__66941 = Vvar__0__C__66942 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__66931,Vvar__0__C__66932,Vvar__1___24Anonymous__66933,Vvar__1___24Anonymous__66934,Vvar__2___24Anonymous__66935,Vvar__2___24Anonymous__66936] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__66931,Vvar__1___24Anonymous__66933,Vvar__2___24Anonymous__66935) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__66932,Vvar__1___24Anonymous__66934,Vvar__2___24Anonymous__66936)
=> ( Vvar__2___24Anonymous__66935 = Vvar__2___24Anonymous__66936
& Vvar__1___24Anonymous__66933 = Vvar__1___24Anonymous__66934
& Vvar__0__C__66931 = Vvar__0__C__66932 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__66937,Vvar__0__C__66938,Vvar__1___24Anonymous__66939,Vvar__1___24Anonymous__66940] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__66937,Vvar__1___24Anonymous__66939) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__66938,Vvar__1___24Anonymous__66940)
=> ( Vvar__1___24Anonymous__66939 = Vvar__1___24Anonymous__66940
& Vvar__0__C__66937 = Vvar__0__C__66938 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__66951,Vvar__0__C__66952,Vvar__1___24Anonymous__66953,Vvar__1___24Anonymous__66954,Vvar__2___24Anonymous__66955,Vvar__2___24Anonymous__66956] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__66951,Vvar__1___24Anonymous__66953,Vvar__2___24Anonymous__66955) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__66952,Vvar__1___24Anonymous__66954,Vvar__2___24Anonymous__66956)
=> ( Vvar__2___24Anonymous__66955 = Vvar__2___24Anonymous__66956
& Vvar__1___24Anonymous__66953 = Vvar__1___24Anonymous__66954
& Vvar__0__C__66951 = Vvar__0__C__66952 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__66925,Vvar__0__C__66926,Vvar__1___24Anonymous__66927,Vvar__1___24Anonymous__66928,Vvar__2___24Anonymous__66929,Vvar__2___24Anonymous__66930] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__66925,Vvar__1___24Anonymous__66927,Vvar__2___24Anonymous__66929) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__66926,Vvar__1___24Anonymous__66928,Vvar__2___24Anonymous__66930)
=> ( Vvar__2___24Anonymous__66929 = Vvar__2___24Anonymous__66930
& Vvar__1___24Anonymous__66927 = Vvar__1___24Anonymous__66928
& Vvar__0__C__66925 = Vvar__0__C__66926 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__67248,Vvar__0__C__67249,Vvar__1__num__67250,Vvar__1__num__67251,Vvar__2__denum__67252,Vvar__2__denum__67253,Vvar__3__condition__67254,Vvar__3__condition__67255] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__67248,Vvar__1__num__67250,Vvar__2__denum__67252,Vvar__3__condition__67254) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__67249,Vvar__1__num__67251,Vvar__2__denum__67253,Vvar__3__condition__67255)
=> ( Vvar__3__condition__67254 = Vvar__3__condition__67255
& Vvar__2__denum__67252 = Vvar__2__denum__67253
& Vvar__1__num__67250 = Vvar__1__num__67251
& Vvar__0__C__67248 = Vvar__0__C__67249 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__186007,Vvar__0__C__186008,Vvar__1__rsplit__left__186009,Vvar__1__rsplit__left__186010,Vvar__2__rsplit__common__186011,Vvar__2__rsplit__common__186012,Vvar__3__rsplit__right__186013,Vvar__3__rsplit__right__186014] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__186007,Vvar__1__rsplit__left__186009,Vvar__2__rsplit__common__186011,Vvar__3__rsplit__right__186013) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__186008,Vvar__1__rsplit__left__186010,Vvar__2__rsplit__common__186012,Vvar__3__rsplit__right__186014)
=> ( Vvar__3__rsplit__right__186013 = Vvar__3__rsplit__right__186014
& Vvar__2__rsplit__common__186011 = Vvar__2__rsplit__common__186012
& Vvar__1__rsplit__left__186009 = Vvar__1__rsplit__left__186010
& Vvar__0__C__186007 = Vvar__0__C__186008 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__23893,Vvar__0__C__23894] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__23893) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__23894)
=> Vvar__0__C__23893 = Vvar__0__C__23894 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__23891,Vvar__0__C__23892] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__23891) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__23892)
=> Vvar__0__C__23891 = Vvar__0__C__23892 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__23899,Vvar__0__C__23900,Vvar__1___24Anonymous__23901,Vvar__1___24Anonymous__23902] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__23899,Vvar__1___24Anonymous__23901) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__23900,Vvar__1___24Anonymous__23902)
=> ( Vvar__1___24Anonymous__23901 = Vvar__1___24Anonymous__23902
& Vvar__0__C__23899 = Vvar__0__C__23900 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__23903,Vvar__0__C__23904,Vvar__1___24Anonymous__23905,Vvar__1___24Anonymous__23906,Vvar__2___24Anonymous__23907,Vvar__2___24Anonymous__23908] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__23903,Vvar__1___24Anonymous__23905,Vvar__2___24Anonymous__23907) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__23904,Vvar__1___24Anonymous__23906,Vvar__2___24Anonymous__23908)
=> ( Vvar__2___24Anonymous__23907 = Vvar__2___24Anonymous__23908
& Vvar__1___24Anonymous__23905 = Vvar__1___24Anonymous__23906
& Vvar__0__C__23903 = Vvar__0__C__23904 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__23895,Vvar__0__C__23896,Vvar__1___24Anonymous__23897,Vvar__1___24Anonymous__23898] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__23895,Vvar__1___24Anonymous__23897) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__23896,Vvar__1___24Anonymous__23898)
=> ( Vvar__1___24Anonymous__23897 = Vvar__1___24Anonymous__23898
& Vvar__0__C__23895 = Vvar__0__C__23896 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__23915,Vvar__0__C__23916,Vvar__1___24Anonymous__23917,Vvar__1___24Anonymous__23918,Vvar__2___24Anonymous__23919,Vvar__2___24Anonymous__23920] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__23915,Vvar__1___24Anonymous__23917,Vvar__2___24Anonymous__23919) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__23916,Vvar__1___24Anonymous__23918,Vvar__2___24Anonymous__23920)
=> ( Vvar__2___24Anonymous__23919 = Vvar__2___24Anonymous__23920
& Vvar__1___24Anonymous__23917 = Vvar__1___24Anonymous__23918
& Vvar__0__C__23915 = Vvar__0__C__23916 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__23921,Vvar__0__C__23922,Vvar__1___24Anonymous__23923,Vvar__1___24Anonymous__23924] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__23921,Vvar__1___24Anonymous__23923) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__23922,Vvar__1___24Anonymous__23924)
=> ( Vvar__1___24Anonymous__23923 = Vvar__1___24Anonymous__23924
& Vvar__0__C__23921 = Vvar__0__C__23922 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__23925,Vvar__0__C__23926,Vvar__1___24Anonymous__23927,Vvar__1___24Anonymous__23928,Vvar__2___24Anonymous__23929,Vvar__2___24Anonymous__23930] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__23925,Vvar__1___24Anonymous__23927,Vvar__2___24Anonymous__23929) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__23926,Vvar__1___24Anonymous__23928,Vvar__2___24Anonymous__23930)
=> ( Vvar__2___24Anonymous__23929 = Vvar__2___24Anonymous__23930
& Vvar__1___24Anonymous__23927 = Vvar__1___24Anonymous__23928
& Vvar__0__C__23925 = Vvar__0__C__23926 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__23909,Vvar__0__C__23910,Vvar__1___24Anonymous__23911,Vvar__1___24Anonymous__23912,Vvar__2___24Anonymous__23913,Vvar__2___24Anonymous__23914] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__23909,Vvar__1___24Anonymous__23911,Vvar__2___24Anonymous__23913) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__23910,Vvar__1___24Anonymous__23912,Vvar__2___24Anonymous__23914)
=> ( Vvar__2___24Anonymous__23913 = Vvar__2___24Anonymous__23914
& Vvar__1___24Anonymous__23911 = Vvar__1___24Anonymous__23912
& Vvar__0__C__23909 = Vvar__0__C__23910 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__23548,Vvar__0__C__23549,Vvar__1___24Anonymous__23550,Vvar__1___24Anonymous__23551,Vvar__2___24Anonymous__23552,Vvar__2___24Anonymous__23553,Vvar__3___24Anonymous__23554,Vvar__3___24Anonymous__23555] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23548,Vvar__1___24Anonymous__23550,Vvar__2___24Anonymous__23552,Vvar__3___24Anonymous__23554) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23549,Vvar__1___24Anonymous__23551,Vvar__2___24Anonymous__23553,Vvar__3___24Anonymous__23555)
=> ( Vvar__3___24Anonymous__23554 = Vvar__3___24Anonymous__23555
& Vvar__2___24Anonymous__23552 = Vvar__2___24Anonymous__23553
& Vvar__1___24Anonymous__23550 = Vvar__1___24Anonymous__23551
& Vvar__0__C__23548 = Vvar__0__C__23549 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__23538,Vvar__0__C__23539,Vvar__1___24Anonymous__23540,Vvar__1___24Anonymous__23541] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23538,Vvar__1___24Anonymous__23540) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23539,Vvar__1___24Anonymous__23541)
=> ( Vvar__1___24Anonymous__23540 = Vvar__1___24Anonymous__23541
& Vvar__0__C__23538 = Vvar__0__C__23539 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__23542,Vvar__0__C__23543,Vvar__1___24Anonymous__23544,Vvar__1___24Anonymous__23545,Vvar__2___24Anonymous__23546,Vvar__2___24Anonymous__23547] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23542,Vvar__1___24Anonymous__23544,Vvar__2___24Anonymous__23546) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23543,Vvar__1___24Anonymous__23545,Vvar__2___24Anonymous__23547)
=> ( Vvar__2___24Anonymous__23546 = Vvar__2___24Anonymous__23547
& Vvar__1___24Anonymous__23544 = Vvar__1___24Anonymous__23545
& Vvar__0__C__23542 = Vvar__0__C__23543 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__23705,Vvar__0___24Anonymous__23706,Vvar__1___24Anonymous__23707,Vvar__1___24Anonymous__23708] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__23705,Vvar__1___24Anonymous__23707) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__23706,Vvar__1___24Anonymous__23708)
=> ( Vvar__1___24Anonymous__23707 = Vvar__1___24Anonymous__23708
& Vvar__0___24Anonymous__23705 = Vvar__0___24Anonymous__23706 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__23701,Vvar__0___24Anonymous__23702,Vvar__1___24Anonymous__23703,Vvar__1___24Anonymous__23704] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__23701,Vvar__1___24Anonymous__23703) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__23702,Vvar__1___24Anonymous__23704)
=> ( Vvar__1___24Anonymous__23703 = Vvar__1___24Anonymous__23704
& Vvar__0___24Anonymous__23701 = Vvar__0___24Anonymous__23702 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__107826,Vvar__0__R__107827,Vvar__1__req__107828,Vvar__1__req__107829,Vvar__2__reqb__107830,Vvar__2__reqb__107831,Vvar__3___24Anonymous__107832,Vvar__3___24Anonymous__107833] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__107826,Vvar__1__req__107828,Vvar__2__reqb__107830) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__107827,Vvar__1__req__107829,Vvar__2__reqb__107831)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__107830 = Vvar__2__reqb__107831
& Vvar__1__req__107828 = Vvar__1__req__107829
& Vvar__0__R__107826 = Vvar__0__R__107827 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__107834,Vvar__0__R__107835,Vvar__1__rO__107836,Vvar__1__rO__107837,Vvar__2__rI__107838,Vvar__2__rI__107839,Vvar__3__radd__107840,Vvar__3__radd__107841,Vvar__4__rmul__107842,Vvar__4__rmul__107843,Vvar__5__rsub__107844,Vvar__5__rsub__107845,Vvar__6__ropp__107846,Vvar__6__ropp__107847,Vvar__7__req__107848,Vvar__7__req__107849,Vvar__8__C__107850,Vvar__8__C__107851,Vvar__9__cO__107852,Vvar__9__cO__107853,Vvar__10__cI__107854,Vvar__10__cI__107855,Vvar__11__cadd__107856,Vvar__11__cadd__107857,Vvar__12__cmul__107858,Vvar__12__cmul__107859,Vvar__13__csub__107860,Vvar__13__csub__107861,Vvar__14__copp__107862,Vvar__14__copp__107863,Vvar__15__ceqb__107864,Vvar__15__ceqb__107865,Vvar__16__phi__107866,Vvar__16__phi__107867,Vvar__17___24Anonymous__107868,Vvar__17___24Anonymous__107869] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__107834,Vvar__1__rO__107836,Vvar__2__rI__107838,Vvar__3__radd__107840,Vvar__4__rmul__107842,Vvar__5__rsub__107844,Vvar__6__ropp__107846,Vvar__7__req__107848,Vvar__8__C__107850,Vvar__9__cO__107852,Vvar__10__cI__107854,Vvar__11__cadd__107856,Vvar__12__cmul__107858,Vvar__13__csub__107860,Vvar__14__copp__107862,Vvar__15__ceqb__107864,Vvar__16__phi__107866) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__107835,Vvar__1__rO__107837,Vvar__2__rI__107839,Vvar__3__radd__107841,Vvar__4__rmul__107843,Vvar__5__rsub__107845,Vvar__6__ropp__107847,Vvar__7__req__107849,Vvar__8__C__107851,Vvar__9__cO__107853,Vvar__10__cI__107855,Vvar__11__cadd__107857,Vvar__12__cmul__107859,Vvar__13__csub__107861,Vvar__14__copp__107863,Vvar__15__ceqb__107865,Vvar__16__phi__107867)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__107866 = Vvar__16__phi__107867
& Vvar__15__ceqb__107864 = Vvar__15__ceqb__107865
& Vvar__14__copp__107862 = Vvar__14__copp__107863
& Vvar__13__csub__107860 = Vvar__13__csub__107861
& Vvar__12__cmul__107858 = Vvar__12__cmul__107859
& Vvar__11__cadd__107856 = Vvar__11__cadd__107857
& Vvar__10__cI__107854 = Vvar__10__cI__107855
& Vvar__9__cO__107852 = Vvar__9__cO__107853
& Vvar__8__C__107850 = Vvar__8__C__107851
& Vvar__7__req__107848 = Vvar__7__req__107849
& Vvar__6__ropp__107846 = Vvar__6__ropp__107847
& Vvar__5__rsub__107844 = Vvar__5__rsub__107845
& Vvar__4__rmul__107842 = Vvar__4__rmul__107843
& Vvar__3__radd__107840 = Vvar__3__radd__107841
& Vvar__2__rI__107838 = Vvar__2__rI__107839
& Vvar__1__rO__107836 = Vvar__1__rO__107837
& Vvar__0__R__107834 = Vvar__0__R__107835 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_ceil_log2_S_0',axiom,
! [Vvar__0__n__31174,Vvar__0__n__31175,Vvar__1___24Anonymous__31176,Vvar__1___24Anonymous__31177] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__31174) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__31175)
=> ( c_24Proof = c_24Proof
& Vvar__0__n__31174 = Vvar__0__n__31175 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_ceil_log2_S_1',axiom,
! [Vvar__0__n__31178,Vvar__0__n__31179,Vvar__1____x__31180,Vvar__1____x__31181,Vvar__2___24Anonymous__31182,Vvar__2___24Anonymous__31183,Vvar__3____res__31184,Vvar__3____res__31185,Vvar__4___24Anonymous__31186,Vvar__4___24Anonymous__31187] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__31178,Vvar__1____x__31180,Vvar__3____res__31184,Vvar__4___24Anonymous__31186) = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__31179,Vvar__1____x__31181,Vvar__3____res__31185,Vvar__4___24Anonymous__31187)
=> ( Vvar__4___24Anonymous__31186 = Vvar__4___24Anonymous__31187
& Vvar__3____res__31184 = Vvar__3____res__31185
& c_24Proof = c_24Proof
& Vvar__1____x__31180 = Vvar__1____x__31181
& Vvar__0__n__31178 = Vvar__0__n__31179 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_floor_log2_S_0',axiom,
! [Vvar__0__n__33304,Vvar__0__n__33305,Vvar__1___24Anonymous__33306,Vvar__1___24Anonymous__33307] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__33304) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__33305)
=> ( c_24Proof = c_24Proof
& Vvar__0__n__33304 = Vvar__0__n__33305 ) ) ).
fof('$_inj_QuicksortComplexity.arith_lems.R_floor_log2_S_1',axiom,
! [Vvar__0__n__33308,Vvar__0__n__33309,Vvar__1__n_27__33310,Vvar__1__n_27__33311,Vvar__2___24Anonymous__33312,Vvar__2___24Anonymous__33313,Vvar__3____res__33314,Vvar__3____res__33315,Vvar__4___24Anonymous__33316,Vvar__4___24Anonymous__33317] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__33308,Vvar__1__n_27__33310,Vvar__3____res__33314,Vvar__4___24Anonymous__33316) = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__33309,Vvar__1__n_27__33311,Vvar__3____res__33315,Vvar__4___24Anonymous__33317)
=> ( Vvar__4___24Anonymous__33316 = Vvar__4___24Anonymous__33317
& Vvar__3____res__33314 = Vvar__3____res__33315
& c_24Proof = c_24Proof
& Vvar__1__n_27__33310 = Vvar__1__n_27__33311
& Vvar__0__n__33308 = Vvar__0__n__33309 ) ) ).
fof('$_inj_QuicksortComplexity.monads.Build_Functor',axiom,
! [Vvar__0__func__38675,Vvar__0__func__38676,Vvar__1__func__map__38677,Vvar__1__func__map__38678,Vvar__2__func__id__38679,Vvar__2__func__id__38680,Vvar__3__func__assoc__38681,Vvar__3__func__assoc__38682] :
( cQuicksortComplexity_2emonads_2eBuild__Functor___24a2(Vvar__0__func__38675,Vvar__1__func__map__38677) = cQuicksortComplexity_2emonads_2eBuild__Functor___24a2(Vvar__0__func__38676,Vvar__1__func__map__38678)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__func__map__38677 = Vvar__1__func__map__38678
& Vvar__0__func__38675 = Vvar__0__func__38676 ) ) ).
fof('$_inj_QuicksortComplexity.monads.Build_Monad',axiom,
! [Vvar__0__mon__279,Vvar__0__mon__280,Vvar__1__bind__281,Vvar__1__bind__282,Vvar__2__ret__283,Vvar__2__ret__284,Vvar__3__mon__lunit__285,Vvar__3__mon__lunit__286,Vvar__4__mon__runit__287,Vvar__4__mon__runit__288,Vvar__5__mon__assoc__289,Vvar__5__mon__assoc__290] :
( cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__279,Vvar__1__bind__281,Vvar__2__ret__283) = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__280,Vvar__1__bind__282,Vvar__2__ret__284)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__ret__283 = Vvar__2__ret__284
& Vvar__1__bind__281 = Vvar__1__bind__282
& Vvar__0__mon__279 = Vvar__0__mon__280 ) ) ).
fof('$_inj_QuicksortComplexity.monads.Build_MonadTrans',axiom,
! [Vvar__0__transMonad__39776,Vvar__0__transMonad__39777,Vvar__1__lift__39778,Vvar__1__lift__39779] :
( cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(Vvar__0__transMonad__39776,Vvar__1__lift__39778) = cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(Vvar__0__transMonad__39777,Vvar__1__lift__39779)
=> ( Vvar__1__lift__39778 = Vvar__1__lift__39779
& Vvar__0__transMonad__39776 = Vvar__0__transMonad__39777 ) ) ).
fof('$_inj_QuicksortComplexity.monoid_monad_trans.Build_Monoid',axiom,
! [Vvar__0__monoid__type__39913,Vvar__0__monoid__type__39914,Vvar__1__monoid__zero__39915,Vvar__1__monoid__zero__39916,Vvar__2__monoid__mult__39917,Vvar__2__monoid__mult__39918,Vvar__3__monoid__lunit__39919,Vvar__3__monoid__lunit__39920,Vvar__4__monoid__runit__39921,Vvar__4__monoid__runit__39922,Vvar__5__monoid__assoc__39923,Vvar__5__monoid__assoc__39924] :
( cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__39913,Vvar__1__monoid__zero__39915,Vvar__2__monoid__mult__39917) = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__39914,Vvar__1__monoid__zero__39916,Vvar__2__monoid__mult__39918)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__monoid__mult__39917 = Vvar__2__monoid__mult__39918
& Vvar__1__monoid__zero__39915 = Vvar__1__monoid__zero__39916
& Vvar__0__monoid__type__39913 = Vvar__0__monoid__type__39914 ) ) ).
fof('$_inj_QuicksortComplexity.nat_below.mkNatBelow',axiom,
! [Vvar__0__v__11052,Vvar__0__v__11053,Vvar__1__p__11054,Vvar__1__p__11055] :
( cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__11052,Vvar__1__p__11054) = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__11053,Vvar__1__p__11055)
=> ( Vvar__1__p__11054 = Vvar__1__p__11055
& Vvar__0__v__11052 = Vvar__0__v__11053 ) ) ).
fof('$_inj_QuicksortComplexity.ne_list.cons',axiom,
! [Vvar__0__T__11072,Vvar__0__T__11073,Vvar__1___24Anonymous__11074,Vvar__1___24Anonymous__11075,Vvar__2___24Anonymous__11076,Vvar__2___24Anonymous__11077] :
( cQuicksortComplexity_2ene__list_2econs___24a3(Vvar__0__T__11072,Vvar__1___24Anonymous__11074,Vvar__2___24Anonymous__11076) = cQuicksortComplexity_2ene__list_2econs___24a3(Vvar__0__T__11073,Vvar__1___24Anonymous__11075,Vvar__2___24Anonymous__11077)
=> ( Vvar__2___24Anonymous__11076 = Vvar__2___24Anonymous__11077
& Vvar__1___24Anonymous__11074 = Vvar__1___24Anonymous__11075
& Vvar__0__T__11072 = Vvar__0__T__11073 ) ) ).
fof('$_inj_QuicksortComplexity.ne_list.one',axiom,
! [Vvar__0__T__11068,Vvar__0__T__11069,Vvar__1___24Anonymous__11070,Vvar__1___24Anonymous__11071] :
( cQuicksortComplexity_2ene__list_2eone___24a2(Vvar__0__T__11068,Vvar__1___24Anonymous__11070) = cQuicksortComplexity_2ene__list_2eone___24a2(Vvar__0__T__11069,Vvar__1___24Anonymous__11071)
=> ( Vvar__1___24Anonymous__11070 = Vvar__1___24Anonymous__11071
& Vvar__0__T__11068 = Vvar__0__T__11069 ) ) ).
fof('$_inj_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_0',axiom,
! [Vvar__0__l__185384,Vvar__0__l__185385,Vvar__1___24Anonymous__185386,Vvar__1___24Anonymous__185387] :
( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0___24a1(Vvar__0__l__185384) = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0___24a1(Vvar__0__l__185385)
=> ( c_24Proof = c_24Proof
& Vvar__0__l__185384 = Vvar__0__l__185385 ) ) ).
fof('$_inj_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_1',axiom,
! [Vvar__0__l__185388,Vvar__0__l__185389,Vvar__1__pivot__185390,Vvar__1__pivot__185391,Vvar__2__t__185392,Vvar__2__t__185393,Vvar__3___24Anonymous__185394,Vvar__3___24Anonymous__185395,Vvar__4____res0__185396,Vvar__4____res0__185397,Vvar__5___24Anonymous__185398,Vvar__5___24Anonymous__185399,Vvar__6____res__185400,Vvar__6____res__185401,Vvar__7___24Anonymous__185402,Vvar__7___24Anonymous__185403] :
( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1___24a7(Vvar__0__l__185388,Vvar__1__pivot__185390,Vvar__2__t__185392,Vvar__4____res0__185396,Vvar__5___24Anonymous__185398,Vvar__6____res__185400,Vvar__7___24Anonymous__185402) = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1___24a7(Vvar__0__l__185389,Vvar__1__pivot__185391,Vvar__2__t__185393,Vvar__4____res0__185397,Vvar__5___24Anonymous__185399,Vvar__6____res__185401,Vvar__7___24Anonymous__185403)
=> ( Vvar__7___24Anonymous__185402 = Vvar__7___24Anonymous__185403
& Vvar__6____res__185400 = Vvar__6____res__185401
& Vvar__5___24Anonymous__185398 = Vvar__5___24Anonymous__185399
& Vvar__4____res0__185396 = Vvar__4____res0__185397
& c_24Proof = c_24Proof
& Vvar__2__t__185392 = Vvar__2__t__185393
& Vvar__1__pivot__185390 = Vvar__1__pivot__185391
& Vvar__0__l__185388 = Vvar__0__l__185389 ) ) ).
fof('$_inj_QuicksortComplexity.sort_order.Build_E',axiom,
! [Vvar__0__Ec__40230,Vvar__0__Ec__40231,Vvar__1__Ecmp__40232,Vvar__1__Ecmp__40233,Vvar__2__Ecmp__sym__40234,Vvar__2__Ecmp__sym__40235,Vvar__3__Ecmp__trans__40236,Vvar__3__Ecmp__trans__40237,Vvar__4__Ecmp__eq__trans__l__40238,Vvar__4__Ecmp__eq__trans__l__40239] :
( cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__40230,Vvar__1__Ecmp__40232) = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__40231,Vvar__1__Ecmp__40233)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__Ecmp__40232 = Vvar__1__Ecmp__40233
& Vvar__0__Ec__40230 = Vvar__0__Ec__40231 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__43927,Vvar__1__k__43929,Vvar__2___24Anonymous__43930] :
( c_24__type__43944___24t(Vvar__0__P__43927,Vvar__1__k__43929,Vvar__2___24Anonymous__43930,Vvar__0__P__43927)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__43929)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__43930)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__43927,Vvar__1__k__43929,Vvar__2___24Anonymous__43930)
=> ( Vvar__2___24Anonymous__43930 = Vvar__1__k__43929
| ? [Vvar__2__l__43938] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__43938)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__43927,Vvar__1__k__43929,Vvar__2__l__43938)
& p(happ(Vvar__0__P__43927,Vvar__2__l__43938))
& Vvar__2___24Anonymous__43930 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__43938) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__21150] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21150)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__21150)
=> ( Vvar__0___24Anonymous__21150 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__21152] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21152)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__21152)
& Vvar__0___24Anonymous__21150 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21152) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__21154] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21154)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__21154)
=> ? [Vvar__0__n__21156] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21156)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__21156)
& Vvar__0___24Anonymous__21154 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21156) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__43952,Vvar__1___24Anonymous__43953,VX43954] :
( cProp___24t(Vvar__0__P__43952)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__43953)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__43952,Vvar__1___24Anonymous__43953,VX43954)
=> ( ( p(Vvar__0__P__43952)
& Vvar__1___24Anonymous__43953 = cCoq_2eInit_2eDatatypes_2etrue
& VX43954 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__43952) )
| ( ~ p(Vvar__0__P__43952)
& Vvar__1___24Anonymous__43953 = cCoq_2eInit_2eDatatypes_2efalse
& VX43954 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__43952) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX42314] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX42314)
=> ( VX42314 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__42315] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__42315)
& ? [Vvar__1___24Anonymous__42316] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__42316)
& ? [Vvar__2___24Anonymous__42317] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__42317)
& VX42314 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__42315,Vvar__1___24Anonymous__42316,Vvar__2___24Anonymous__42317) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX43974] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX43974)
=> ( VX43974 = cCoq_2eInit_2eByte_2ex00
| VX43974 = cCoq_2eInit_2eByte_2ex01
| VX43974 = cCoq_2eInit_2eByte_2ex02
| VX43974 = cCoq_2eInit_2eByte_2ex03
| VX43974 = cCoq_2eInit_2eByte_2ex04
| VX43974 = cCoq_2eInit_2eByte_2ex05
| VX43974 = cCoq_2eInit_2eByte_2ex06
| VX43974 = cCoq_2eInit_2eByte_2ex07
| VX43974 = cCoq_2eInit_2eByte_2ex08
| VX43974 = cCoq_2eInit_2eByte_2ex09
| VX43974 = cCoq_2eInit_2eByte_2ex0a
| VX43974 = cCoq_2eInit_2eByte_2ex0b
| VX43974 = cCoq_2eInit_2eByte_2ex0c
| VX43974 = cCoq_2eInit_2eByte_2ex0d
| VX43974 = cCoq_2eInit_2eByte_2ex0e
| VX43974 = cCoq_2eInit_2eByte_2ex0f
| VX43974 = cCoq_2eInit_2eByte_2ex10
| VX43974 = cCoq_2eInit_2eByte_2ex11
| VX43974 = cCoq_2eInit_2eByte_2ex12
| VX43974 = cCoq_2eInit_2eByte_2ex13
| VX43974 = cCoq_2eInit_2eByte_2ex14
| VX43974 = cCoq_2eInit_2eByte_2ex15
| VX43974 = cCoq_2eInit_2eByte_2ex16
| VX43974 = cCoq_2eInit_2eByte_2ex17
| VX43974 = cCoq_2eInit_2eByte_2ex18
| VX43974 = cCoq_2eInit_2eByte_2ex19
| VX43974 = cCoq_2eInit_2eByte_2ex1a
| VX43974 = cCoq_2eInit_2eByte_2ex1b
| VX43974 = cCoq_2eInit_2eByte_2ex1c
| VX43974 = cCoq_2eInit_2eByte_2ex1d
| VX43974 = cCoq_2eInit_2eByte_2ex1e
| VX43974 = cCoq_2eInit_2eByte_2ex1f
| VX43974 = cCoq_2eInit_2eByte_2ex20
| VX43974 = cCoq_2eInit_2eByte_2ex21
| VX43974 = cCoq_2eInit_2eByte_2ex22
| VX43974 = cCoq_2eInit_2eByte_2ex23
| VX43974 = cCoq_2eInit_2eByte_2ex24
| VX43974 = cCoq_2eInit_2eByte_2ex25
| VX43974 = cCoq_2eInit_2eByte_2ex26
| VX43974 = cCoq_2eInit_2eByte_2ex27
| VX43974 = cCoq_2eInit_2eByte_2ex28
| VX43974 = cCoq_2eInit_2eByte_2ex29
| VX43974 = cCoq_2eInit_2eByte_2ex2a
| VX43974 = cCoq_2eInit_2eByte_2ex2b
| VX43974 = cCoq_2eInit_2eByte_2ex2c
| VX43974 = cCoq_2eInit_2eByte_2ex2d
| VX43974 = cCoq_2eInit_2eByte_2ex2e
| VX43974 = cCoq_2eInit_2eByte_2ex2f
| VX43974 = cCoq_2eInit_2eByte_2ex30
| VX43974 = cCoq_2eInit_2eByte_2ex31
| VX43974 = cCoq_2eInit_2eByte_2ex32
| VX43974 = cCoq_2eInit_2eByte_2ex33
| VX43974 = cCoq_2eInit_2eByte_2ex34
| VX43974 = cCoq_2eInit_2eByte_2ex35
| VX43974 = cCoq_2eInit_2eByte_2ex36
| VX43974 = cCoq_2eInit_2eByte_2ex37
| VX43974 = cCoq_2eInit_2eByte_2ex38
| VX43974 = cCoq_2eInit_2eByte_2ex39
| VX43974 = cCoq_2eInit_2eByte_2ex3a
| VX43974 = cCoq_2eInit_2eByte_2ex3b
| VX43974 = cCoq_2eInit_2eByte_2ex3c
| VX43974 = cCoq_2eInit_2eByte_2ex3d
| VX43974 = cCoq_2eInit_2eByte_2ex3e
| VX43974 = cCoq_2eInit_2eByte_2ex3f
| VX43974 = cCoq_2eInit_2eByte_2ex40
| VX43974 = cCoq_2eInit_2eByte_2ex41
| VX43974 = cCoq_2eInit_2eByte_2ex42
| VX43974 = cCoq_2eInit_2eByte_2ex43
| VX43974 = cCoq_2eInit_2eByte_2ex44
| VX43974 = cCoq_2eInit_2eByte_2ex45
| VX43974 = cCoq_2eInit_2eByte_2ex46
| VX43974 = cCoq_2eInit_2eByte_2ex47
| VX43974 = cCoq_2eInit_2eByte_2ex48
| VX43974 = cCoq_2eInit_2eByte_2ex49
| VX43974 = cCoq_2eInit_2eByte_2ex4a
| VX43974 = cCoq_2eInit_2eByte_2ex4b
| VX43974 = cCoq_2eInit_2eByte_2ex4c
| VX43974 = cCoq_2eInit_2eByte_2ex4d
| VX43974 = cCoq_2eInit_2eByte_2ex4e
| VX43974 = cCoq_2eInit_2eByte_2ex4f
| VX43974 = cCoq_2eInit_2eByte_2ex50
| VX43974 = cCoq_2eInit_2eByte_2ex51
| VX43974 = cCoq_2eInit_2eByte_2ex52
| VX43974 = cCoq_2eInit_2eByte_2ex53
| VX43974 = cCoq_2eInit_2eByte_2ex54
| VX43974 = cCoq_2eInit_2eByte_2ex55
| VX43974 = cCoq_2eInit_2eByte_2ex56
| VX43974 = cCoq_2eInit_2eByte_2ex57
| VX43974 = cCoq_2eInit_2eByte_2ex58
| VX43974 = cCoq_2eInit_2eByte_2ex59
| VX43974 = cCoq_2eInit_2eByte_2ex5a
| VX43974 = cCoq_2eInit_2eByte_2ex5b
| VX43974 = cCoq_2eInit_2eByte_2ex5c
| VX43974 = cCoq_2eInit_2eByte_2ex5d
| VX43974 = cCoq_2eInit_2eByte_2ex5e
| VX43974 = cCoq_2eInit_2eByte_2ex5f
| VX43974 = cCoq_2eInit_2eByte_2ex60
| VX43974 = cCoq_2eInit_2eByte_2ex61
| VX43974 = cCoq_2eInit_2eByte_2ex62
| VX43974 = cCoq_2eInit_2eByte_2ex63
| VX43974 = cCoq_2eInit_2eByte_2ex64
| VX43974 = cCoq_2eInit_2eByte_2ex65
| VX43974 = cCoq_2eInit_2eByte_2ex66
| VX43974 = cCoq_2eInit_2eByte_2ex67
| VX43974 = cCoq_2eInit_2eByte_2ex68
| VX43974 = cCoq_2eInit_2eByte_2ex69
| VX43974 = cCoq_2eInit_2eByte_2ex6a
| VX43974 = cCoq_2eInit_2eByte_2ex6b
| VX43974 = cCoq_2eInit_2eByte_2ex6c
| VX43974 = cCoq_2eInit_2eByte_2ex6d
| VX43974 = cCoq_2eInit_2eByte_2ex6e
| VX43974 = cCoq_2eInit_2eByte_2ex6f
| VX43974 = cCoq_2eInit_2eByte_2ex70
| VX43974 = cCoq_2eInit_2eByte_2ex71
| VX43974 = cCoq_2eInit_2eByte_2ex72
| VX43974 = cCoq_2eInit_2eByte_2ex73
| VX43974 = cCoq_2eInit_2eByte_2ex74
| VX43974 = cCoq_2eInit_2eByte_2ex75
| VX43974 = cCoq_2eInit_2eByte_2ex76
| VX43974 = cCoq_2eInit_2eByte_2ex77
| VX43974 = cCoq_2eInit_2eByte_2ex78
| VX43974 = cCoq_2eInit_2eByte_2ex79
| VX43974 = cCoq_2eInit_2eByte_2ex7a
| VX43974 = cCoq_2eInit_2eByte_2ex7b
| VX43974 = cCoq_2eInit_2eByte_2ex7c
| VX43974 = cCoq_2eInit_2eByte_2ex7d
| VX43974 = cCoq_2eInit_2eByte_2ex7e
| VX43974 = cCoq_2eInit_2eByte_2ex7f
| VX43974 = cCoq_2eInit_2eByte_2ex80
| VX43974 = cCoq_2eInit_2eByte_2ex81
| VX43974 = cCoq_2eInit_2eByte_2ex82
| VX43974 = cCoq_2eInit_2eByte_2ex83
| VX43974 = cCoq_2eInit_2eByte_2ex84
| VX43974 = cCoq_2eInit_2eByte_2ex85
| VX43974 = cCoq_2eInit_2eByte_2ex86
| VX43974 = cCoq_2eInit_2eByte_2ex87
| VX43974 = cCoq_2eInit_2eByte_2ex88
| VX43974 = cCoq_2eInit_2eByte_2ex89
| VX43974 = cCoq_2eInit_2eByte_2ex8a
| VX43974 = cCoq_2eInit_2eByte_2ex8b
| VX43974 = cCoq_2eInit_2eByte_2ex8c
| VX43974 = cCoq_2eInit_2eByte_2ex8d
| VX43974 = cCoq_2eInit_2eByte_2ex8e
| VX43974 = cCoq_2eInit_2eByte_2ex8f
| VX43974 = cCoq_2eInit_2eByte_2ex90
| VX43974 = cCoq_2eInit_2eByte_2ex91
| VX43974 = cCoq_2eInit_2eByte_2ex92
| VX43974 = cCoq_2eInit_2eByte_2ex93
| VX43974 = cCoq_2eInit_2eByte_2ex94
| VX43974 = cCoq_2eInit_2eByte_2ex95
| VX43974 = cCoq_2eInit_2eByte_2ex96
| VX43974 = cCoq_2eInit_2eByte_2ex97
| VX43974 = cCoq_2eInit_2eByte_2ex98
| VX43974 = cCoq_2eInit_2eByte_2ex99
| VX43974 = cCoq_2eInit_2eByte_2ex9a
| VX43974 = cCoq_2eInit_2eByte_2ex9b
| VX43974 = cCoq_2eInit_2eByte_2ex9c
| VX43974 = cCoq_2eInit_2eByte_2ex9d
| VX43974 = cCoq_2eInit_2eByte_2ex9e
| VX43974 = cCoq_2eInit_2eByte_2ex9f
| VX43974 = cCoq_2eInit_2eByte_2exa0
| VX43974 = cCoq_2eInit_2eByte_2exa1
| VX43974 = cCoq_2eInit_2eByte_2exa2
| VX43974 = cCoq_2eInit_2eByte_2exa3
| VX43974 = cCoq_2eInit_2eByte_2exa4
| VX43974 = cCoq_2eInit_2eByte_2exa5
| VX43974 = cCoq_2eInit_2eByte_2exa6
| VX43974 = cCoq_2eInit_2eByte_2exa7
| VX43974 = cCoq_2eInit_2eByte_2exa8
| VX43974 = cCoq_2eInit_2eByte_2exa9
| VX43974 = cCoq_2eInit_2eByte_2exaa
| VX43974 = cCoq_2eInit_2eByte_2exab
| VX43974 = cCoq_2eInit_2eByte_2exac
| VX43974 = cCoq_2eInit_2eByte_2exad
| VX43974 = cCoq_2eInit_2eByte_2exae
| VX43974 = cCoq_2eInit_2eByte_2exaf
| VX43974 = cCoq_2eInit_2eByte_2exb0
| VX43974 = cCoq_2eInit_2eByte_2exb1
| VX43974 = cCoq_2eInit_2eByte_2exb2
| VX43974 = cCoq_2eInit_2eByte_2exb3
| VX43974 = cCoq_2eInit_2eByte_2exb4
| VX43974 = cCoq_2eInit_2eByte_2exb5
| VX43974 = cCoq_2eInit_2eByte_2exb6
| VX43974 = cCoq_2eInit_2eByte_2exb7
| VX43974 = cCoq_2eInit_2eByte_2exb8
| VX43974 = cCoq_2eInit_2eByte_2exb9
| VX43974 = cCoq_2eInit_2eByte_2exba
| VX43974 = cCoq_2eInit_2eByte_2exbb
| VX43974 = cCoq_2eInit_2eByte_2exbc
| VX43974 = cCoq_2eInit_2eByte_2exbd
| VX43974 = cCoq_2eInit_2eByte_2exbe
| VX43974 = cCoq_2eInit_2eByte_2exbf
| VX43974 = cCoq_2eInit_2eByte_2exc0
| VX43974 = cCoq_2eInit_2eByte_2exc1
| VX43974 = cCoq_2eInit_2eByte_2exc2
| VX43974 = cCoq_2eInit_2eByte_2exc3
| VX43974 = cCoq_2eInit_2eByte_2exc4
| VX43974 = cCoq_2eInit_2eByte_2exc5
| VX43974 = cCoq_2eInit_2eByte_2exc6
| VX43974 = cCoq_2eInit_2eByte_2exc7
| VX43974 = cCoq_2eInit_2eByte_2exc8
| VX43974 = cCoq_2eInit_2eByte_2exc9
| VX43974 = cCoq_2eInit_2eByte_2exca
| VX43974 = cCoq_2eInit_2eByte_2excb
| VX43974 = cCoq_2eInit_2eByte_2excc
| VX43974 = cCoq_2eInit_2eByte_2excd
| VX43974 = cCoq_2eInit_2eByte_2exce
| VX43974 = cCoq_2eInit_2eByte_2excf
| VX43974 = cCoq_2eInit_2eByte_2exd0
| VX43974 = cCoq_2eInit_2eByte_2exd1
| VX43974 = cCoq_2eInit_2eByte_2exd2
| VX43974 = cCoq_2eInit_2eByte_2exd3
| VX43974 = cCoq_2eInit_2eByte_2exd4
| VX43974 = cCoq_2eInit_2eByte_2exd5
| VX43974 = cCoq_2eInit_2eByte_2exd6
| VX43974 = cCoq_2eInit_2eByte_2exd7
| VX43974 = cCoq_2eInit_2eByte_2exd8
| VX43974 = cCoq_2eInit_2eByte_2exd9
| VX43974 = cCoq_2eInit_2eByte_2exda
| VX43974 = cCoq_2eInit_2eByte_2exdb
| VX43974 = cCoq_2eInit_2eByte_2exdc
| VX43974 = cCoq_2eInit_2eByte_2exdd
| VX43974 = cCoq_2eInit_2eByte_2exde
| VX43974 = cCoq_2eInit_2eByte_2exdf
| VX43974 = cCoq_2eInit_2eByte_2exe0
| VX43974 = cCoq_2eInit_2eByte_2exe1
| VX43974 = cCoq_2eInit_2eByte_2exe2
| VX43974 = cCoq_2eInit_2eByte_2exe3
| VX43974 = cCoq_2eInit_2eByte_2exe4
| VX43974 = cCoq_2eInit_2eByte_2exe5
| VX43974 = cCoq_2eInit_2eByte_2exe6
| VX43974 = cCoq_2eInit_2eByte_2exe7
| VX43974 = cCoq_2eInit_2eByte_2exe8
| VX43974 = cCoq_2eInit_2eByte_2exe9
| VX43974 = cCoq_2eInit_2eByte_2exea
| VX43974 = cCoq_2eInit_2eByte_2exeb
| VX43974 = cCoq_2eInit_2eByte_2exec
| VX43974 = cCoq_2eInit_2eByte_2exed
| VX43974 = cCoq_2eInit_2eByte_2exee
| VX43974 = cCoq_2eInit_2eByte_2exef
| VX43974 = cCoq_2eInit_2eByte_2exf0
| VX43974 = cCoq_2eInit_2eByte_2exf1
| VX43974 = cCoq_2eInit_2eByte_2exf2
| VX43974 = cCoq_2eInit_2eByte_2exf3
| VX43974 = cCoq_2eInit_2eByte_2exf4
| VX43974 = cCoq_2eInit_2eByte_2exf5
| VX43974 = cCoq_2eInit_2eByte_2exf6
| VX43974 = cCoq_2eInit_2eByte_2exf7
| VX43974 = cCoq_2eInit_2eByte_2exf8
| VX43974 = cCoq_2eInit_2eByte_2exf9
| VX43974 = cCoq_2eInit_2eByte_2exfa
| VX43974 = cCoq_2eInit_2eByte_2exfb
| VX43974 = cCoq_2eInit_2eByte_2exfc
| VX43974 = cCoq_2eInit_2eByte_2exfd
| VX43974 = cCoq_2eInit_2eByte_2exfe
| VX43974 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__43978,Vvar__1__Q__43979,Vvar__2___24Anonymous__43980] :
( cProp___24t(Vvar__0__P__43978)
=> ( cProp___24t(Vvar__1__Q__43979)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__43980)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__43978,Vvar__1__Q__43979,Vvar__2___24Anonymous__43980)
=> ( ( p(Vvar__0__P__43978)
& Vvar__2___24Anonymous__43980 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__43979)
& Vvar__2___24Anonymous__43980 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__21070,Vvar__1__Plt__21071,Vvar__2__Pgt__21072,Vvar__3___24Anonymous__21073] :
( cProp___24t(Vvar__0__Peq__21070)
=> ( cProp___24t(Vvar__1__Plt__21071)
=> ( cProp___24t(Vvar__2__Pgt__21072)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__21073)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__21070,Vvar__1__Plt__21071,Vvar__2__Pgt__21072,Vvar__3___24Anonymous__21073)
=> ( ( p(Vvar__0__Peq__21070)
& Vvar__3___24Anonymous__21073 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__21071)
& Vvar__3___24Anonymous__21073 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__21072)
& Vvar__3___24Anonymous__21073 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__176810,Vvar__1__Plt__176811,Vvar__2__Pgt__176812,Vvar__3___24Anonymous__176813,VX176814] :
( cProp___24t(Vvar__0__Peq__176810)
=> ( cProp___24t(Vvar__1__Plt__176811)
=> ( cProp___24t(Vvar__2__Pgt__176812)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__176813)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__176810,Vvar__1__Plt__176811,Vvar__2__Pgt__176812,Vvar__3___24Anonymous__176813,VX176814)
=> ( ( p(Vvar__0__Peq__176810)
& Vvar__3___24Anonymous__176813 = cCoq_2eInit_2eDatatypes_2eEq
& VX176814 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__176810,Vvar__1__Plt__176811,Vvar__2__Pgt__176812) )
| ( p(Vvar__1__Plt__176811)
& Vvar__3___24Anonymous__176813 = cCoq_2eInit_2eDatatypes_2eLt
& VX176814 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__176810,Vvar__1__Plt__176811,Vvar__2__Pgt__176812) )
| ( p(Vvar__2__Pgt__176812)
& Vvar__3___24Anonymous__176813 = cCoq_2eInit_2eDatatypes_2eGt
& VX176814 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__176810,Vvar__1__Plt__176811,Vvar__2__Pgt__176812) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX6)
=> ( VX6 = cCoq_2eInit_2eDatatypes_2etrue
| VX6 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX10205] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX10205)
=> ( VX10205 = cCoq_2eInit_2eDatatypes_2eEq
| VX10205 = cCoq_2eInit_2eDatatypes_2eLt
| VX10205 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__2521,VX2522] :
( cType___24t(Vvar__0__A__2521)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2521,VX2522)
=> ( VX2522 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2521)
| ? [Vvar__1___24Anonymous__2525] :
( t(Vvar__1___24Anonymous__2525,Vvar__0__A__2521)
& ? [Vvar__2___24Anonymous__2526] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2521,Vvar__2___24Anonymous__2526)
& VX2522 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2521,Vvar__1___24Anonymous__2525,Vvar__2___24Anonymous__2526) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX7] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX7)
=> ( VX7 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__8] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8)
& VX7 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__6458,VX6459] :
( cType___24t(Vvar__0__A__6458)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__6458,VX6459)
=> ( ? [Vvar__1___24Anonymous__6461] :
( t(Vvar__1___24Anonymous__6461,Vvar__0__A__6458)
& VX6459 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__6458,Vvar__1___24Anonymous__6461) )
| VX6459 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__6458) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__14,Vvar__1__B__15,VX16] :
( cType___24t(Vvar__0__A__14)
=> ( cType___24t(Vvar__1__B__15)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__14,Vvar__1__B__15,VX16)
=> ? [Vvar__2___24Anonymous__19] :
( t(Vvar__2___24Anonymous__19,Vvar__0__A__14)
& ? [Vvar__3___24Anonymous__20] :
( t(Vvar__3___24Anonymous__20,Vvar__1__B__15)
& VX16 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__14,Vvar__1__B__15,Vvar__2___24Anonymous__19,Vvar__3___24Anonymous__20) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__21032,Vvar__1__B__21033,VX21034] :
( cType___24t(Vvar__0__A__21032)
=> ( cType___24t(Vvar__1__B__21033)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__21032,Vvar__1__B__21033,VX21034)
=> ( ? [Vvar__2___24Anonymous__21037] :
( t(Vvar__2___24Anonymous__21037,Vvar__0__A__21032)
& VX21034 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__21032,Vvar__1__B__21033,Vvar__2___24Anonymous__21037) )
| ? [Vvar__2___24Anonymous__21040] :
( t(Vvar__2___24Anonymous__21040,Vvar__1__B__21033)
& VX21034 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__21032,Vvar__1__B__21033,Vvar__2___24Anonymous__21040) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX21009] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX21009)
=> VX21009 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2598,Vvar__1___24Anonymous__2599] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2598)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2599)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2598,Vvar__1___24Anonymous__2599))
=> ( Vvar__1___24Anonymous__2599 = Vvar__0__n__2598
| ? [Vvar__1__m__2603] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2603)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2598,Vvar__1__m__2603))
& Vvar__1___24Anonymous__2599 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2603) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__81,Vvar__1__P__82,VX85] :
( cType___24t(Vvar__0__A__81)
=> ( c_24__type__95___24t(Vvar__0__A__81,Vvar__1__P__82,Vvar__1__P__82)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__81,Vvar__1__P__82,VX85)
=> ? [Vvar__2__x__90] :
( t(Vvar__2__x__90,Vvar__0__A__81)
& p(happ(Vvar__1__P__82,Vvar__2__x__90))
& VX85 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__81,Vvar__1__P__82,Vvar__2__x__90) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__25400,Vvar__1__P__25401,Vvar__2__Q__25404,VX25407] :
( cType___24t(Vvar__0__A__25400)
=> ( c_24__type__25424___24t(Vvar__0__A__25400,Vvar__1__P__25401,Vvar__2__Q__25404,Vvar__1__P__25401)
=> ( c_24__type__25432___24t(Vvar__0__A__25400,Vvar__1__P__25401,Vvar__2__Q__25404,Vvar__2__Q__25404)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__25400,Vvar__1__P__25401,Vvar__2__Q__25404,VX25407)
=> ? [Vvar__3__x__25415] :
( t(Vvar__3__x__25415,Vvar__0__A__25400)
& p(happ(Vvar__1__P__25401,Vvar__3__x__25415))
& p(happ(Vvar__2__Q__25404,Vvar__3__x__25415))
& VX25407 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__25400,Vvar__1__P__25401,Vvar__2__Q__25404,Vvar__3__x__25415) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__10361,Vvar__1__P__10362,VX10365] :
( cType___24t(Vvar__0__A__10361)
=> ( c_24__type__10375___24t(Vvar__0__A__10361,Vvar__1__P__10362,Vvar__1__P__10362)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__10361,Vvar__1__P__10362,VX10365)
=> ? [Vvar__2__x__10370] :
( t(Vvar__2__x__10370,Vvar__0__A__10361)
& ? [Vvar__3___24Anonymous__10371] :
( t(Vvar__3___24Anonymous__10371,happ(Vvar__1__P__10362,Vvar__2__x__10370))
& VX10365 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__10361,Vvar__1__P__10362,Vvar__2__x__10370,Vvar__3___24Anonymous__10371) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__55213,Vvar__1__P__55214,Vvar__2__Q__55217,VX55220] :
( cType___24t(Vvar__0__A__55213)
=> ( c_24__type__55237___24t(Vvar__0__A__55213,Vvar__1__P__55214,Vvar__2__Q__55217,Vvar__1__P__55214)
=> ( c_24__type__55245___24t(Vvar__0__A__55213,Vvar__1__P__55214,Vvar__2__Q__55217,Vvar__2__Q__55217)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__55213,Vvar__1__P__55214,Vvar__2__Q__55217,VX55220)
=> ? [Vvar__3__x__55228] :
( t(Vvar__3__x__55228,Vvar__0__A__55213)
& ? [Vvar__4___24Anonymous__55229] :
( t(Vvar__4___24Anonymous__55229,happ(Vvar__1__P__55214,Vvar__3__x__55228))
& ? [Vvar__5___24Anonymous__55230] :
( t(Vvar__5___24Anonymous__55230,happ(Vvar__2__Q__55217,Vvar__3__x__55228))
& VX55220 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__55213,Vvar__1__P__55214,Vvar__2__Q__55217,Vvar__3__x__55228,Vvar__4___24Anonymous__55229,Vvar__5___24Anonymous__55230) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__28511,Vvar__1__B__28512,VX28513] :
( cProp___24t(Vvar__0__A__28511)
=> ( cProp___24t(Vvar__1__B__28512)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__28511,Vvar__1__B__28512,VX28513)
=> ( ( p(Vvar__0__A__28511)
& VX28513 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__28511,Vvar__1__B__28512) )
| ( p(Vvar__1__B__28512)
& VX28513 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28511,Vvar__1__B__28512) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__10400,Vvar__1__B__10401,VX10402] :
( cType___24t(Vvar__0__A__10400)
=> ( cProp___24t(Vvar__1__B__10401)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__10400,Vvar__1__B__10401,VX10402)
=> ( ? [Vvar__2___24Anonymous__10405] :
( t(Vvar__2___24Anonymous__10405,Vvar__0__A__10400)
& VX10402 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__10400,Vvar__1__B__10401,Vvar__2___24Anonymous__10405) )
| ( p(Vvar__1__B__10401)
& VX10402 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__10400,Vvar__1__B__10401) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__6712,Vvar__1__R__6713,Vvar__2__x__6718] :
( cType___24t(Vvar__0__A__6712)
=> ( c_24__type__6747___24t(Vvar__0__A__6712,Vvar__1__R__6713,Vvar__2__x__6718,Vvar__1__R__6713)
=> ( t(Vvar__2__x__6718,Vvar__0__A__6712)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__6712,Vvar__1__R__6713,Vvar__2__x__6718)
=> ( ! [Vvar__var__var__var__var__3__y__6728__6730__6732__6734__6736] :
( t(Vvar__var__var__var__var__3__y__6728__6730__6732__6734__6736,Vvar__0__A__6712)
=> ( p(happ(happ(Vvar__1__R__6713,Vvar__var__var__var__var__3__y__6728__6730__6732__6734__6736),Vvar__2__x__6718))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__6712,Vvar__1__R__6713,Vvar__var__var__var__var__3__y__6728__6730__6732__6734__6736) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__68996,Vvar__1__P__68997,Vvar__2___24Anonymous__69000] :
( cType___24t(Vvar__0__A__68996)
=> ( c_24__type__69018___24t(Vvar__0__A__68996,Vvar__1__P__68997,Vvar__2___24Anonymous__69000,Vvar__1__P__68997)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__68996,Vvar__2___24Anonymous__69000)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__68996,Vvar__1__P__68997,Vvar__2___24Anonymous__69000)
=> ( Vvar__2___24Anonymous__69000 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__68996)
| ? [Vvar__2__x__69010] :
( t(Vvar__2__x__69010,Vvar__0__A__68996)
& ? [Vvar__3__l__69011] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__68996,Vvar__3__l__69011)
& p(happ(Vvar__1__P__68997,Vvar__2__x__69010))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__68996,Vvar__1__P__68997,Vvar__3__l__69011)
& Vvar__2___24Anonymous__69000 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__68996,Vvar__2__x__69010,Vvar__3__l__69011) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__6589,Vvar__1___24Anonymous__6590] :
( cType___24t(Vvar__0__A__6589)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6589,Vvar__1___24Anonymous__6590)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__6589,Vvar__1___24Anonymous__6590)
=> ( Vvar__1___24Anonymous__6590 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__6589)
| ? [Vvar__1__x__6594] :
( t(Vvar__1__x__6594,Vvar__0__A__6589)
& ? [Vvar__2__l__6595] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__6589,Vvar__2__l__6595)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__6589,Vvar__1__x__6594,Vvar__2__l__6595)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__6589,Vvar__2__l__6595)
& Vvar__1___24Anonymous__6590 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__6589,Vvar__1__x__6594,Vvar__2__l__6595) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__25249,Vvar__1__eqA__25250,Vvar__2__x__25255,Vvar__3___24Anonymous__25256] :
( cType___24t(Vvar__0__A__25249)
=> ( c_24__type__25289___24t(Vvar__0__A__25249,Vvar__1__eqA__25250,Vvar__2__x__25255,Vvar__3___24Anonymous__25256,Vvar__1__eqA__25250)
=> ( t(Vvar__2__x__25255,Vvar__0__A__25249)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__25249,Vvar__3___24Anonymous__25256)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__25249,Vvar__1__eqA__25250,Vvar__2__x__25255,Vvar__3___24Anonymous__25256)
=> ( ? [Vvar__3__y__25265] :
( t(Vvar__3__y__25265,Vvar__0__A__25249)
& ? [Vvar__4__l__25266] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__25249,Vvar__4__l__25266)
& p(happ(happ(Vvar__1__eqA__25250,Vvar__2__x__25255),Vvar__3__y__25265))
& Vvar__3___24Anonymous__25256 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__25249,Vvar__3__y__25265,Vvar__4__l__25266) ) )
| ? [Vvar__3__y__25275] :
( t(Vvar__3__y__25275,Vvar__0__A__25249)
& ? [Vvar__4__l__25276] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__25249,Vvar__4__l__25276)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__25249,Vvar__1__eqA__25250,Vvar__2__x__25255,Vvar__4__l__25276)
& Vvar__3___24Anonymous__25256 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__25249,Vvar__3__y__25275,Vvar__4__l__25276) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__25294,Vvar__1__eqA__25295,Vvar__2___24Anonymous__25300] :
( cType___24t(Vvar__0__A__25294)
=> ( c_24__type__25327___24t(Vvar__0__A__25294,Vvar__1__eqA__25295,Vvar__2___24Anonymous__25300,Vvar__1__eqA__25295)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__25294,Vvar__2___24Anonymous__25300)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__25294,Vvar__1__eqA__25295,Vvar__2___24Anonymous__25300)
=> ( Vvar__2___24Anonymous__25300 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__25294)
| ? [Vvar__2__x__25314] :
( t(Vvar__2__x__25314,Vvar__0__A__25294)
& ? [Vvar__3__l__25315] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__25294,Vvar__3__l__25315)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__25294,Vvar__1__eqA__25295,Vvar__2__x__25314,Vvar__3__l__25315)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__25294,Vvar__1__eqA__25295,Vvar__3__l__25315)
& Vvar__2___24Anonymous__25300 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__25294,Vvar__2__x__25314,Vvar__3__l__25315) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__185939,Vvar__1__P__185940,Vvar__2__p__185943,Vvar__3__x__185944,Vvar__4__q__185945,Vvar__5___24Anonymous__185946] :
( cType___24t(Vvar__0__U__185939)
=> ( c_24__type__185961___24t(Vvar__0__U__185939,Vvar__1__P__185940,Vvar__2__p__185943,Vvar__3__x__185944,Vvar__4__q__185945,Vvar__5___24Anonymous__185946,Vvar__1__P__185940)
=> ( t(Vvar__2__p__185943,Vvar__0__U__185939)
=> ( t(Vvar__3__x__185944,happ(Vvar__1__P__185940,Vvar__2__p__185943))
=> ( t(Vvar__4__q__185945,Vvar__0__U__185939)
=> ( t(Vvar__5___24Anonymous__185946,happ(Vvar__1__P__185940,Vvar__4__q__185945))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__185939,Vvar__1__P__185940,Vvar__2__p__185943,Vvar__3__x__185944,Vvar__4__q__185945,Vvar__5___24Anonymous__185946)
=> ( Vvar__5___24Anonymous__185946 = Vvar__3__x__185944
& Vvar__4__q__185945 = Vvar__2__p__185943 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__176978,Vvar__1__P__176979,Vvar__2__p__176982,Vvar__3__x__176983,Vvar__4__q__176984,Vvar__5__y__176985] :
( cType___24t(Vvar__0__U__176978)
=> ( c_24__type__177004___24t(Vvar__0__U__176978,Vvar__1__P__176979,Vvar__2__p__176982,Vvar__3__x__176983,Vvar__4__q__176984,Vvar__5__y__176985,Vvar__1__P__176979)
=> ( t(Vvar__2__p__176982,Vvar__0__U__176978)
=> ( t(Vvar__3__x__176983,happ(Vvar__1__P__176979,Vvar__2__p__176982))
=> ( t(Vvar__4__q__176984,Vvar__0__U__176978)
=> ( t(Vvar__5__y__176985,happ(Vvar__1__P__176979,Vvar__4__q__176984))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__176978,Vvar__1__P__176979,Vvar__2__p__176982,Vvar__3__x__176983,Vvar__4__q__176984,Vvar__5__y__176985)
=> ( Vvar__4__q__176984 = Vvar__2__p__176982
& Vvar__3__x__176983 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__176978,Vvar__4__q__176984,Vvar__1__P__176979,Vvar__5__y__176985,Vvar__2__p__176982)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.JMeq.JMeq',axiom,
! [Vvar__0__A__186053,Vvar__1__x__186054,Vvar__2__B__186055,Vvar__3___24Anonymous__186056] :
( cType___24t(Vvar__0__A__186053)
=> ( t(Vvar__1__x__186054,Vvar__0__A__186053)
=> ( cType___24t(Vvar__2__B__186055)
=> ( t(Vvar__3___24Anonymous__186056,Vvar__2__B__186055)
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(Vvar__0__A__186053,Vvar__1__x__186054,Vvar__2__B__186055,Vvar__3___24Anonymous__186056)
=> ( Vvar__3___24Anonymous__186056 = Vvar__1__x__186054
& Vvar__2__B__186055 = Vvar__0__A__186053 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX13618] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX13618)
=> ( VX13618 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__13619] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13619)
& VX13618 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13619) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX10157] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX10157)
=> ( VX10157 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__10158] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10158)
& VX10157 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10158) )
| ? [Vvar__0___24Anonymous__10159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10159)
& VX10157 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10159) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX10146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX10146)
=> ( ? [Vvar__0___24Anonymous__10147] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10147)
& VX10146 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__10147) )
| ? [Vvar__0___24Anonymous__10148] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10148)
& VX10146 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__10148) )
| VX10146 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__186814,Vvar__1__q__186815,Vvar__2___24Anonymous__186816] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__186814)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__186815)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__186816)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__186814,Vvar__1__q__186815,Vvar__2___24Anonymous__186816)
=> ( ( Vvar__0__p__186814 = Vvar__1__q__186815
& Vvar__2___24Anonymous__186816 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__186823] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__186823)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__186815,Vvar__2__r__186823) = Vvar__0__p__186814
& Vvar__2___24Anonymous__186816 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__186823) )
| ? [Vvar__2__r__186827] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__186827)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__186814,Vvar__2__r__186827) = Vvar__1__q__186815
& Vvar__2___24Anonymous__186816 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX107996] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX107996)
=> ( VX107996 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__107997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__107997)
& VX107996 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__107997) )
| VX107996 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX46839] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX46839)
=> ? [Vvar__0__Qnum__46840] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__46840)
& ? [Vvar__1__Qden__46841] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__46841)
& VX46839 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__46840,Vvar__1__Qden__46841) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX186066] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX186066)
=> ? [Vvar__0__nonzero__186067] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__186067)
& Vvar__0__nonzero__186067 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX186066 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__186067) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__186222,Vvar__1___24Anonymous__186223,VX186224] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__186222)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__186223)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__186222,Vvar__1___24Anonymous__186223,VX186224)
=> ( ( Vvar__0__x__186222 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__186223 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX186224 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__186222) )
| ? [Vvar__1__n__186228] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__186228)
& Vvar__0__x__186222 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__186228)
& Vvar__1___24Anonymous__186223 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24186248___24a3(Vvar__0__x__186222,Vvar__1___24Anonymous__186223,Vvar__1__n__186228)
& VX186224 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__186222,Vvar__1__n__186228) )
| ? [Vvar__1__n__186233] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__186233)
& Vvar__0__x__186222 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__186233))
& Vvar__1___24Anonymous__186223 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265___24a3(Vvar__0__x__186222,Vvar__1___24Anonymous__186223,Vvar__1__n__186233)
& VX186224 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__186222,Vvar__1__n__186233) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__10341,Vvar__1___24Anonymous__10342,Vvar__2___24Anonymous__10343] :
( cType___24t(Vvar__0__A__10341)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__1___24Anonymous__10342)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__2___24Anonymous__10343)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__10341,Vvar__1___24Anonymous__10342,Vvar__2___24Anonymous__10343)
=> ( ( Vvar__2___24Anonymous__10343 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10341)
& Vvar__1___24Anonymous__10342 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10341) )
| ? [Vvar__1__x__10347] :
( t(Vvar__1__x__10347,Vvar__0__A__10341)
& ? [Vvar__2__l__10348] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__2__l__10348)
& ? [Vvar__3__l_27__10349] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__3__l_27__10349)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__10341,Vvar__2__l__10348,Vvar__3__l_27__10349)
& Vvar__2___24Anonymous__10343 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__1__x__10347,Vvar__3__l_27__10349)
& Vvar__1___24Anonymous__10342 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__1__x__10347,Vvar__2__l__10348) ) ) )
| ? [Vvar__1__x__10352] :
( t(Vvar__1__x__10352,Vvar__0__A__10341)
& ? [Vvar__2__y__10353] :
( t(Vvar__2__y__10353,Vvar__0__A__10341)
& ? [Vvar__3__l__10354] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__3__l__10354)
& Vvar__2___24Anonymous__10343 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__1__x__10352,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__2__y__10353,Vvar__3__l__10354))
& Vvar__1___24Anonymous__10342 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__2__y__10353,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10341,Vvar__1__x__10352,Vvar__3__l__10354)) ) ) )
| ? [Vvar__1__l__10356] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__1__l__10356)
& ? [Vvar__2__l_27__10357] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__2__l_27__10357)
& ? [Vvar__3__l_27_27__10358] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10341,Vvar__3__l_27_27__10358)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__10341,Vvar__1__l__10356,Vvar__2__l_27__10357)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__10341,Vvar__2__l_27__10357,Vvar__3__l_27_27__10358)
& Vvar__2___24Anonymous__10343 = Vvar__3__l_27_27__10358
& Vvar__1___24Anonymous__10342 = Vvar__1__l__10356 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__71297,Vvar__1__R__71298,Vvar__2___24Anonymous__71303] :
( cType___24t(Vvar__0__A__71297)
=> ( c_24__type__71330___24t(Vvar__0__A__71297,Vvar__1__R__71298,Vvar__2___24Anonymous__71303,Vvar__1__R__71298)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__71297,Vvar__2___24Anonymous__71303)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__71297,Vvar__1__R__71298,Vvar__2___24Anonymous__71303)
=> ( Vvar__2___24Anonymous__71303 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__71297)
| ? [Vvar__2__a__71317] :
( t(Vvar__2__a__71317,Vvar__0__A__71297)
& ? [Vvar__3__l__71318] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__71297,Vvar__3__l__71318)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__71297,Vvar__1__R__71298,Vvar__3__l__71318)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__71297,happ(Vvar__1__R__71298,Vvar__2__a__71317),Vvar__3__l__71318)
& Vvar__2___24Anonymous__71303 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__71297,Vvar__2__a__71317,Vvar__3__l__71318) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX13515] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX13515)
=> ? [Vvar__0___24Anonymous__13516] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__13516)
& ? [Vvar__1___24Anonymous__13517] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__13517)
& ? [Vvar__2___24Anonymous__13518] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__13518)
& ? [Vvar__3___24Anonymous__13519] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__13519)
& ? [Vvar__4___24Anonymous__13520] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__13520)
& ? [Vvar__5___24Anonymous__13521] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__13521)
& ? [Vvar__6___24Anonymous__13522] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__13522)
& ? [Vvar__7___24Anonymous__13523] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__13523)
& VX13515 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__13516,Vvar__1___24Anonymous__13517,Vvar__2___24Anonymous__13518,Vvar__3___24Anonymous__13519,Vvar__4___24Anonymous__13520,Vvar__5___24Anonymous__13521,Vvar__6___24Anonymous__13522,Vvar__7___24Anonymous__13523) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX44311] :
( cCoq_2eStrings_2eString_2estring___24t(VX44311)
=> ( VX44311 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__44312] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__44312)
& ? [Vvar__1___24Anonymous__44313] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__44313)
& VX44311 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44312,Vvar__1___24Anonymous__44313) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883,VX177884] :
( cType___24t(Vvar__0__X__177871)
=> ( c_24__type__177944___24t(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883,Vvar__1__lt__177872)
=> ( c_24__type__177963___24t(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883,Vvar__2__eq__177877)
=> ( t(Vvar__3__x__177882,Vvar__0__X__177871)
=> ( t(Vvar__4__y__177883,Vvar__0__X__177871)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883,VX177884)
=> ( ( p(happ(happ(Vvar__1__lt__177872,Vvar__3__x__177882),Vvar__4__y__177883))
& VX177884 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883) )
| ( p(happ(happ(Vvar__2__eq__177877,Vvar__3__x__177882),Vvar__4__y__177883))
& VX177884 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883) )
| ( p(happ(happ(Vvar__1__lt__177872,Vvar__4__y__177883),Vvar__3__x__177882))
& VX177884 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__177871,Vvar__1__lt__177872,Vvar__2__eq__177877,Vvar__3__x__177882,Vvar__4__y__177883) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__186843,Vvar__1___24Anonymous__186844] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__186843)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__186844)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__186843,Vvar__1___24Anonymous__186844)
=> ( ? [Vvar__0__a__186846] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__186846)
& ? [Vvar__1__s__186847] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__186847)
& Vvar__1___24Anonymous__186844 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__186846,Vvar__1__s__186847)
& Vvar__0___24Anonymous__186843 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__186848] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__186848)
& ? [Vvar__1__s1__186849] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__186849)
& ? [Vvar__2__s2__186850] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__186850)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__186849,Vvar__2__s2__186850)
& Vvar__1___24Anonymous__186844 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__186848,Vvar__2__s2__186850)
& Vvar__0___24Anonymous__186843 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__186848,Vvar__1__s1__186849) ) ) )
| ? [Vvar__0__a__186852] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__186852)
& ? [Vvar__1__b__186853] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__186853)
& ? [Vvar__2__s1__186854] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__186854)
& ? [Vvar__3__s2__186855] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__186855)
& p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__186852),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__186853)))
& Vvar__1___24Anonymous__186844 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__186853,Vvar__3__s2__186855)
& Vvar__0___24Anonymous__186843 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__186852,Vvar__2__s1__186854) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX178156] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX178156)
=> ( VX178156 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX178156 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX178156 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__21158,VX21159] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__21158)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__21158,VX21159)
=> ( ? [Vvar__0__n__21160] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21160)
& Vvar__0___24Anonymous__21158 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21160)
& VX21159 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__21160) )
| ? [Vvar__0__n__21161] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__21161)
& ? [Vvar__1___24Anonymous__21162] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__21161,Vvar__1___24Anonymous__21162)
& Vvar__0___24Anonymous__21158 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__21161)
& VX21159 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21161,Vvar__1___24Anonymous__21162) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__10440,Vvar__1___24Anonymous__10441,VX10442] :
( cType___24t(Vvar__0__A__10440)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__10441)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__10440,Vvar__1___24Anonymous__10441,VX10442)
=> ( ( Vvar__1___24Anonymous__10441 = cCoq_2eInit_2eDatatypes_2eO
& VX10442 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__10440) )
| ? [Vvar__1__h__10445] :
( t(Vvar__1__h__10445,Vvar__0__A__10440)
& ? [Vvar__2__n__10446] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__10446)
& ? [Vvar__3___24Anonymous__10447] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__10440,Vvar__2__n__10446,Vvar__3___24Anonymous__10447)
& Vvar__1___24Anonymous__10441 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__10446)
& VX10442 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__10440,Vvar__1__h__10445,Vvar__2__n__10446,Vvar__3___24Anonymous__10447) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__186719,Vvar__1__b__186720,Vvar__2__d__186721] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__186719)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__186720)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__186721)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__186719,Vvar__1__b__186720,Vvar__2__d__186721)
=> ? [Vvar__3__u__186726] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__186726)
& ? [Vvar__4__v__186727] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__186727)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__186726,Vvar__0__a__186719),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__186727,Vvar__1__b__186720)) = Vvar__2__d__186721
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__183712,Vvar__1__b__183713,VX183714] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__183712)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__183713)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__183712,Vvar__1__b__183713,VX183714)
=> ? [Vvar__2__u__183717] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__183717)
& ? [Vvar__3__v__183718] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__183718)
& ? [Vvar__4__d__183719] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__183719)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__183717,Vvar__0__a__183712),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__183718,Vvar__1__b__183713)) = Vvar__4__d__183719
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__183712,Vvar__1__b__183713,Vvar__4__d__183719)
& VX183714 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__183712,Vvar__1__b__183713,Vvar__2__u__183717,Vvar__3__v__183718,Vvar__4__d__183719) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__183684,Vvar__1__b__183685,Vvar__2__g__183686] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__183684)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__183685)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__183686)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__183684,Vvar__1__b__183685,Vvar__2__g__183686)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__183686,Vvar__0__a__183684)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__183686,Vvar__1__b__183685)
& ! [Vvar__var__var__var__var__5__x__183694__183697__183700__183703__183706] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__183694__183697__183700__183703__183706)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__183694__183697__183700__183703__183706,Vvar__0__a__183684)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__183694__183697__183700__183703__183706,Vvar__1__b__183685)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__183694__183697__183700__183703__183706,Vvar__2__g__183686) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__183771,Vvar__1__p__183772,VX183773] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__183771)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__183772)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__183771,Vvar__1__p__183772,VX183773)
=> ? [Vvar__2__q__183776] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__183776)
& ? [Vvar__3__r__183777] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__183777)
& Vvar__0__x__183771 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__183776,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__183772)),Vvar__3__r__183777)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__183777))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__183777,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__183772))
& VX183773 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__183771,Vvar__1__p__183772,Vvar__2__q__183776,Vvar__3__r__183777) ) ) ) ) ) ).
fof('$_inversion_Coq.funind.Recdef.max_type',axiom,
! [Vvar__0__m__6619,Vvar__1__n__6620,VX6621] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__m__6619)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__6620)
=> ( cCoq_2efunind_2eRecdef_2emax__type___24t(Vvar__0__m__6619,Vvar__1__n__6620,VX6621)
=> ? [Vvar__2__v__6624] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__v__6624)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__m__6619,Vvar__2__v__6624))
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__n__6620,Vvar__2__v__6624))
& VX6621 = cCoq_2efunind_2eRecdef_2ecmt___24a3(Vvar__0__m__6619,Vvar__1__n__6620,Vvar__2__v__6624) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX185901] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX185901)
=> ( VX185901 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__185902] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185902)
& ? [Vvar__1___24Anonymous__185903] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__185903)
& VX185901 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__185902,Vvar__1___24Anonymous__185903) ) )
| ? [Vvar__0___24Anonymous__185904] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__185904)
& ? [Vvar__1___24Anonymous__185905] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__185905)
& VX185901 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__185904,Vvar__1___24Anonymous__185905) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__185707,VX185708] :
( cType___24t(Vvar__0__C__185707)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,VX185708)
=> ( ? [Vvar__1___24Anonymous__185710] :
( t(Vvar__1___24Anonymous__185710,Vvar__0__C__185707)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__185707,Vvar__1___24Anonymous__185710) )
| ? [Vvar__1___24Anonymous__185712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__185712)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__185707,Vvar__1___24Anonymous__185712) )
| ? [Vvar__1___24Anonymous__185714] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__1___24Anonymous__185714)
& ? [Vvar__2___24Anonymous__185715] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__2___24Anonymous__185715)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__185707,Vvar__1___24Anonymous__185714,Vvar__2___24Anonymous__185715) ) )
| ? [Vvar__1___24Anonymous__185717] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__1___24Anonymous__185717)
& ? [Vvar__2___24Anonymous__185718] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__2___24Anonymous__185718)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__185707,Vvar__1___24Anonymous__185717,Vvar__2___24Anonymous__185718) ) )
| ? [Vvar__1___24Anonymous__185720] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__1___24Anonymous__185720)
& ? [Vvar__2___24Anonymous__185721] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__2___24Anonymous__185721)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__185707,Vvar__1___24Anonymous__185720,Vvar__2___24Anonymous__185721) ) )
| ? [Vvar__1___24Anonymous__185723] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__1___24Anonymous__185723)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__185707,Vvar__1___24Anonymous__185723) )
| ? [Vvar__1___24Anonymous__185725] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__185707,Vvar__1___24Anonymous__185725)
& ? [Vvar__2___24Anonymous__185726] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__185726)
& VX185708 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__185707,Vvar__1___24Anonymous__185725,Vvar__2___24Anonymous__185726) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__65615,VX65616] :
( cType___24t(Vvar__0__C__65615)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__65615,VX65616)
=> ( ? [Vvar__1___24Anonymous__65618] :
( t(Vvar__1___24Anonymous__65618,Vvar__0__C__65615)
& VX65616 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__65615,Vvar__1___24Anonymous__65618) )
| ? [Vvar__1___24Anonymous__65620] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__65620)
& ? [Vvar__2___24Anonymous__65621] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__65615,Vvar__2___24Anonymous__65621)
& VX65616 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__65615,Vvar__1___24Anonymous__65620,Vvar__2___24Anonymous__65621) ) )
| ? [Vvar__1___24Anonymous__65623] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__65615,Vvar__1___24Anonymous__65623)
& ? [Vvar__2___24Anonymous__65624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__65624)
& ? [Vvar__3___24Anonymous__65625] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__65615,Vvar__3___24Anonymous__65625)
& VX65616 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__65615,Vvar__1___24Anonymous__65623,Vvar__2___24Anonymous__65624,Vvar__3___24Anonymous__65625) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754] :
( cType___24t(Vvar__0__R__45723)
=> ( t(Vvar__1__rO__45724,Vvar__0__R__45723)
=> ( t(Vvar__2__rI__45725,Vvar__0__R__45723)
=> ( c_24__type__46155___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__3__rplus__45726)
=> ( c_24__type__46256___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__4__rtimes__45731)
=> ( c_24__type__46357___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__5__rminus__45736)
=> ( c_24__type__46447___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__6__ropp__45741)
=> ( c_24__type__46548___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__7__req__45744)
=> ( c_24__type__46649___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__8__rle__45749)
=> ( c_24__type__46750___24t(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754,Vvar__9__rlt__45754)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744,Vvar__8__rle__45749,Vvar__9__rlt__45754)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__45723,Vvar__7__req__45744)
& ! [Vvar__var__var__var__var__11__x1__45798__45804__45909__45915__45921] :
( t(Vvar__var__var__var__var__11__x1__45798__45804__45909__45915__45921,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__12__x2__45799__45805__45910__45916__45922] :
( t(Vvar__var__var__var__var__12__x2__45799__45805__45910__45916__45922,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__11__x1__45798__45804__45909__45915__45921),Vvar__var__var__var__var__12__x2__45799__45805__45910__45916__45922))
=> ! [Vvar__var__var__var__var__14__y1__45800__45806__45911__45917__45923] :
( t(Vvar__var__var__var__var__14__y1__45800__45806__45911__45917__45923,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__15__y2__45801__45807__45912__45918__45924] :
( t(Vvar__var__var__var__var__15__y2__45801__45807__45912__45918__45924,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__14__y1__45800__45806__45911__45917__45923),Vvar__var__var__var__var__15__y2__45801__45807__45912__45918__45924))
=> p(happ(happ(Vvar__7__req__45744,happ(happ(Vvar__3__rplus__45726,Vvar__var__var__var__var__11__x1__45798__45804__45909__45915__45921),Vvar__var__var__var__var__14__y1__45800__45806__45911__45917__45923)),happ(happ(Vvar__3__rplus__45726,Vvar__var__var__var__var__12__x2__45799__45805__45910__45916__45922),Vvar__var__var__var__var__15__y2__45801__45807__45912__45918__45924))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__45811__45817__45927__45933__45939] :
( t(Vvar__var__var__var__var__12__x1__45811__45817__45927__45933__45939,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__13__x2__45812__45818__45928__45934__45940] :
( t(Vvar__var__var__var__var__13__x2__45812__45818__45928__45934__45940,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__12__x1__45811__45817__45927__45933__45939),Vvar__var__var__var__var__13__x2__45812__45818__45928__45934__45940))
=> ! [Vvar__var__var__var__var__15__y1__45813__45819__45929__45935__45941] :
( t(Vvar__var__var__var__var__15__y1__45813__45819__45929__45935__45941,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__16__y2__45814__45820__45930__45936__45942] :
( t(Vvar__var__var__var__var__16__y2__45814__45820__45930__45936__45942,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__15__y1__45813__45819__45929__45935__45941),Vvar__var__var__var__var__16__y2__45814__45820__45930__45936__45942))
=> p(happ(happ(Vvar__7__req__45744,happ(happ(Vvar__4__rtimes__45731,Vvar__var__var__var__var__12__x1__45811__45817__45927__45933__45939),Vvar__var__var__var__var__15__y1__45813__45819__45929__45935__45941)),happ(happ(Vvar__4__rtimes__45731,Vvar__var__var__var__var__13__x2__45812__45818__45928__45934__45940),Vvar__var__var__var__var__16__y2__45814__45820__45930__45936__45942))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__45824__45827__45945__45948__45951] :
( t(Vvar__var__var__var__var__13__x1__45824__45827__45945__45948__45951,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__14__x2__45825__45828__45946__45949__45952] :
( t(Vvar__var__var__var__var__14__x2__45825__45828__45946__45949__45952,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__13__x1__45824__45827__45945__45948__45951),Vvar__var__var__var__var__14__x2__45825__45828__45946__45949__45952))
=> p(happ(happ(Vvar__7__req__45744,happ(Vvar__6__ropp__45741,Vvar__var__var__var__var__13__x1__45824__45827__45945__45948__45951)),happ(Vvar__6__ropp__45741,Vvar__var__var__var__var__14__x2__45825__45828__45946__45949__45952))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__45831__45837__45954__45960__45966] :
( t(Vvar__var__var__var__var__14__x1__45831__45837__45954__45960__45966,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__15__x2__45832__45838__45955__45961__45967] :
( t(Vvar__var__var__var__var__15__x2__45832__45838__45955__45961__45967,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__14__x1__45831__45837__45954__45960__45966),Vvar__var__var__var__var__15__x2__45832__45838__45955__45961__45967))
=> ! [Vvar__var__var__var__var__17__y1__45833__45839__45956__45962__45968] :
( t(Vvar__var__var__var__var__17__y1__45833__45839__45956__45962__45968,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__18__y2__45834__45840__45957__45963__45969] :
( t(Vvar__var__var__var__var__18__y2__45834__45840__45957__45963__45969,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__17__y1__45833__45839__45956__45962__45968),Vvar__var__var__var__var__18__y2__45834__45840__45957__45963__45969))
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__14__x1__45831__45837__45954__45960__45966),Vvar__var__var__var__var__17__y1__45833__45839__45956__45962__45968))
<=> p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__15__x2__45832__45838__45955__45961__45967),Vvar__var__var__var__var__18__y2__45834__45840__45957__45963__45969)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__45844__45850__45972__45978__45984] :
( t(Vvar__var__var__var__var__15__x1__45844__45850__45972__45978__45984,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__16__x2__45845__45851__45973__45979__45985] :
( t(Vvar__var__var__var__var__16__x2__45845__45851__45973__45979__45985,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__15__x1__45844__45850__45972__45978__45984),Vvar__var__var__var__var__16__x2__45845__45851__45973__45979__45985))
=> ! [Vvar__var__var__var__var__18__y1__45846__45852__45974__45980__45986] :
( t(Vvar__var__var__var__var__18__y1__45846__45852__45974__45980__45986,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__19__y2__45847__45853__45975__45981__45987] :
( t(Vvar__var__var__var__var__19__y2__45847__45853__45975__45981__45987,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__18__y1__45846__45852__45974__45980__45986),Vvar__var__var__var__var__19__y2__45847__45853__45975__45981__45987))
=> ( p(happ(happ(Vvar__9__rlt__45754,Vvar__var__var__var__var__15__x1__45844__45850__45972__45978__45984),Vvar__var__var__var__var__18__y1__45846__45852__45974__45980__45986))
<=> p(happ(happ(Vvar__9__rlt__45754,Vvar__var__var__var__var__16__x2__45845__45851__45973__45979__45985),Vvar__var__var__var__var__19__y2__45847__45853__45975__45981__45987)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__45723,Vvar__1__rO__45724,Vvar__2__rI__45725,Vvar__3__rplus__45726,Vvar__4__rtimes__45731,Vvar__5__rminus__45736,Vvar__6__ropp__45741,Vvar__7__req__45744)
& ! [Vvar__var__var__var__17__n__45858__45859__45990__45991] :
( t(Vvar__var__var__var__17__n__45858__45859__45990__45991,Vvar__0__R__45723)
=> p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__17__n__45858__45859__45990__45991),Vvar__var__var__var__17__n__45858__45859__45990__45991)) )
& ! [Vvar__var__var__var__var__18__n__45861__45865__45992__45996__46000] :
( t(Vvar__var__var__var__var__18__n__45861__45865__45992__45996__46000,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__19__m__45862__45866__45993__45997__46001] :
( t(Vvar__var__var__var__var__19__m__45862__45866__45993__45997__46001,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__18__n__45861__45865__45992__45996__46000),Vvar__var__var__var__var__19__m__45862__45866__45993__45997__46001))
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__19__m__45862__45866__45993__45997__46001),Vvar__var__var__var__var__18__n__45861__45865__45992__45996__46000))
=> p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__18__n__45861__45865__45992__45996__46000),Vvar__var__var__var__var__19__m__45862__45866__45993__45997__46001)) ) ) ) )
& ! [Vvar__var__var__var__19__n__45870__45875__46004__46009] :
( t(Vvar__var__var__var__19__n__45870__45875__46004__46009,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__20__m__45871__45876__46005__46010] :
( t(Vvar__var__var__var__20__m__45871__45876__46005__46010,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__21__p__45872__45877__46006__46011] :
( t(Vvar__var__var__var__21__p__45872__45877__46006__46011,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__19__n__45870__45875__46004__46009),Vvar__var__var__var__20__m__45871__45876__46005__46010))
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__20__m__45871__45876__46005__46010),Vvar__var__var__var__21__p__45872__45877__46006__46011))
=> p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__19__n__45870__45875__46004__46009),Vvar__var__var__var__21__p__45872__45877__46006__46011)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__45881__45883__46014__46016__46018__46020] :
( t(Vvar__var__var__var__var__var__20__n__45881__45883__46014__46016__46018__46020,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__var__21__m__45882__45884__46015__46017__46019__46021] :
( t(Vvar__var__var__var__var__var__21__m__45882__45884__46015__46017__46019__46021,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__9__rlt__45754,Vvar__var__var__var__var__var__20__n__45881__45883__46014__46016__46018__46020),Vvar__var__var__var__var__var__21__m__45882__45884__46015__46017__46019__46021))
<=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__var__20__n__45881__45883__46014__46016__46018__46020),Vvar__var__var__var__var__var__21__m__45882__45884__46015__46017__46019__46021))
& ~ p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__var__20__n__45881__45883__46014__46016__46018__46020),Vvar__var__var__var__var__var__21__m__45882__45884__46015__46017__46019__46021)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__45886__45888__46022__46024__46026] :
( t(Vvar__var__var__var__var__21__n__45886__45888__46022__46024__46026,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__22__m__45887__45889__46023__46025__46027] :
( t(Vvar__var__var__var__var__22__m__45887__45889__46023__46025__46027,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__9__rlt__45754,Vvar__var__var__var__var__21__n__45886__45888__46022__46024__46026),Vvar__var__var__var__var__22__m__45887__45889__46023__46025__46027))
| p(happ(happ(Vvar__7__req__45744,Vvar__var__var__var__var__21__n__45886__45888__46022__46024__46026),Vvar__var__var__var__var__22__m__45887__45889__46023__46025__46027))
| p(happ(happ(Vvar__9__rlt__45754,Vvar__var__var__var__var__22__m__45887__45889__46023__46025__46027),Vvar__var__var__var__var__21__n__45886__45888__46022__46024__46026)) ) ) )
& ! [Vvar__var__var__var__var__22__n__45891__45895__46028__46032__46036] :
( t(Vvar__var__var__var__var__22__n__45891__45895__46028__46032__46036,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__23__m__45892__45896__46029__46033__46037] :
( t(Vvar__var__var__var__var__23__m__45892__45896__46029__46033__46037,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__24__p__45893__45897__46030__46034__46038] :
( t(Vvar__var__var__var__var__24__p__45893__45897__46030__46034__46038,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__8__rle__45749,Vvar__var__var__var__var__22__n__45891__45895__46028__46032__46036),Vvar__var__var__var__var__23__m__45892__45896__46029__46033__46037))
=> p(happ(happ(Vvar__8__rle__45749,happ(happ(Vvar__3__rplus__45726,Vvar__var__var__var__var__24__p__45893__45897__46030__46034__46038),Vvar__var__var__var__var__22__n__45891__45895__46028__46032__46036)),happ(happ(Vvar__3__rplus__45726,Vvar__var__var__var__var__24__p__45893__45897__46030__46034__46038),Vvar__var__var__var__var__23__m__45892__45896__46029__46033__46037))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__45900__45904__46040__46044__46048__46052] :
( t(Vvar__var__var__var__var__var__23__n__45900__45904__46040__46044__46048__46052,Vvar__0__R__45723)
=> ! [Vvar__var__var__var__var__var__24__m__45901__45905__46041__46045__46049__46053] :
( t(Vvar__var__var__var__var__var__24__m__45901__45905__46041__46045__46049__46053,Vvar__0__R__45723)
=> ( p(happ(happ(Vvar__9__rlt__45754,Vvar__1__rO__45724),Vvar__var__var__var__var__var__23__n__45900__45904__46040__46044__46048__46052))
=> ( p(happ(happ(Vvar__9__rlt__45754,Vvar__1__rO__45724),Vvar__var__var__var__var__var__24__m__45901__45905__46041__46045__46049__46053))
=> p(happ(happ(Vvar__9__rlt__45754,Vvar__1__rO__45724),happ(happ(Vvar__4__rtimes__45731,Vvar__var__var__var__var__var__23__n__45900__45904__46040__46044__46048__46052),Vvar__var__var__var__var__var__24__m__45901__45905__46041__46045__46049__46053))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__45744,Vvar__1__rO__45724),Vvar__2__rI__45725))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX186073] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX186073)
=> ( VX186073 = cCoq_2emicromega_2eRMicromega_2eC0
| VX186073 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__186074] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__186074)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__186074) )
| ? [Vvar__0__r__186075] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__186075)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__186075) )
| ? [Vvar__0__r1__186076] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__186076)
& ? [Vvar__1__r2__186077] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__186077)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__186076,Vvar__1__r2__186077) ) )
| ? [Vvar__0__r1__186078] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__186078)
& ? [Vvar__1__r2__186079] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__186079)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__186078,Vvar__1__r2__186079) ) )
| ? [Vvar__0__r1__186080] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__186080)
& ? [Vvar__1__r2__186081] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__186081)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__186080,Vvar__1__r2__186081) ) )
| ? [Vvar__0__r1__186082] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__186082)
& ? [Vvar__1__z__186083] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__186083)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__186082,Vvar__1__z__186083) ) )
| ? [Vvar__0__r__186084] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__186084)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__186084) )
| ? [Vvar__0__r__186085] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__186085)
& VX186073 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__186085) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__69217,VX69218] :
( cType___24t(Vvar__0__T__69217)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__69217,VX69218)
=> ? [Vvar__1__Flhs__69220] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__69217,Vvar__1__Flhs__69220)
& ? [Vvar__2__Fop__69221] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__69221)
& ? [Vvar__3__Frhs__69222] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__69217,Vvar__3__Frhs__69222)
& VX69218 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__69217,Vvar__1__Flhs__69220,Vvar__2__Fop__69221,Vvar__3__Frhs__69222) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX69070] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX69070)
=> ( VX69070 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX69070 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX69070 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX69070 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX186311] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX186311)
=> ( VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX186311 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__69071,VX69072] :
( cType___24t(Vvar__0__C__69071)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,VX69072)
=> ( ? [Vvar__1___24Anonymous__69074] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__69074)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__69071,Vvar__1___24Anonymous__69074) )
| ? [Vvar__1___24Anonymous__69076] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__69071,Vvar__1___24Anonymous__69076)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__69071,Vvar__1___24Anonymous__69076) )
| ? [Vvar__1___24Anonymous__69078] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__69071,Vvar__1___24Anonymous__69078)
& ? [Vvar__2___24Anonymous__69079] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,Vvar__2___24Anonymous__69079)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__69071,Vvar__1___24Anonymous__69078,Vvar__2___24Anonymous__69079) ) )
| ? [Vvar__1___24Anonymous__69081] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,Vvar__1___24Anonymous__69081)
& ? [Vvar__2___24Anonymous__69082] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,Vvar__2___24Anonymous__69082)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__69071,Vvar__1___24Anonymous__69081,Vvar__2___24Anonymous__69082) ) )
| ? [Vvar__1___24Anonymous__69084] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,Vvar__1___24Anonymous__69084)
& ? [Vvar__2___24Anonymous__69085] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__69071,Vvar__2___24Anonymous__69085)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__69071,Vvar__1___24Anonymous__69084,Vvar__2___24Anonymous__69085) ) )
| ? [Vvar__1___24Anonymous__69087] :
( t(Vvar__1___24Anonymous__69087,Vvar__0__C__69071)
& VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__69071,Vvar__1___24Anonymous__69087) )
| VX69072 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__69071) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033] :
( cType___24t(Vvar__0__R__46964)
=> ( t(Vvar__1__rO__46965,Vvar__0__R__46964)
=> ( t(Vvar__2__rI__46966,Vvar__0__R__46964)
=> ( c_24__type__47497___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__3__rplus__46967)
=> ( c_24__type__47843___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__4__rtimes__46972)
=> ( c_24__type__48189___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__5__rminus__46977)
=> ( c_24__type__48512___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__6__ropp__46982)
=> ( c_24__type__48858___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__7__req__46985)
=> ( c_24__type__49204___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__8__rle__46990)
=> ( cType___24t(Vvar__9__C__46995)
=> ( t(Vvar__10__cO__46996,Vvar__9__C__46995)
=> ( t(Vvar__11__cI__46997,Vvar__9__C__46995)
=> ( c_24__type__49550___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__12__cplus__46998)
=> ( c_24__type__49896___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__13__ctimes__47003)
=> ( c_24__type__50242___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__14__cminus__47008)
=> ( c_24__type__50565___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__15__copp__47013)
=> ( c_24__type__50911___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__16__ceqb__47016)
=> ( c_24__type__51257___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__17__cleb__47021)
=> ( c_24__type__51580___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__18__phi__47026)
=> ( cType___24t(Vvar__19__E__47029)
=> ( c_24__type__51903___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__20__pow__phi__47030)
=> ( c_24__type__52249___24t(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033,Vvar__21__rpow__47033)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__8__rle__46990,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__17__cleb__47021,Vvar__18__phi__47026,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__46964,Vvar__1__rO__46965,Vvar__2__rI__46966,Vvar__3__rplus__46967,Vvar__4__rtimes__46972,Vvar__5__rminus__46977,Vvar__6__ropp__46982,Vvar__7__req__46985,Vvar__9__C__46995,Vvar__10__cO__46996,Vvar__11__cI__46997,Vvar__12__cplus__46998,Vvar__13__ctimes__47003,Vvar__14__cminus__47008,Vvar__15__copp__47013,Vvar__16__ceqb__47016,Vvar__18__phi__47026)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__46964,Vvar__2__rI__46966,Vvar__4__rtimes__46972,Vvar__7__req__46985,Vvar__19__E__47029,Vvar__20__pow__phi__47030,Vvar__21__rpow__47033)
& ! [Vvar__var__var__var__var__var__24__x__47116__47119__47129__47132__47135__47138] :
( t(Vvar__var__var__var__var__var__24__x__47116__47119__47129__47132__47135__47138,Vvar__9__C__46995)
=> ! [Vvar__var__var__var__var__var__25__y__47117__47120__47130__47133__47136__47139] :
( t(Vvar__var__var__var__var__var__25__y__47117__47120__47130__47133__47136__47139,Vvar__9__C__46995)
=> ( happ(happ(Vvar__16__ceqb__47016,Vvar__var__var__var__var__var__24__x__47116__47119__47129__47132__47135__47138),Vvar__var__var__var__var__var__25__y__47117__47120__47130__47133__47136__47139) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__46985,happ(Vvar__18__phi__47026,Vvar__var__var__var__var__var__24__x__47116__47119__47129__47132__47135__47138)),happ(Vvar__18__phi__47026,Vvar__var__var__var__var__var__25__y__47117__47120__47130__47133__47136__47139))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__47123__47126__47141__47144__47147__47150] :
( t(Vvar__var__var__var__var__var__25__x__47123__47126__47141__47144__47147__47150,Vvar__9__C__46995)
=> ! [Vvar__var__var__var__var__var__26__y__47124__47127__47142__47145__47148__47151] :
( t(Vvar__var__var__var__var__var__26__y__47124__47127__47142__47145__47148__47151,Vvar__9__C__46995)
=> ( happ(happ(Vvar__17__cleb__47021,Vvar__var__var__var__var__var__25__x__47123__47126__47141__47144__47147__47150),Vvar__var__var__var__var__var__26__y__47124__47127__47142__47145__47148__47151) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__46990,happ(Vvar__18__phi__47026,Vvar__var__var__var__var__var__25__x__47123__47126__47141__47144__47147__47150)),happ(Vvar__18__phi__47026,Vvar__var__var__var__var__var__26__y__47124__47127__47142__47145__47148__47151))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,VX71339] :
( cType___24t(Vvar__0__TA__71335)
=> ( cType___24t(Vvar__1__TX__71336)
=> ( cType___24t(Vvar__2__AA__71337)
=> ( cType___24t(Vvar__3__AF__71338)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,VX71339)
=> ( VX71339 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338)
| VX71339 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338)
| ? [Vvar__4___24Anonymous__71352] :
( t(Vvar__4___24Anonymous__71352,Vvar__1__TX__71336)
& VX71339 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71352) )
| ? [Vvar__4___24Anonymous__71357] :
( t(Vvar__4___24Anonymous__71357,Vvar__0__TA__71335)
& ? [Vvar__5___24Anonymous__71358] :
( t(Vvar__5___24Anonymous__71358,Vvar__2__AA__71337)
& VX71339 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71357,Vvar__5___24Anonymous__71358) ) )
| ? [Vvar__4___24Anonymous__71363] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71363)
& ? [Vvar__5___24Anonymous__71364] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__5___24Anonymous__71364)
& VX71339 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71363,Vvar__5___24Anonymous__71364) ) )
| ? [Vvar__4___24Anonymous__71369] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71369)
& ? [Vvar__5___24Anonymous__71370] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__5___24Anonymous__71370)
& VX71339 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71369,Vvar__5___24Anonymous__71370) ) )
| ? [Vvar__4___24Anonymous__71375] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71375)
& VX71339 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71375) )
| ? [Vvar__4___24Anonymous__71380] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71380)
& ? [Vvar__5___24Anonymous__71381] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__71338,Vvar__5___24Anonymous__71381)
& ? [Vvar__6___24Anonymous__71382] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__6___24Anonymous__71382)
& VX71339 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__71335,Vvar__1__TX__71336,Vvar__2__AA__71337,Vvar__3__AF__71338,Vvar__4___24Anonymous__71380,Vvar__5___24Anonymous__71381,Vvar__6___24Anonymous__71382) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__186636,VX186637] :
( cType___24t(Vvar__0__A__186636)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__186636,VX186637)
=> ( VX186637 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__186636)
| ? [Vvar__1___24Anonymous__186640] :
( t(Vvar__1___24Anonymous__186640,Vvar__0__A__186636)
& VX186637 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__186636,Vvar__1___24Anonymous__186640) )
| ? [Vvar__1___24Anonymous__186642] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__186636,Vvar__1___24Anonymous__186642)
& ? [Vvar__2___24Anonymous__186643] :
( t(Vvar__2___24Anonymous__186643,Vvar__0__A__186636)
& ? [Vvar__3___24Anonymous__186644] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__186636,Vvar__3___24Anonymous__186644)
& VX186637 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__186636,Vvar__1___24Anonymous__186642,Vvar__2___24Anonymous__186643,Vvar__3___24Anonymous__186644) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__186766] :
( cProp___24t(Vvar__0___24Anonymous__186766)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__186766)
=> ( ? [Vvar__0__S__186768] :
( cType___24t(Vvar__0__S__186768)
& ? [Vvar__1__x__186769] :
( t(Vvar__1__x__186769,Vvar__0__S__186768)
& ? [Vvar__2__y__186770] :
( t(Vvar__2__y__186770,Vvar__0__S__186768)
& Vvar__0___24Anonymous__186766 = c_24__prop__186790___24a4(Vvar__0___24Anonymous__186766,Vvar__0__S__186768,Vvar__1__x__186769,Vvar__2__y__186770) ) ) )
| ? [Vvar__0__x__186771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__186771)
& ? [Vvar__1__y__186772] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__186772)
& Vvar__0___24Anonymous__186766 = c_24__prop__186791___24a3(Vvar__0___24Anonymous__186766,Vvar__0__x__186771,Vvar__1__y__186772) ) )
| ? [Vvar__0__x__186773] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__186773)
& ? [Vvar__1__s__186774] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__186774)
& Vvar__0___24Anonymous__186766 = c_24__prop__186792___24a3(Vvar__0___24Anonymous__186766,Vvar__0__x__186773,Vvar__1__s__186774) ) )
| Vvar__0___24Anonymous__186766 = c_24True
| Vvar__0___24Anonymous__186766 = c_24False
| ? [Vvar__0__P__186775] :
( cProp___24t(Vvar__0__P__186775)
& ? [Vvar__1__Q__186776] :
( cProp___24t(Vvar__1__Q__186776)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__186775)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__186776)
& Vvar__0___24Anonymous__186766 = c_24__prop__186793___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186775,Vvar__1__Q__186776) ) )
| ? [Vvar__0__P__186779] :
( cProp___24t(Vvar__0__P__186779)
& ? [Vvar__1__Q__186780] :
( cProp___24t(Vvar__1__Q__186780)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__186779)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__186780)
& Vvar__0___24Anonymous__186766 = c_24__prop__186794___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186779,Vvar__1__Q__186780) ) )
| ? [Vvar__0__P__186783] :
( cProp___24t(Vvar__0__P__186783)
& ? [Vvar__1__Q__186784] :
( cProp___24t(Vvar__1__Q__186784)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__186783)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__186784)
& Vvar__0___24Anonymous__186766 = c_24__prop__186795___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186783,Vvar__1__Q__186784) ) )
| ? [Vvar__0__P__186788] :
( cProp___24t(Vvar__0__P__186788)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__186788)
& Vvar__0___24Anonymous__186766 = c_24__prop__186796___24a2(Vvar__0___24Anonymous__186766,Vvar__0__P__186788) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__186673,Vvar__1__env__186674,Vvar__2__env_27__186677,Vvar__3__x__186680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__186673)
=> ( c_24__type__186701___24t(Vvar__0__fr__186673,Vvar__1__env__186674,Vvar__2__env_27__186677,Vvar__3__x__186680,Vvar__1__env__186674)
=> ( c_24__type__186710___24t(Vvar__0__fr__186673,Vvar__1__env__186674,Vvar__2__env_27__186677,Vvar__3__x__186680,Vvar__2__env_27__186677)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__186680)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__186673,Vvar__1__env__186674,Vvar__2__env_27__186677,Vvar__3__x__186680)
=> ( happ(Vvar__1__env__186674,Vvar__3__x__186680) = happ(Vvar__2__env_27__186677,Vvar__3__x__186680)
& happ(Vvar__1__env__186674,Vvar__3__x__186680) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__186677,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__186673,Vvar__3__x__186680))),happ(Vvar__2__env_27__186677,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__186673,Vvar__3__x__186680))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__186677,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__186673,Vvar__3__x__186680))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__186677,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__186673,Vvar__3__x__186680))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__66630,VX66631] :
( cType___24t(Vvar__0__C__66630)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,VX66631)
=> ( VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__66630)
| VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__66630)
| ? [Vvar__1___24Anonymous__66635] :
( t(Vvar__1___24Anonymous__66635,Vvar__0__C__66630)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__66630,Vvar__1___24Anonymous__66635) )
| ? [Vvar__1___24Anonymous__66637] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__66637)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__66630,Vvar__1___24Anonymous__66637) )
| ? [Vvar__1___24Anonymous__66639] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66639)
& ? [Vvar__2___24Anonymous__66640] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__2___24Anonymous__66640)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__66630,Vvar__1___24Anonymous__66639,Vvar__2___24Anonymous__66640) ) )
| ? [Vvar__1___24Anonymous__66642] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66642)
& ? [Vvar__2___24Anonymous__66643] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__2___24Anonymous__66643)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__66630,Vvar__1___24Anonymous__66642,Vvar__2___24Anonymous__66643) ) )
| ? [Vvar__1___24Anonymous__66645] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66645)
& ? [Vvar__2___24Anonymous__66646] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__2___24Anonymous__66646)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__66630,Vvar__1___24Anonymous__66645,Vvar__2___24Anonymous__66646) ) )
| ? [Vvar__1___24Anonymous__66648] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66648)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__66630,Vvar__1___24Anonymous__66648) )
| ? [Vvar__1___24Anonymous__66650] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66650)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__66630,Vvar__1___24Anonymous__66650) )
| ? [Vvar__1___24Anonymous__66652] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66652)
& ? [Vvar__2___24Anonymous__66653] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__2___24Anonymous__66653)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__66630,Vvar__1___24Anonymous__66652,Vvar__2___24Anonymous__66653) ) )
| ? [Vvar__1___24Anonymous__66655] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__66630,Vvar__1___24Anonymous__66655)
& ? [Vvar__2___24Anonymous__66656] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__66656)
& VX66631 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__66630,Vvar__1___24Anonymous__66655,Vvar__2___24Anonymous__66656) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694] :
( cType___24t(Vvar__0__R__65665)
=> ( t(Vvar__1__rO__65666,Vvar__0__R__65665)
=> ( t(Vvar__2__rI__65667,Vvar__0__R__65665)
=> ( c_24__type__65859___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__3__radd__65668)
=> ( c_24__type__65952___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__4__rmul__65673)
=> ( c_24__type__66045___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__5__rsub__65678)
=> ( c_24__type__66127___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__6__ropp__65683)
=> ( c_24__type__66220___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__7__rdiv__65686)
=> ( c_24__type__66302___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__8__rinv__65691)
=> ( c_24__type__66395___24t(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694,Vvar__9__req__65694)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__7__rdiv__65686,Vvar__8__rinv__65691,Vvar__9__req__65694)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__65665,Vvar__1__rO__65666,Vvar__2__rI__65667,Vvar__3__radd__65668,Vvar__4__rmul__65673,Vvar__5__rsub__65678,Vvar__6__ropp__65683,Vvar__9__req__65694)
& ~ p(happ(happ(Vvar__9__req__65694,Vvar__2__rI__65667),Vvar__1__rO__65666))
& ! [Vvar__var__var__var__var__var__var__12__p__65737__65739__65746__65748__65750__65752__65754] :
( t(Vvar__var__var__var__var__var__var__12__p__65737__65739__65746__65748__65750__65752__65754,Vvar__0__R__65665)
=> ! [Vvar__var__var__var__var__var__var__13__q__65738__65740__65747__65749__65751__65753__65755] :
( t(Vvar__var__var__var__var__var__var__13__q__65738__65740__65747__65749__65751__65753__65755,Vvar__0__R__65665)
=> p(happ(happ(Vvar__9__req__65694,happ(happ(Vvar__7__rdiv__65686,Vvar__var__var__var__var__var__var__12__p__65737__65739__65746__65748__65750__65752__65754),Vvar__var__var__var__var__var__var__13__q__65738__65740__65747__65749__65751__65753__65755)),happ(happ(Vvar__4__rmul__65673,Vvar__var__var__var__var__var__var__12__p__65737__65739__65746__65748__65750__65752__65754),happ(Vvar__8__rinv__65691,Vvar__var__var__var__var__var__var__13__q__65738__65740__65747__65749__65751__65753__65755)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__65742__65744__65756__65758__65760__65762__65764__65766] :
( t(Vvar__var__var__var__var__var__var__var__13__p__65742__65744__65756__65758__65760__65762__65764__65766,Vvar__0__R__65665)
=> ( ~ p(happ(happ(Vvar__9__req__65694,Vvar__var__var__var__var__var__var__var__13__p__65742__65744__65756__65758__65760__65762__65764__65766),Vvar__1__rO__65666))
=> p(happ(happ(Vvar__9__req__65694,happ(happ(Vvar__4__rmul__65673,happ(Vvar__8__rinv__65691,Vvar__var__var__var__var__var__var__var__13__p__65742__65744__65756__65758__65760__65762__65764__65766)),Vvar__var__var__var__var__var__var__var__13__p__65742__65744__65756__65758__65760__65762__65764__65766)),Vvar__2__rI__65667)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__67242,VX67243] :
( cType___24t(Vvar__0__C__67242)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__67242,VX67243)
=> ? [Vvar__1__num__67245] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__67242,Vvar__1__num__67245)
& ? [Vvar__2__denum__67246] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__67242,Vvar__2__denum__67246)
& ? [Vvar__3__condition__67247] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__67242),Vvar__3__condition__67247)
& VX67243 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__67242,Vvar__1__num__67245,Vvar__2__denum__67246,Vvar__3__condition__67247) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__186001,VX186002] :
( cType___24t(Vvar__0__C__186001)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__186001,VX186002)
=> ? [Vvar__1__rsplit__left__186004] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__186001,Vvar__1__rsplit__left__186004)
& ? [Vvar__2__rsplit__common__186005] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__186001,Vvar__2__rsplit__common__186005)
& ? [Vvar__3__rsplit__right__186006] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__186001,Vvar__3__rsplit__right__186006)
& VX186002 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__186001,Vvar__1__rsplit__left__186004,Vvar__2__rsplit__common__186005,Vvar__3__rsplit__right__186006) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX23688] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX23688)
=> ( VX23688 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__23689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23689)
& ? [Vvar__1___24Anonymous__23690] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__23690)
& VX23688 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__23689,Vvar__1___24Anonymous__23690) ) )
| ? [Vvar__0___24Anonymous__23691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23691)
& ? [Vvar__1___24Anonymous__23692] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__23692)
& VX23688 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__23691,Vvar__1___24Anonymous__23692) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__23709,VX23710] :
( cType___24t(Vvar__0__C__23709)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,VX23710)
=> ( VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__23709)
| VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__23709)
| ? [Vvar__1___24Anonymous__23714] :
( t(Vvar__1___24Anonymous__23714,Vvar__0__C__23709)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__23709,Vvar__1___24Anonymous__23714) )
| ? [Vvar__1___24Anonymous__23716] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23716)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__23709,Vvar__1___24Anonymous__23716) )
| ? [Vvar__1___24Anonymous__23718] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__1___24Anonymous__23718)
& ? [Vvar__2___24Anonymous__23719] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__2___24Anonymous__23719)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__23709,Vvar__1___24Anonymous__23718,Vvar__2___24Anonymous__23719) ) )
| ? [Vvar__1___24Anonymous__23721] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__1___24Anonymous__23721)
& ? [Vvar__2___24Anonymous__23722] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__2___24Anonymous__23722)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__23709,Vvar__1___24Anonymous__23721,Vvar__2___24Anonymous__23722) ) )
| ? [Vvar__1___24Anonymous__23724] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__1___24Anonymous__23724)
& ? [Vvar__2___24Anonymous__23725] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__2___24Anonymous__23725)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__23709,Vvar__1___24Anonymous__23724,Vvar__2___24Anonymous__23725) ) )
| ? [Vvar__1___24Anonymous__23727] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__1___24Anonymous__23727)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__23709,Vvar__1___24Anonymous__23727) )
| ? [Vvar__1___24Anonymous__23729] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__23709,Vvar__1___24Anonymous__23729)
& ? [Vvar__2___24Anonymous__23730] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23730)
& VX23710 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__23709,Vvar__1___24Anonymous__23729,Vvar__2___24Anonymous__23730) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__23509,VX23510] :
( cType___24t(Vvar__0__C__23509)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23509,VX23510)
=> ( ? [Vvar__1___24Anonymous__23512] :
( t(Vvar__1___24Anonymous__23512,Vvar__0__C__23509)
& VX23510 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__23509,Vvar__1___24Anonymous__23512) )
| ? [Vvar__1___24Anonymous__23514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23514)
& ? [Vvar__2___24Anonymous__23515] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23509,Vvar__2___24Anonymous__23515)
& VX23510 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__23509,Vvar__1___24Anonymous__23514,Vvar__2___24Anonymous__23515) ) )
| ? [Vvar__1___24Anonymous__23517] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23509,Vvar__1___24Anonymous__23517)
& ? [Vvar__2___24Anonymous__23518] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__23518)
& ? [Vvar__3___24Anonymous__23519] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__23509,Vvar__3___24Anonymous__23519)
& VX23510 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__23509,Vvar__1___24Anonymous__23517,Vvar__2___24Anonymous__23518,Vvar__3___24Anonymous__23519) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463] :
( cType___24t(Vvar__0__R__69442)
=> ( t(Vvar__1__rO__69443,Vvar__0__R__69442)
=> ( t(Vvar__2__rI__69444,Vvar__0__R__69442)
=> ( c_24__type__69691___24t(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463,Vvar__3__radd__69445)
=> ( c_24__type__69754___24t(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463,Vvar__4__rmul__69450)
=> ( c_24__type__69817___24t(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463,Vvar__5__rsub__69455)
=> ( c_24__type__69871___24t(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463,Vvar__6__ropp__69460)
=> ( c_24__type__69934___24t(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463,Vvar__7__req__69463)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__69442,Vvar__1__rO__69443,Vvar__2__rI__69444,Vvar__3__radd__69445,Vvar__4__rmul__69450,Vvar__5__rsub__69455,Vvar__6__ropp__69460,Vvar__7__req__69463)
=> ( ! [Vvar__var__var__var__var__var__8__x__69496__69497__69550__69551__69552__69553] :
( t(Vvar__var__var__var__var__var__8__x__69496__69497__69550__69551__69552__69553,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__3__radd__69445,Vvar__1__rO__69443),Vvar__var__var__var__var__var__8__x__69496__69497__69550__69551__69552__69553)),Vvar__var__var__var__var__var__8__x__69496__69497__69550__69551__69552__69553)) )
& ! [Vvar__var__var__var__var__9__x__69499__69501__69554__69556__69558] :
( t(Vvar__var__var__var__var__9__x__69499__69501__69554__69556__69558,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__10__y__69500__69502__69555__69557__69559] :
( t(Vvar__var__var__var__var__10__y__69500__69502__69555__69557__69559,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__9__x__69499__69501__69554__69556__69558),Vvar__var__var__var__var__10__y__69500__69502__69555__69557__69559)),happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__10__y__69500__69502__69555__69557__69559),Vvar__var__var__var__var__9__x__69499__69501__69554__69556__69558))) ) )
& ! [Vvar__var__var__var__var__10__x__69504__69507__69560__69563__69566] :
( t(Vvar__var__var__var__var__10__x__69504__69507__69560__69563__69566,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__11__y__69505__69508__69561__69564__69567] :
( t(Vvar__var__var__var__var__11__y__69505__69508__69561__69564__69567,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__12__z__69506__69509__69562__69565__69568] :
( t(Vvar__var__var__var__var__12__z__69506__69509__69562__69565__69568,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__10__x__69504__69507__69560__69563__69566),happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__11__y__69505__69508__69561__69564__69567),Vvar__var__var__var__var__12__z__69506__69509__69562__69565__69568))),happ(happ(Vvar__3__radd__69445,happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__10__x__69504__69507__69560__69563__69566),Vvar__var__var__var__var__11__y__69505__69508__69561__69564__69567)),Vvar__var__var__var__var__12__z__69506__69509__69562__69565__69568))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__69511__69512__69569__69570__69571__69572] :
( t(Vvar__var__var__var__var__var__11__x__69511__69512__69569__69570__69571__69572,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__4__rmul__69450,Vvar__2__rI__69444),Vvar__var__var__var__var__var__11__x__69511__69512__69569__69570__69571__69572)),Vvar__var__var__var__var__var__11__x__69511__69512__69569__69570__69571__69572)) )
& ! [Vvar__var__var__var__var__var__12__x__69514__69515__69573__69574__69575__69576] :
( t(Vvar__var__var__var__var__var__12__x__69514__69515__69573__69574__69575__69576,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__4__rmul__69450,Vvar__1__rO__69443),Vvar__var__var__var__var__var__12__x__69514__69515__69573__69574__69575__69576)),Vvar__1__rO__69443)) )
& ! [Vvar__var__var__var__var__13__x__69517__69519__69577__69579__69581] :
( t(Vvar__var__var__var__var__13__x__69517__69519__69577__69579__69581,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__14__y__69518__69520__69578__69580__69582] :
( t(Vvar__var__var__var__var__14__y__69518__69520__69578__69580__69582,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__13__x__69517__69519__69577__69579__69581),Vvar__var__var__var__var__14__y__69518__69520__69578__69580__69582)),happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__14__y__69518__69520__69578__69580__69582),Vvar__var__var__var__var__13__x__69517__69519__69577__69579__69581))) ) )
& ! [Vvar__var__var__var__var__14__x__69522__69525__69583__69586__69589] :
( t(Vvar__var__var__var__var__14__x__69522__69525__69583__69586__69589,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__15__y__69523__69526__69584__69587__69590] :
( t(Vvar__var__var__var__var__15__y__69523__69526__69584__69587__69590,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__16__z__69524__69527__69585__69588__69591] :
( t(Vvar__var__var__var__var__16__z__69524__69527__69585__69588__69591,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__14__x__69522__69525__69583__69586__69589),happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__15__y__69523__69526__69584__69587__69590),Vvar__var__var__var__var__16__z__69524__69527__69585__69588__69591))),happ(happ(Vvar__4__rmul__69450,happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__14__x__69522__69525__69583__69586__69589),Vvar__var__var__var__var__15__y__69523__69526__69584__69587__69590)),Vvar__var__var__var__var__16__z__69524__69527__69585__69588__69591))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__69529__69532__69592__69595__69598__69601] :
( t(Vvar__var__var__var__var__var__15__x__69529__69532__69592__69595__69598__69601,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__var__16__y__69530__69533__69593__69596__69599__69602] :
( t(Vvar__var__var__var__var__var__16__y__69530__69533__69593__69596__69599__69602,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__var__17__z__69531__69534__69594__69597__69600__69603] :
( t(Vvar__var__var__var__var__var__17__z__69531__69534__69594__69597__69600__69603,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__4__rmul__69450,happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__var__15__x__69529__69532__69592__69595__69598__69601),Vvar__var__var__var__var__var__16__y__69530__69533__69593__69596__69599__69602)),Vvar__var__var__var__var__var__17__z__69531__69534__69594__69597__69600__69603)),happ(happ(Vvar__3__radd__69445,happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__var__15__x__69529__69532__69592__69595__69598__69601),Vvar__var__var__var__var__var__17__z__69531__69534__69594__69597__69600__69603)),happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__var__16__y__69530__69533__69593__69596__69599__69602),Vvar__var__var__var__var__var__17__z__69531__69534__69594__69597__69600__69603)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__69536__69538__69604__69606__69608__69610] :
( t(Vvar__var__var__var__var__var__16__x__69536__69538__69604__69606__69608__69610,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__var__17__y__69537__69539__69605__69607__69609__69611] :
( t(Vvar__var__var__var__var__var__17__y__69537__69539__69605__69607__69609__69611,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(Vvar__6__ropp__69460,happ(happ(Vvar__4__rmul__69450,Vvar__var__var__var__var__var__16__x__69536__69538__69604__69606__69608__69610),Vvar__var__var__var__var__var__17__y__69537__69539__69605__69607__69609__69611))),happ(happ(Vvar__4__rmul__69450,happ(Vvar__6__ropp__69460,Vvar__var__var__var__var__var__16__x__69536__69538__69604__69606__69608__69610)),Vvar__var__var__var__var__var__17__y__69537__69539__69605__69607__69609__69611))) ) )
& ! [Vvar__var__var__var__var__var__17__x__69541__69543__69612__69614__69616__69618] :
( t(Vvar__var__var__var__var__var__17__x__69541__69543__69612__69614__69616__69618,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__var__18__y__69542__69544__69613__69615__69617__69619] :
( t(Vvar__var__var__var__var__var__18__y__69542__69544__69613__69615__69617__69619,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(Vvar__6__ropp__69460,happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__var__17__x__69541__69543__69612__69614__69616__69618),Vvar__var__var__var__var__var__18__y__69542__69544__69613__69615__69617__69619))),happ(happ(Vvar__3__radd__69445,happ(Vvar__6__ropp__69460,Vvar__var__var__var__var__var__17__x__69541__69543__69612__69614__69616__69618)),happ(Vvar__6__ropp__69460,Vvar__var__var__var__var__var__18__y__69542__69544__69613__69615__69617__69619)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__69546__69548__69620__69622__69624__69626__69628] :
( t(Vvar__var__var__var__var__var__var__18__x__69546__69548__69620__69622__69624__69626__69628,Vvar__0__R__69442)
=> ! [Vvar__var__var__var__var__var__var__19__y__69547__69549__69621__69623__69625__69627__69629] :
( t(Vvar__var__var__var__var__var__var__19__y__69547__69549__69621__69623__69625__69627__69629,Vvar__0__R__69442)
=> p(happ(happ(Vvar__7__req__69463,happ(happ(Vvar__5__rsub__69455,Vvar__var__var__var__var__var__var__18__x__69546__69548__69620__69622__69624__69626__69628),Vvar__var__var__var__var__var__var__19__y__69547__69549__69621__69623__69625__69627__69629)),happ(happ(Vvar__3__radd__69445,Vvar__var__var__var__var__var__var__18__x__69546__69548__69620__69622__69624__69626__69628),happ(Vvar__6__ropp__69460,Vvar__var__var__var__var__var__var__19__y__69547__69549__69621__69623__69625__69627__69629)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739] :
( cType___24t(Vvar__0__R__70719)
=> ( c_24__type__70859___24t(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__1__req__70720)
=> ( cType___24t(Vvar__2__C__70725)
=> ( c_24__type__70909___24t(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__3__cadd__70726)
=> ( c_24__type__70959___24t(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__4__cmul__70731)
=> ( c_24__type__71001___24t(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__5__phi__70736)
=> ( c_24__type__71051___24t(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__6__cdiv__70739)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__70771__70776__70781__70786__70791__70796__70801__70806] :
( t(Vvar__var__var__var__var__var__var__var__7__a__70771__70776__70781__70786__70791__70796__70801__70806,Vvar__2__C__70725)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__70772__70777__70782__70787__70792__70797__70802__70807] :
( t(Vvar__var__var__var__var__var__var__var__8__b__70772__70777__70782__70787__70792__70797__70802__70807,Vvar__2__C__70725)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2471114___24a9(Vvar__0__R__70719,Vvar__1__req__70720,Vvar__2__C__70725,Vvar__3__cadd__70726,Vvar__4__cmul__70731,Vvar__5__phi__70736,Vvar__6__cdiv__70739,Vvar__var__var__var__var__var__var__var__7__a__70771__70776__70781__70786__70791__70796__70801__70806,Vvar__var__var__var__var__var__var__var__8__b__70772__70777__70782__70787__70792__70797__70802__70807) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977] :
( cType___24t(Vvar__0__R__54961)
=> ( t(Vvar__1__rI__54962,Vvar__0__R__54961)
=> ( c_24__type__55063___24t(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977,Vvar__2__rmul__54963)
=> ( c_24__type__55107___24t(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977,Vvar__3__req__54968)
=> ( cType___24t(Vvar__4__Cpow__54973)
=> ( c_24__type__55143___24t(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977,Vvar__5__Cp__phi__54974)
=> ( c_24__type__55187___24t(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977,Vvar__6__rpow__54977)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__3__req__54968,Vvar__4__Cpow__54973,Vvar__5__Cp__phi__54974,Vvar__6__rpow__54977)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__55005__55007__55009__55011__55013__55015__55017__55019] :
( t(Vvar__var__var__var__var__var__var__var__7__r__55005__55007__55009__55011__55013__55015__55017__55019,Vvar__0__R__54961)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__55006__55008__55010__55012__55014__55016__55018__55020] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__55006__55008__55010__55012__55014__55016__55018__55020)
=> p(happ(happ(Vvar__3__req__54968,happ(happ(Vvar__6__rpow__54977,Vvar__var__var__var__var__var__var__var__7__r__55005__55007__55009__55011__55013__55015__55017__55019),happ(Vvar__5__Cp__phi__54974,Vvar__var__var__var__var__var__var__var__8__n__55006__55008__55010__55012__55014__55016__55018__55020))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__54961,Vvar__1__rI__54962,Vvar__2__rmul__54963,Vvar__var__var__var__var__var__var__var__7__r__55005__55007__55009__55011__55013__55015__55017__55019,Vvar__var__var__var__var__var__var__var__8__n__55006__55008__55010__55012__55014__55016__55018__55020))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050] :
( cType___24t(Vvar__0__R__70036)
=> ( c_24__type__70141___24t(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050,Vvar__1__radd__70037)
=> ( c_24__type__70171___24t(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050,Vvar__2__rmul__70042)
=> ( c_24__type__70195___24t(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050,Vvar__3__ropp__70047)
=> ( c_24__type__70225___24t(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050,Vvar__4__req__70050)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__70255___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__70036,c_24__type__70279___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050),Vvar__4__req__70050,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__70036,Vvar__0__R__70036,Vvar__4__req__70050,Vvar__4__req__70050)),Vvar__1__radd__70037)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__70312___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__70036,c_24__type__70336___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050),Vvar__4__req__70050,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__70036,Vvar__0__R__70036,Vvar__4__req__70050,Vvar__4__req__70050)),Vvar__2__rmul__70042)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__70363___24a5(Vvar__0__R__70036,Vvar__1__radd__70037,Vvar__2__rmul__70042,Vvar__3__ropp__70047,Vvar__4__req__70050),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__70036,Vvar__0__R__70036,Vvar__4__req__70050,Vvar__4__req__70050),Vvar__3__ropp__70047)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX107661] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX107661)
=> ( VX107661 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__107662] :
( cType___24t(Vvar__0__R__107662)
& ? [Vvar__1__req__107663] :
( c_24__type__6754___24t(Vvar__0__R__107662,Vvar__1__req__107663)
& ? [Vvar__2__reqb__107668] :
( c_24__type__8059___24t(Vvar__0__R__107662,Vvar__2__reqb__107668)
& ! [Vvar__var__3__x__107674__107677] :
( t(Vvar__var__3__x__107674__107677,Vvar__0__R__107662)
=> ! [Vvar__var__4__y__107675__107678] :
( t(Vvar__var__4__y__107675__107678,Vvar__0__R__107662)
=> ( happ(happ(Vvar__2__reqb__107668,Vvar__var__3__x__107674__107677),Vvar__var__4__y__107675__107678) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__107663,Vvar__var__3__x__107674__107677),Vvar__var__4__y__107675__107678)) ) ) )
& VX107661 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__107662,Vvar__1__req__107663,Vvar__2__reqb__107668) ) ) )
| ? [Vvar__0__R__107680] :
( cType___24t(Vvar__0__R__107680)
& ? [Vvar__1__rO__107681] :
( t(Vvar__1__rO__107681,Vvar__0__R__107680)
& ? [Vvar__2__rI__107682] :
( t(Vvar__2__rI__107682,Vvar__0__R__107680)
& ? [Vvar__3__radd__107683] :
( c_24__type__1053___24t(Vvar__0__R__107680,Vvar__3__radd__107683)
& ? [Vvar__4__rmul__107688] :
( c_24__type__1053___24t(Vvar__0__R__107680,Vvar__4__rmul__107688)
& ? [Vvar__5__rsub__107693] :
( c_24__type__1053___24t(Vvar__0__R__107680,Vvar__5__rsub__107693)
& ? [Vvar__6__ropp__107698] :
( c_24__type__6617___24t(Vvar__0__R__107680,Vvar__6__ropp__107698)
& ? [Vvar__7__req__107701] :
( c_24__type__6754___24t(Vvar__0__R__107680,Vvar__7__req__107701)
& ? [Vvar__8__C__107706] :
( cType___24t(Vvar__8__C__107706)
& ? [Vvar__9__cO__107707] :
( t(Vvar__9__cO__107707,Vvar__8__C__107706)
& ? [Vvar__10__cI__107708] :
( t(Vvar__10__cI__107708,Vvar__8__C__107706)
& ? [Vvar__11__cadd__107709] :
( c_24__type__24835___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__11__cadd__107709)
& ? [Vvar__12__cmul__107714] :
( c_24__type__24835___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__12__cmul__107714)
& ? [Vvar__13__csub__107719] :
( c_24__type__24835___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__13__csub__107719)
& ? [Vvar__14__copp__107724] :
( c_24__type__24849___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__14__copp__107724)
& ? [Vvar__15__ceqb__107727] :
( c_24__type__24856___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__15__ceqb__107727)
& ? [Vvar__16__phi__107732] :
( c_24__type__24136___24t(Vvar__0__R__107680,Vvar__8__C__107706,Vvar__16__phi__107732)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__107680,Vvar__1__rO__107681,Vvar__2__rI__107682,Vvar__3__radd__107683,Vvar__4__rmul__107688,Vvar__5__rsub__107693,Vvar__6__ropp__107698,Vvar__7__req__107701,Vvar__8__C__107706,Vvar__9__cO__107707,Vvar__10__cI__107708,Vvar__11__cadd__107709,Vvar__12__cmul__107714,Vvar__13__csub__107719,Vvar__14__copp__107724,Vvar__15__ceqb__107727,Vvar__16__phi__107732)
& VX107661 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__107680,Vvar__1__rO__107681,Vvar__2__rI__107682,Vvar__3__radd__107683,Vvar__4__rmul__107688,Vvar__5__rsub__107693,Vvar__6__ropp__107698,Vvar__7__req__107701,Vvar__8__C__107706,Vvar__9__cO__107707,Vvar__10__cI__107708,Vvar__11__cadd__107709,Vvar__12__cmul__107714,Vvar__13__csub__107719,Vvar__14__copp__107724,Vvar__15__ceqb__107727,Vvar__16__phi__107732) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529] :
( cType___24t(Vvar__0__R__52477)
=> ( t(Vvar__1__rO__52478,Vvar__0__R__52477)
=> ( t(Vvar__2__rI__52479,Vvar__0__R__52477)
=> ( c_24__type__52873___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__3__radd__52480)
=> ( c_24__type__53086___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__4__rmul__52485)
=> ( c_24__type__53299___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__5__rsub__52490)
=> ( c_24__type__53494___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__6__ropp__52495)
=> ( c_24__type__53707___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__7__req__52498)
=> ( cType___24t(Vvar__8__C__52503)
=> ( t(Vvar__9__cO__52504,Vvar__8__C__52503)
=> ( t(Vvar__10__cI__52505,Vvar__8__C__52503)
=> ( c_24__type__53920___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__11__cadd__52506)
=> ( c_24__type__54133___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__12__cmul__52511)
=> ( c_24__type__54346___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__13__csub__52516)
=> ( c_24__type__54541___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__14__copp__52521)
=> ( c_24__type__54754___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__15__ceqb__52524)
=> ( c_24__type__54949___24t(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529,Vvar__16__phi__52529)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__52477,Vvar__1__rO__52478,Vvar__2__rI__52479,Vvar__3__radd__52480,Vvar__4__rmul__52485,Vvar__5__rsub__52490,Vvar__6__ropp__52495,Vvar__7__req__52498,Vvar__8__C__52503,Vvar__9__cO__52504,Vvar__10__cI__52505,Vvar__11__cadd__52506,Vvar__12__cmul__52511,Vvar__13__csub__52516,Vvar__14__copp__52521,Vvar__15__ceqb__52524,Vvar__16__phi__52529)
=> ( p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,Vvar__9__cO__52504)),Vvar__1__rO__52478))
& p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,Vvar__10__cI__52505)),Vvar__2__rI__52479))
& ! [Vvar__var__var__var__var__var__var__19__x__52591__52593__52615__52617__52619__52621__52623] :
( t(Vvar__var__var__var__var__var__var__19__x__52591__52593__52615__52617__52619__52621__52623,Vvar__8__C__52503)
=> ! [Vvar__var__var__var__var__var__var__20__y__52592__52594__52616__52618__52620__52622__52624] :
( t(Vvar__var__var__var__var__var__var__20__y__52592__52594__52616__52618__52620__52622__52624,Vvar__8__C__52503)
=> p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,happ(happ(Vvar__11__cadd__52506,Vvar__var__var__var__var__var__var__19__x__52591__52593__52615__52617__52619__52621__52623),Vvar__var__var__var__var__var__var__20__y__52592__52594__52616__52618__52620__52622__52624))),happ(happ(Vvar__3__radd__52480,happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__19__x__52591__52593__52615__52617__52619__52621__52623)),happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__20__y__52592__52594__52616__52618__52620__52622__52624)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__52596__52598__52625__52627__52629__52631__52633] :
( t(Vvar__var__var__var__var__var__var__20__x__52596__52598__52625__52627__52629__52631__52633,Vvar__8__C__52503)
=> ! [Vvar__var__var__var__var__var__var__21__y__52597__52599__52626__52628__52630__52632__52634] :
( t(Vvar__var__var__var__var__var__var__21__y__52597__52599__52626__52628__52630__52632__52634,Vvar__8__C__52503)
=> p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,happ(happ(Vvar__13__csub__52516,Vvar__var__var__var__var__var__var__20__x__52596__52598__52625__52627__52629__52631__52633),Vvar__var__var__var__var__var__var__21__y__52597__52599__52626__52628__52630__52632__52634))),happ(happ(Vvar__5__rsub__52490,happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__20__x__52596__52598__52625__52627__52629__52631__52633)),happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__21__y__52597__52599__52626__52628__52630__52632__52634)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__52601__52603__52635__52637__52639__52641__52643] :
( t(Vvar__var__var__var__var__var__var__21__x__52601__52603__52635__52637__52639__52641__52643,Vvar__8__C__52503)
=> ! [Vvar__var__var__var__var__var__var__22__y__52602__52604__52636__52638__52640__52642__52644] :
( t(Vvar__var__var__var__var__var__var__22__y__52602__52604__52636__52638__52640__52642__52644,Vvar__8__C__52503)
=> p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,happ(happ(Vvar__12__cmul__52511,Vvar__var__var__var__var__var__var__21__x__52601__52603__52635__52637__52639__52641__52643),Vvar__var__var__var__var__var__var__22__y__52602__52604__52636__52638__52640__52642__52644))),happ(happ(Vvar__4__rmul__52485,happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__21__x__52601__52603__52635__52637__52639__52641__52643)),happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__22__y__52602__52604__52636__52638__52640__52642__52644)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__52606__52607__52645__52646__52647__52648__52649] :
( t(Vvar__var__var__var__var__var__var__22__x__52606__52607__52645__52646__52647__52648__52649,Vvar__8__C__52503)
=> p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,happ(Vvar__14__copp__52521,Vvar__var__var__var__var__var__var__22__x__52606__52607__52645__52646__52647__52648__52649))),happ(Vvar__6__ropp__52495,happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__var__22__x__52606__52607__52645__52646__52647__52648__52649)))) )
& ! [Vvar__var__var__var__var__var__23__x__52609__52612__52650__52653__52656__52659] :
( t(Vvar__var__var__var__var__var__23__x__52609__52612__52650__52653__52656__52659,Vvar__8__C__52503)
=> ! [Vvar__var__var__var__var__var__24__y__52610__52613__52651__52654__52657__52660] :
( t(Vvar__var__var__var__var__var__24__y__52610__52613__52651__52654__52657__52660,Vvar__8__C__52503)
=> ( happ(happ(Vvar__15__ceqb__52524,Vvar__var__var__var__var__var__23__x__52609__52612__52650__52653__52656__52659),Vvar__var__var__var__var__var__24__y__52610__52613__52651__52654__52657__52660) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__52498,happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__23__x__52609__52612__52650__52653__52656__52659)),happ(Vvar__16__phi__52529,Vvar__var__var__var__var__var__24__y__52610__52613__52651__52654__52657__52660))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619] :
( cType___24t(Vvar__0__R__106583)
=> ( t(Vvar__1__rO__106584,Vvar__0__R__106583)
=> ( t(Vvar__2__rI__106585,Vvar__0__R__106583)
=> ( c_24__type__106836___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__3__radd__106586)
=> ( c_24__type__106961___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__4__rmul__106591)
=> ( c_24__type__107086___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__5__req__106596)
=> ( cType___24t(Vvar__6__C__106601)
=> ( t(Vvar__7__cO__106602,Vvar__6__C__106601)
=> ( t(Vvar__8__cI__106603,Vvar__6__C__106601)
=> ( c_24__type__107211___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__9__cadd__106604)
=> ( c_24__type__107336___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__10__cmul__106609)
=> ( c_24__type__107461___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__11__ceqb__106614)
=> ( c_24__type__107572___24t(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619,Vvar__12__phi__106619)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__106583,Vvar__1__rO__106584,Vvar__2__rI__106585,Vvar__3__radd__106586,Vvar__4__rmul__106591,Vvar__5__req__106596,Vvar__6__C__106601,Vvar__7__cO__106602,Vvar__8__cI__106603,Vvar__9__cadd__106604,Vvar__10__cmul__106609,Vvar__11__ceqb__106614,Vvar__12__phi__106619)
=> ( p(happ(happ(Vvar__5__req__106596,happ(Vvar__12__phi__106619,Vvar__7__cO__106602)),Vvar__1__rO__106584))
& p(happ(happ(Vvar__5__req__106596,happ(Vvar__12__phi__106619,Vvar__8__cI__106603)),Vvar__2__rI__106585))
& ! [Vvar__var__var__var__var__var__var__15__x__106665__106667__106681__106683__106685__106687__106689] :
( t(Vvar__var__var__var__var__var__var__15__x__106665__106667__106681__106683__106685__106687__106689,Vvar__6__C__106601)
=> ! [Vvar__var__var__var__var__var__var__16__y__106666__106668__106682__106684__106686__106688__106690] :
( t(Vvar__var__var__var__var__var__var__16__y__106666__106668__106682__106684__106686__106688__106690,Vvar__6__C__106601)
=> p(happ(happ(Vvar__5__req__106596,happ(Vvar__12__phi__106619,happ(happ(Vvar__9__cadd__106604,Vvar__var__var__var__var__var__var__15__x__106665__106667__106681__106683__106685__106687__106689),Vvar__var__var__var__var__var__var__16__y__106666__106668__106682__106684__106686__106688__106690))),happ(happ(Vvar__3__radd__106586,happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__var__15__x__106665__106667__106681__106683__106685__106687__106689)),happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__var__16__y__106666__106668__106682__106684__106686__106688__106690)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__106670__106672__106691__106693__106695__106697__106699] :
( t(Vvar__var__var__var__var__var__var__16__x__106670__106672__106691__106693__106695__106697__106699,Vvar__6__C__106601)
=> ! [Vvar__var__var__var__var__var__var__17__y__106671__106673__106692__106694__106696__106698__106700] :
( t(Vvar__var__var__var__var__var__var__17__y__106671__106673__106692__106694__106696__106698__106700,Vvar__6__C__106601)
=> p(happ(happ(Vvar__5__req__106596,happ(Vvar__12__phi__106619,happ(happ(Vvar__10__cmul__106609,Vvar__var__var__var__var__var__var__16__x__106670__106672__106691__106693__106695__106697__106699),Vvar__var__var__var__var__var__var__17__y__106671__106673__106692__106694__106696__106698__106700))),happ(happ(Vvar__4__rmul__106591,happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__var__16__x__106670__106672__106691__106693__106695__106697__106699)),happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__var__17__y__106671__106673__106692__106694__106696__106698__106700)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__106675__106678__106701__106704__106707__106710] :
( t(Vvar__var__var__var__var__var__17__x__106675__106678__106701__106704__106707__106710,Vvar__6__C__106601)
=> ! [Vvar__var__var__var__var__var__18__y__106676__106679__106702__106705__106708__106711] :
( t(Vvar__var__var__var__var__var__18__y__106676__106679__106702__106705__106708__106711,Vvar__6__C__106601)
=> ( happ(happ(Vvar__11__ceqb__106614,Vvar__var__var__var__var__var__17__x__106675__106678__106701__106704__106707__106710),Vvar__var__var__var__var__var__18__y__106676__106679__106702__106705__106708__106711) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__106596,happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__17__x__106675__106678__106701__106704__106707__106710)),happ(Vvar__12__phi__106619,Vvar__var__var__var__var__var__18__y__106676__106679__106702__106705__106708__106711))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__70625,Vvar__1__copp__70626,Vvar__2__ceqb__70629,Vvar__3__get__sign__70634] :
( cType___24t(Vvar__0__C__70625)
=> ( c_24__type__70681___24t(Vvar__0__C__70625,Vvar__1__copp__70626,Vvar__2__ceqb__70629,Vvar__3__get__sign__70634,Vvar__1__copp__70626)
=> ( c_24__type__70700___24t(Vvar__0__C__70625,Vvar__1__copp__70626,Vvar__2__ceqb__70629,Vvar__3__get__sign__70634,Vvar__2__ceqb__70629)
=> ( c_24__type__70714___24t(Vvar__0__C__70625,Vvar__1__copp__70626,Vvar__2__ceqb__70629,Vvar__3__get__sign__70634,Vvar__3__get__sign__70634)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__70625,Vvar__1__copp__70626,Vvar__2__ceqb__70629,Vvar__3__get__sign__70634)
=> ( ! [Vvar__var__var__var__var__var__4__c__70651__70654__70657__70660__70663__70666] :
( t(Vvar__var__var__var__var__var__4__c__70651__70654__70657__70660__70663__70666,Vvar__0__C__70625)
=> ! [Vvar__var__var__var__var__var__5__c_27__70652__70655__70658__70661__70664__70667] :
( t(Vvar__var__var__var__var__var__5__c_27__70652__70655__70658__70661__70664__70667,Vvar__0__C__70625)
=> ( happ(Vvar__3__get__sign__70634,Vvar__var__var__var__var__var__4__c__70651__70654__70657__70660__70663__70666) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__70625,Vvar__var__var__var__var__var__5__c_27__70652__70655__70658__70661__70664__70667)
=> happ(happ(Vvar__2__ceqb__70629,Vvar__var__var__var__var__var__4__c__70651__70654__70657__70660__70663__70666),happ(Vvar__1__copp__70626,Vvar__var__var__var__var__var__5__c_27__70652__70655__70658__70661__70664__70667)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412] :
( cType___24t(Vvar__0__R__186401)
=> ( c_24__type__186487___24t(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412,Vvar__1__radd__186402)
=> ( c_24__type__186510___24t(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412,Vvar__2__rmul__186407)
=> ( c_24__type__186533___24t(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412,Vvar__3__req__186412)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__186556___24a4(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__186401,c_24__type__186574___24a4(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412),Vvar__3__req__186412,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__186401,Vvar__0__R__186401,Vvar__3__req__186412,Vvar__3__req__186412)),Vvar__1__radd__186402)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__186600___24a4(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__186401,c_24__type__186618___24a4(Vvar__0__R__186401,Vvar__1__radd__186402,Vvar__2__rmul__186407,Vvar__3__req__186412),Vvar__3__req__186412,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__186401,Vvar__0__R__186401,Vvar__3__req__186412,Vvar__3__req__186412)),Vvar__2__rmul__186407)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.arith_lems.R_ceil_log2_S',axiom,
! [Vvar__0__n__31156,Vvar__1___24Anonymous__31157,VX31158] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31156)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__31157)
=> ( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(Vvar__0__n__31156,Vvar__1___24Anonymous__31157,VX31158)
=> ( ? [Vvar__0__n__31159] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31159)
& Vvar__0__n__31159 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__31157 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__0__n__31156 = cCoq_2eInit_2eDatatypes_2eO
& VX31158 = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0___24a1(Vvar__0__n__31159) )
| ? [Vvar__0__n__31161] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31161)
& ? [Vvar__1____x__31162] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1____x__31162)
& Vvar__0__n__31161 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1____x__31162)
& ? [Vvar__3____res__31164] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3____res__31164)
& ? [Vvar__4___24Anonymous__31165] :
( cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0__n__31161),Vvar__3____res__31164,Vvar__4___24Anonymous__31165)
& Vvar__1___24Anonymous__31157 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3____res__31164)
& Vvar__0__n__31156 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1____x__31162)
& VX31158 = cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__1___24a4(Vvar__0__n__31161,Vvar__1____x__31162,Vvar__3____res__31164,Vvar__4___24Anonymous__31165) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.arith_lems.R_floor_log2_S',axiom,
! [Vvar__0__n__33286,Vvar__1___24Anonymous__33287,VX33288] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__33286)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__33287)
=> ( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(Vvar__0__n__33286,Vvar__1___24Anonymous__33287,VX33288)
=> ( ? [Vvar__0__n__33289] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__33289)
& Vvar__0__n__33289 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__33287 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__0__n__33286 = cCoq_2eInit_2eDatatypes_2eO
& VX33288 = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0___24a1(Vvar__0__n__33289) )
| ? [Vvar__0__n__33291] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__33291)
& ? [Vvar__1__n_27__33292] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n_27__33292)
& Vvar__0__n__33291 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__n_27__33292)
& ? [Vvar__3____res__33294] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3____res__33294)
& ? [Vvar__4___24Anonymous__33295] :
( cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__1__n_27__33292),Vvar__3____res__33294,Vvar__4___24Anonymous__33295)
& Vvar__1___24Anonymous__33287 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3____res__33294)
& Vvar__0__n__33286 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__n_27__33292)
& VX33288 = cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__1___24a4(Vvar__0__n__33291,Vvar__1__n_27__33292,Vvar__3____res__33294,Vvar__4___24Anonymous__33295) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.elemsR',axiom,
! [Vvar__0__A__10499,Vvar__1__B__10500,Vvar__2__R__10501,Vvar__3___24Anonymous__10506,Vvar__4___24Anonymous__10507] :
( cType___24t(Vvar__0__A__10499)
=> ( cType___24t(Vvar__1__B__10500)
=> ( c_24__type__10544___24t(Vvar__0__A__10499,Vvar__1__B__10500,Vvar__2__R__10501,Vvar__3___24Anonymous__10506,Vvar__4___24Anonymous__10507,Vvar__2__R__10501)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10499,Vvar__3___24Anonymous__10506)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__10500,Vvar__4___24Anonymous__10507)
=> ( cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__10499,Vvar__1__B__10500,Vvar__2__R__10501,Vvar__3___24Anonymous__10506,Vvar__4___24Anonymous__10507)
=> ( ( Vvar__4___24Anonymous__10507 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__10500)
& Vvar__3___24Anonymous__10506 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__10499) )
| ? [Vvar__3__a__10523] :
( t(Vvar__3__a__10523,Vvar__0__A__10499)
& ? [Vvar__4__b__10524] :
( t(Vvar__4__b__10524,Vvar__1__B__10500)
& p(happ(happ(Vvar__2__R__10501,Vvar__3__a__10523),Vvar__4__b__10524))
& ? [Vvar__6__l__10526] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10499,Vvar__6__l__10526)
& ? [Vvar__7__l_27__10527] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__10500,Vvar__7__l_27__10527)
& cQuicksortComplexity_2elist__utils_2eelemsR___24a5(Vvar__0__A__10499,Vvar__1__B__10500,Vvar__2__R__10501,Vvar__6__l__10526,Vvar__7__l_27__10527)
& Vvar__4___24Anonymous__10507 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__10500,Vvar__4__b__10524,Vvar__7__l_27__10527)
& Vvar__3___24Anonymous__10506 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10499,Vvar__3__a__10523,Vvar__6__l__10526) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.list_utils.merges_spec',axiom,
! [Vvar__0__T__6989,Vvar__1___24Anonymous__6990,Vvar__2___24Anonymous__6991,Vvar__3___24Anonymous__6992] :
( cType___24t(Vvar__0__T__6989)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__1___24Anonymous__6990)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__2___24Anonymous__6991)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989),Vvar__3___24Anonymous__6992)
=> ( cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__6989,Vvar__1___24Anonymous__6990,Vvar__2___24Anonymous__6991,Vvar__3___24Anonymous__6992)
=> ( ? [Vvar__1__x__6995] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__1__x__6995)
& Vvar__3___24Anonymous__6992 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989),Vvar__1__x__6995,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989)))
& Vvar__2___24Anonymous__6991 = Vvar__1__x__6995
& Vvar__1___24Anonymous__6990 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__6989) )
| ? [Vvar__1__x__6997] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__1__x__6997)
& Vvar__3___24Anonymous__6992 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989),Vvar__1__x__6997,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989)))
& Vvar__2___24Anonymous__6991 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__T__6989)
& Vvar__1___24Anonymous__6990 = Vvar__1__x__6997 )
| ? [Vvar__1__x__6999] :
( t(Vvar__1__x__6999,Vvar__0__T__6989)
& ? [Vvar__2__y__7000] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__2__y__7000)
& ? [Vvar__3__h__7001] :
( t(Vvar__3__h__7001,Vvar__0__T__6989)
& ? [Vvar__4__t__7002] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__T__6989,Vvar__4__t__7002)
& ? [Vvar__5__r__7003] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989),Vvar__5__r__7003)
& ? [Vvar__6__r_27__7004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vvar__0__T__6989),Vvar__6__r_27__7004)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__6989,Vvar__2__y__7000,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__6989,Vvar__3__h__7001,Vvar__4__t__7002),Vvar__5__r__7003)
& cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(Vvar__0__T__6989,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__6989,Vvar__1__x__6999,Vvar__2__y__7000),Vvar__4__t__7002,Vvar__6__r_27__7004)
& Vvar__3___24Anonymous__6992 = c_24__case__Coq_2eInit_2eDatatypes_2elist_247499___24a8(Vvar__0__T__6989,Vvar__1___24Anonymous__6990,Vvar__2___24Anonymous__6991,Vvar__3___24Anonymous__6992,Vvar__1__x__6999,Vvar__3__h__7001,Vvar__5__r__7003,Vvar__6__r_27__7004)
& Vvar__2___24Anonymous__6991 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__6989,Vvar__3__h__7001,Vvar__4__t__7002)
& Vvar__1___24Anonymous__6990 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__T__6989,Vvar__1__x__6999,Vvar__2__y__7000) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.monads.Functor',axiom,
! [VX38591] :
( cQuicksortComplexity_2emonads_2eFunctor___24t(VX38591)
=> ? [Vvar__0__func__38592] :
( c_24__type__199___24t(Vvar__0__func__38592)
& ? [Vvar__1__func__map__38594] :
( c_24__type__38642___24t(Vvar__0__func__38592,Vvar__1__func__map__38594)
& ! [Vvar__var__2__X__38606__38609] :
( cType___24t(Vvar__var__2__X__38606__38609)
=> happ(happ(happ(Vvar__1__func__map__38594,Vvar__var__2__X__38606__38609),Vvar__var__2__X__38606__38609),c_24__lam__38648___24a2(Vvar__0__func__38592,Vvar__var__2__X__38606__38609)) = c_24__lam__38651___24a2(Vvar__0__func__38592,Vvar__var__2__X__38606__38609) )
& ! [Vvar__var__3__a__38613__38621] :
( cType___24t(Vvar__var__3__a__38613__38621)
=> ! [Vvar__var__4__b__38614__38622] :
( cType___24t(Vvar__var__4__b__38614__38622)
=> ! [Vvar__var__5__c__38615__38623] :
( cType___24t(Vvar__var__5__c__38615__38623)
=> ! [Vvar__var__6__x__38620__38628] :
( t(Vvar__var__6__x__38620__38628,happ(Vvar__0__func__38592,Vvar__var__3__a__38613__38621))
=> ! [Vvar__var__7__f__38618__38626] :
( c_24__type__38659___24t(Vvar__0__func__38592,Vvar__var__3__a__38613__38621,Vvar__var__4__b__38614__38622,Vvar__var__5__c__38615__38623,Vvar__var__7__f__38618__38626)
=> ! [Vvar__var__8__g__38619__38627] :
( c_24__type__38665___24t(Vvar__0__func__38592,Vvar__var__3__a__38613__38621,Vvar__var__4__b__38614__38622,Vvar__var__5__c__38615__38623,Vvar__var__8__g__38619__38627)
=> happ(happ(happ(happ(Vvar__1__func__map__38594,Vvar__var__3__a__38613__38621),Vvar__var__5__c__38615__38623),cCoq_2eProgram_2eBasics_2ecompose___24a5(Vvar__var__3__a__38613__38621,Vvar__var__4__b__38614__38622,Vvar__var__5__c__38615__38623,Vvar__var__7__f__38618__38626,Vvar__var__8__g__38619__38627)),Vvar__var__6__x__38620__38628) = happ(happ(happ(happ(Vvar__1__func__map__38594,Vvar__var__4__b__38614__38622),Vvar__var__5__c__38615__38623),Vvar__var__7__f__38618__38626),happ(happ(happ(happ(Vvar__1__func__map__38594,Vvar__var__3__a__38613__38621),Vvar__var__4__b__38614__38622),Vvar__var__8__g__38619__38627),Vvar__var__6__x__38620__38628)) ) ) ) ) ) )
& VX38591 = cQuicksortComplexity_2emonads_2eBuild__Functor___24a2(Vvar__0__func__38592,Vvar__1__func__map__38594) ) ) ) ).
fof('$_inversion_QuicksortComplexity.monads.Monad',axiom,
! [VX145] :
( cQuicksortComplexity_2emonads_2eMonad___24t(VX145)
=> ? [Vvar__0__mon__146] :
( c_24__type__199___24t(Vvar__0__mon__146)
& ? [Vvar__1__bind__148] :
( c_24__type__215___24t(Vvar__0__mon__146,Vvar__1__bind__148)
& ? [Vvar__2__ret__159] :
( c_24__type__225___24t(Vvar__0__mon__146,Vvar__2__ret__159)
& ! [Vvar__var__3__a__165__170] :
( cType___24t(Vvar__var__3__a__165__170)
=> ! [Vvar__var__4__b__166__171] :
( cType___24t(Vvar__var__4__b__166__171)
=> ! [Vvar__var__5__x__168__173] :
( t(Vvar__var__5__x__168__173,Vvar__var__3__a__165__170)
=> ! [Vvar__var__6__f__169__174] :
( c_24__type__220___24t(Vvar__0__mon__146,Vvar__var__3__a__165__170,Vvar__var__4__b__166__171,Vvar__var__6__f__169__174)
=> happ(happ(happ(happ(Vvar__1__bind__148,Vvar__var__3__a__165__170),Vvar__var__4__b__166__171),happ(happ(Vvar__2__ret__159,Vvar__var__3__a__165__170),Vvar__var__5__x__168__173)),Vvar__var__6__f__169__174) = happ(Vvar__var__6__f__169__174,Vvar__var__5__x__168__173) ) ) ) )
& ! [Vvar__var__4__a__176__178] :
( cType___24t(Vvar__var__4__a__176__178)
=> ! [Vvar__var__5__f__177__179] :
( t(Vvar__var__5__f__177__179,happ(Vvar__0__mon__146,Vvar__var__4__a__176__178))
=> happ(happ(happ(happ(Vvar__1__bind__148,Vvar__var__4__a__176__178),Vvar__var__4__a__176__178),Vvar__var__5__f__177__179),happ(Vvar__2__ret__159,Vvar__var__4__a__176__178)) = Vvar__var__5__f__177__179 ) )
& ! [Vvar__var__5__a__181__190] :
( cType___24t(Vvar__var__5__a__181__190)
=> ! [Vvar__var__6__b__182__191] :
( cType___24t(Vvar__var__6__b__182__191)
=> ! [Vvar__var__7__c__184__193] :
( cType___24t(Vvar__var__7__c__184__193)
=> ! [Vvar__var__8__n__186__195] :
( t(Vvar__var__8__n__186__195,happ(Vvar__0__mon__146,Vvar__var__5__a__181__190))
=> ! [Vvar__var__9__f__187__196] :
( c_24__type__220___24t(Vvar__0__mon__146,Vvar__var__5__a__181__190,Vvar__var__6__b__182__191,Vvar__var__9__f__187__196)
=> ! [Vvar__var__10__g__188__197] :
( c_24__type__244___24t(Vvar__0__mon__146,Vvar__var__5__a__181__190,Vvar__var__6__b__182__191,Vvar__var__7__c__184__193,Vvar__var__10__g__188__197)
=> happ(happ(happ(happ(Vvar__1__bind__148,Vvar__var__6__b__182__191),Vvar__var__7__c__184__193),happ(happ(happ(happ(Vvar__1__bind__148,Vvar__var__5__a__181__190),Vvar__var__6__b__182__191),Vvar__var__8__n__186__195),Vvar__var__9__f__187__196)),Vvar__var__10__g__188__197) = happ(happ(happ(happ(Vvar__1__bind__148,Vvar__var__5__a__181__190),Vvar__var__7__c__184__193),Vvar__var__8__n__186__195),c_24__lam__269___24a7(Vvar__0__mon__146,Vvar__1__bind__148,Vvar__var__5__a__181__190,Vvar__var__6__b__182__191,Vvar__var__7__c__184__193,Vvar__var__9__f__187__196,Vvar__var__10__g__188__197)) ) ) ) ) ) )
& VX145 = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(Vvar__0__mon__146,Vvar__1__bind__148,Vvar__2__ret__159) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.monads.MonadTrans',axiom,
! [VX39748] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(VX39748)
=> ? [Vvar__0__transMonad__39749] :
( c_24__type__39762___24t(Vvar__0__transMonad__39749)
& ? [Vvar__1__lift__39752] :
( c_24__type__39774___24t(Vvar__0__transMonad__39749,Vvar__1__lift__39752)
& VX39748 = cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(Vvar__0__transMonad__39749,Vvar__1__lift__39752) ) ) ) ).
fof('$_inversion_QuicksortComplexity.monoid_monad_trans.Monoid',axiom,
! [VX39884] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(VX39884)
=> ? [Vvar__0__monoid__type__39885] :
( cType___24t(Vvar__0__monoid__type__39885)
& ? [Vvar__1__monoid__zero__39886] :
( t(Vvar__1__monoid__zero__39886,Vvar__0__monoid__type__39885)
& ? [Vvar__2__monoid__mult__39887] :
( c_24__type__1053___24t(Vvar__0__monoid__type__39885,Vvar__2__monoid__mult__39887)
& ! [Vvar__var__3__x__39893__39894] :
( t(Vvar__var__3__x__39893__39894,Vvar__0__monoid__type__39885)
=> happ(happ(Vvar__2__monoid__mult__39887,Vvar__1__monoid__zero__39886),Vvar__var__3__x__39893__39894) = Vvar__var__3__x__39893__39894 )
& ! [Vvar__var__4__x__39896__39897] :
( t(Vvar__var__4__x__39896__39897,Vvar__0__monoid__type__39885)
=> happ(happ(Vvar__2__monoid__mult__39887,Vvar__var__4__x__39896__39897),Vvar__1__monoid__zero__39886) = Vvar__var__4__x__39896__39897 )
& ! [Vvar__var__5__x__39899__39902] :
( t(Vvar__var__5__x__39899__39902,Vvar__0__monoid__type__39885)
=> ! [Vvar__var__6__y__39900__39903] :
( t(Vvar__var__6__y__39900__39903,Vvar__0__monoid__type__39885)
=> ! [Vvar__var__7__z__39901__39904] :
( t(Vvar__var__7__z__39901__39904,Vvar__0__monoid__type__39885)
=> happ(happ(Vvar__2__monoid__mult__39887,happ(happ(Vvar__2__monoid__mult__39887,Vvar__var__5__x__39899__39902),Vvar__var__6__y__39900__39903)),Vvar__var__7__z__39901__39904) = happ(happ(Vvar__2__monoid__mult__39887,Vvar__var__5__x__39899__39902),happ(happ(Vvar__2__monoid__mult__39887,Vvar__var__6__y__39900__39903),Vvar__var__7__z__39901__39904)) ) ) )
& VX39884 = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(Vvar__0__monoid__type__39885,Vvar__1__monoid__zero__39886,Vvar__2__monoid__mult__39887) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.nat_below.natBelow',axiom,
! [Vvar__0___24Anonymous__10979,VX10980] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10979)
=> ( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vvar__0___24Anonymous__10979,VX10980)
=> ? [Vvar__0__v__10981] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__v__10981)
& ? [Vvar__1__p__10982] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__p__10982)
& Vvar__0___24Anonymous__10979 = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2411029___24a3(Vvar__0___24Anonymous__10979,Vvar__0__v__10981,Vvar__1__p__10982))
& VX10980 = cQuicksortComplexity_2enat__below_2emkNatBelow___24a2(Vvar__0__v__10981,Vvar__1__p__10982) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.ne_list.L',axiom,
! [Vvar__0__T__11056,VX11057] :
( cType___24t(Vvar__0__T__11056)
=> ( cQuicksortComplexity_2ene__list_2eL___24t(Vvar__0__T__11056,VX11057)
=> ( ? [Vvar__1___24Anonymous__11059] :
( t(Vvar__1___24Anonymous__11059,Vvar__0__T__11056)
& VX11057 = cQuicksortComplexity_2ene__list_2eone___24a2(Vvar__0__T__11056,Vvar__1___24Anonymous__11059) )
| ? [Vvar__1___24Anonymous__11061] :
( t(Vvar__1___24Anonymous__11061,Vvar__0__T__11056)
& ? [Vvar__2___24Anonymous__11062] :
( cQuicksortComplexity_2ene__list_2eL___24t(Vvar__0__T__11056,Vvar__2___24Anonymous__11062)
& VX11057 = cQuicksortComplexity_2ene__list_2econs___24a3(Vvar__0__T__11056,Vvar__1___24Anonymous__11061,Vvar__2___24Anonymous__11062) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs',axiom,
! [Vvar__0__l__185208,Vvar__1___24Anonymous__185209,VX185210] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__0__l__185208)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__1___24Anonymous__185209)
=> ( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24t(Vvar__0__l__185208,Vvar__1___24Anonymous__185209,VX185210)
=> ( ? [Vvar__0__l__185211] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__0__l__185211)
& Vvar__0__l__185211 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& Vvar__1___24Anonymous__185209 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& Vvar__0__l__185208 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2enat)
& VX185210 = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0___24a1(Vvar__0__l__185211) )
| ? [Vvar__0__l__185213] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__0__l__185213)
& ? [Vvar__1__pivot__185214] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__pivot__185214)
& ? [Vvar__2__t__185215] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__2__t__185215)
& Vvar__0__l__185213 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1__pivot__185214,Vvar__2__t__185215)
& ? [Vvar__4____res0__185217] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__4____res0__185217)
& ? [Vvar__5___24Anonymous__185218] :
( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24t(cCoq_2eLists_2eList_2efilter___24a3(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2earith__lems_2egeb___24a1(Vvar__1__pivot__185214),Vvar__2__t__185215),Vvar__4____res0__185217,Vvar__5___24Anonymous__185218)
& ? [Vvar__6____res__185219] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__6____res__185219)
& ? [Vvar__7___24Anonymous__185220] :
( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24t(cCoq_2eLists_2eList_2efilter___24a3(cCoq_2eInit_2eDatatypes_2enat,cQuicksortComplexity_2earith__lems_2eltb___24a1(Vvar__1__pivot__185214),Vvar__2__t__185215),Vvar__6____res__185219,Vvar__7___24Anonymous__185220)
& Vvar__1___24Anonymous__185209 = c_24__case__Coq_2eInit_2eDatatypes_2elist_24185329___24a6(Vvar__0__l__185208,Vvar__1___24Anonymous__185209,Vvar__1__pivot__185214,Vvar__2__t__185215,Vvar__4____res0__185217,Vvar__6____res__185219)
& Vvar__0__l__185208 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__1__pivot__185214,Vvar__2__t__185215)
& VX185210 = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1___24a7(Vvar__0__l__185213,Vvar__1__pivot__185214,Vvar__2__t__185215,Vvar__4____res0__185217,Vvar__5___24Anonymous__185218,Vvar__6____res__185219,Vvar__7___24Anonymous__185220) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_QuicksortComplexity.sort_order.E',axiom,
! [VX40173] :
( cQuicksortComplexity_2esort__order_2eE___24t(VX40173)
=> ? [Vvar__0__Ec__40174] :
( cType___24t(Vvar__0__Ec__40174)
& ? [Vvar__1__Ecmp__40175] :
( c_24__type__40214___24t(Vvar__0__Ec__40174,Vvar__1__Ecmp__40175)
& ! [Vvar__var__2__x__40181__40183] :
( t(Vvar__var__2__x__40181__40183,Vvar__0__Ec__40174)
=> ! [Vvar__var__3__y__40182__40184] :
( t(Vvar__var__3__y__40182__40184,Vvar__0__Ec__40174)
=> happ(happ(Vvar__1__Ecmp__40175,Vvar__var__2__x__40181__40183),Vvar__var__3__y__40182__40184) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(happ(happ(Vvar__1__Ecmp__40175,Vvar__var__3__y__40182__40184),Vvar__var__2__x__40181__40183)) ) )
& ! [Vvar__var__3__x__40186__40192] :
( t(Vvar__var__3__x__40186__40192,Vvar__0__Ec__40174)
=> ! [Vvar__var__4__y__40187__40193] :
( t(Vvar__var__4__y__40187__40193,Vvar__0__Ec__40174)
=> ! [Vvar__var__5__z__40189__40195] :
( t(Vvar__var__5__z__40189__40195,Vvar__0__Ec__40174)
=> ! [Vvar__var__6__c__40188__40194] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__6__c__40188__40194)
=> ( happ(happ(Vvar__1__Ecmp__40175,Vvar__var__3__x__40186__40192),Vvar__var__4__y__40187__40193) = Vvar__var__6__c__40188__40194
=> ( happ(happ(Vvar__1__Ecmp__40175,Vvar__var__4__y__40187__40193),Vvar__var__5__z__40189__40195) = Vvar__var__6__c__40188__40194
=> happ(happ(Vvar__1__Ecmp__40175,Vvar__var__3__x__40186__40192),Vvar__var__5__z__40189__40195) = Vvar__var__6__c__40188__40194 ) ) ) ) ) )
& ! [Vvar__var__4__x__40199__40205] :
( t(Vvar__var__4__x__40199__40205,Vvar__0__Ec__40174)
=> ! [Vvar__var__5__y__40200__40206] :
( t(Vvar__var__5__y__40200__40206,Vvar__0__Ec__40174)
=> ! [Vvar__var__6__z__40201__40207] :
( t(Vvar__var__6__z__40201__40207,Vvar__0__Ec__40174)
=> ! [Vvar__var__7__c__40202__40208] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__var__7__c__40202__40208)
=> ( happ(happ(Vvar__1__Ecmp__40175,Vvar__var__4__x__40199__40205),Vvar__var__5__y__40200__40206) = cCoq_2eInit_2eDatatypes_2eEq
=> ( happ(happ(Vvar__1__Ecmp__40175,Vvar__var__5__y__40200__40206),Vvar__var__6__z__40201__40207) = Vvar__var__7__c__40202__40208
=> happ(happ(Vvar__1__Ecmp__40175,Vvar__var__4__x__40199__40205),Vvar__var__6__z__40201__40207) = Vvar__var__7__c__40202__40208 ) ) ) ) ) )
& VX40173 = cQuicksortComplexity_2esort__order_2eBuild__E___24a2(Vvar__0__Ec__40174,Vvar__1__Ecmp__40175) ) ) ) ).
fof('$_lam_1062',axiom,
! [Vv__CANONICAL__0] : c_24__lam__1062___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0) ).
fof('$_lam_1063',axiom,
! [Vv__CANONICAL__0] : c_24__lam__1063___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eLogic_2eeq__sym___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2ePeano_2eplus__n__O___24a1(Vv__CANONICAL__0)) ).
fof('$_lam_1069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1069___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eLogic_2eeq__sym___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)),cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2),cCoq_2eArith_2ePeanoNat_2eNat_2eadd__assoc___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ).
fof('$_lam_1102',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1102___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2emonads_2emon___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1105___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ).
fof('$_lam_1105',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1105___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ).
fof('$_lam_1108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1108___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1)))) ) ).
fof('$_lam_11082',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__11082___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cQuicksortComplexity_2ene__list_2eone___24a2(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,Vv__CANONICAL__1)) ).
fof('$_lam_11085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__11085___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2ene__list_2econs___24a3(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2),cQuicksortComplexity_2ene__list_2efrom__vec___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cQuicksortComplexity_2evec_2etail___24a3(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__0,Vv__CANONICAL__2))) ).
fof('$_lam_11133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__11133___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2evec_2enatBelow0__rect___24a2(Vv__CANONICAL__2,Vv__CANONICAL__0) ).
fof('$_lam_11139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__11139___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('$_lam_11160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__11160___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__type__11163___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) ).
fof('$_lam_11167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__11167___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2evec_2etail___24a2(Vv__CANONICAL__2,Vv__CANONICAL__0) ).
fof('$_lam_11186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__11186___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vv__CANONICAL__0,cQuicksortComplexity_2evec_2ehead___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__5),cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__2,Vv__CANONICAL__3),happ(Vv__CANONICAL__4,cQuicksortComplexity_2evec_2etail___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0,Vv__CANONICAL__5))) ).
fof('$_lam_11200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__11200___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('$_lam_11370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__11370___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) ) ).
fof('$_lam_11375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__11375___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ).
fof('$_lam_11422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__11422___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11426___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)),cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11375___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)),cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),c_24__lam__11447___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_11426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11426___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eGt))),Vv__CANONICAL__2) ) ).
fof('$_lam_11447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__11447___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11451___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)),cQuicksortComplexity_2elist__utils_2eaddToPartitioning___24a5(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__3,Vv__CANONICAL__2,Vv__CANONICAL__5)) ).
fof('$_lam_11451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__11451___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_11500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__11500___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2eGt))),Vv__CANONICAL__3) ) ).
fof('$_lam_11575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__11575___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0) ).
fof('$_lam_11788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__11788___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0) ).
fof('$_lam_11881',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__11881___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11426___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)),cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11375___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)),cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),c_24__lam__11447___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_12041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
( c_24__lam__12041___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__6,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__6,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__6,cCoq_2eInit_2eDatatypes_2eGt))),cQuicksortComplexity_2evec_2eto__list___24a3(Vv__CANONICAL__0,c_24__fix__12068__v__CANONICAL__3___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__4),cQuicksortComplexity_2evec_2eremove___24a4(Vv__CANONICAL__0,c_24__fix__12068__v__CANONICAL__3___24a4(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__4),cQuicksortComplexity_2evec_2efrom__list___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)),Vv__CANONICAL__5))) ) ).
fof('$_lam_1444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__1444___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1449___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__lam__1725___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_1449',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__1449___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)))) ) ).
fof('$_lam_1725',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__1725___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1729___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)),cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1449___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)),Vv__CANONICAL__4,c_24__lam__1955___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_1729',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1729___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ).
fof('$_lam_186044',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__186044___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_186052',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__186052___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_186319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__186319___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_186327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__186327___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_186335',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__186335___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_186343',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__186343___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_1955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__1955___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1959___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)),c_24__case__Coq_2eInit_2eDatatypes_2ebool_242139___24a5(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_1959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1959___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)))) ) ).
fof('$_lam_2200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__2200___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0) ).
fof('$_lam_2258',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2258___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1) ).
fof('$_lam_22801',axiom,
! [Vv__CANONICAL__0] : c_24__lam__22801___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_2481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2481___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1) ).
fof('$_lam_2636',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__2636___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__6),Vv__CANONICAL__5) ).
fof('$_lam_2678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__2678___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cQuicksortComplexity_2emonads_2efilterM___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4),c_24__lam__2688___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_2688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__2688___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),c_24__case__Coq_2eInit_2eDatatypes_2ebool_242693___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_269',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__269___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_2757',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2757___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(Vv__CANONICAL__1),happ(Vv__CANONICAL__3,Vv__CANONICAL__2)) ).
fof('$_lam_2759',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__2759___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1) ).
fof('$_lam_2790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__2790___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(Vv__CANONICAL__2),cQuicksortComplexity_2emonads_2eIdMonad_2ebind___24a4(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,c_24__lam__2803___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4,Vv__CANONICAL__5))) ).
fof('$_lam_2803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__2803___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eIdMonad_2ebind___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__4) ).
fof('$_lam_34597',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__34597___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eGt))),Vv__CANONICAL__1) ) ).
fof('$_lam_34758',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__34758___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ).
fof('$_lam_34800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__5)
=> ( ( Vv__CANONICAL__1 = Vv__CANONICAL__5
& cQuicksortComplexity_2eutil_2ecmp__cmp___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__34811___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),c_24__prop__34812___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
& c_24__lam__34800___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_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__34597___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4,Vv__CANONICAL__5)) )
| ( Vv__CANONICAL__1 != Vv__CANONICAL__5
& cQuicksortComplexity_2eutil_2ecmp__cmp___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__34815___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),c_24__prop__34816___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
& c_24__lam__34800___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__34597___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4,Vv__CANONICAL__5) ) ) ) ) ) ) ).
fof('$_lam_34845',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__34845___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ).
fof('$_lam_34849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__34849___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) ) ).
fof('$_lam_34851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__34851___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0) ).
fof('$_lam_34856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__34856___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eEq),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eLt),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eGt))),cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) ) ).
fof('$_lam_38581',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__38581___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_38648',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38648___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38651',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38651___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38779',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38779___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38782___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38903___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__38906___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 ).
fof('$_lam_38981',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__38981___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3,cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__4,Vv__CANONICAL__6)),happ(Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_39002',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__39002___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(happ(Vv__CANONICAL__5,Vv__CANONICAL__6),happ(Vv__CANONICAL__4,Vv__CANONICAL__6)) ).
fof('$_lam_39010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__39010___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_39048',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__39048___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_39157',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__39157___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24Proof ).
fof('$_lam_39502',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__39502___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = c_24Proof ).
fof('$_lam_39622',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__39622___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__4,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5,c_24__lam__39635___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6)) ).
fof('$_lam_39635',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] : c_24__lam__39635___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__4,Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__6)) ).
fof('$_lam_39695',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__39695___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2efoldlM___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__4) ).
fof('$_lam_39747',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__39747___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2efoldlM___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__4) ).
fof('$_lam_41953',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41953___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),c_24__cast__41954___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5),cCoq_2eProgram_2eBasics_2ecompose___24a5(cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cQuicksortComplexity_2emonads_2emon___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),cQuicksortComplexity_2emonads_2eret___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),c_24__lam__41960___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5))) ).
fof('$_lam_41960',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41960___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2epair___24a4(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5)),cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5)) ).
fof('$_lam_41981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41981___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),c_24__cast__41982___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5),c_24__lam__41988___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_41988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__41988___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2epair___24a4(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5)),cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5))) ).
fof('$_lam_42055',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__42055___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),Vv__CANONICAL__3,cCoq_2eProgram_2eBasics_2ecompose___24a5(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2),cQuicksortComplexity_2emonads_2emon___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),cQuicksortComplexity_2emonads_2eret___24a2(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)),cCoq_2eInit_2eDatatypes_2epair___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(Vv__CANONICAL__0)))) ).
fof('$_lam_42071',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__42071___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3),happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5)),c_24__lam__5544___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_4357',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__4357___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = c_24Proof ).
fof('$_lam_44151',axiom,
! [Vv__CANONICAL__0] : c_24__lam__44151___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_4461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__4461___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24Proof ).
fof('$_lam_504',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__504___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_5521',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__5521___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) = c_24Proof ).
fof('$_lam_5538',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__5538___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3),happ(Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__5)),c_24__lam__5544___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_5544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__5544___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2epair___24a4(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2efst___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__5)),cCoq_2eInit_2eDatatypes_2esnd___24a3(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3,Vv__CANONICAL__5))) ).
fof('$_lam_5573',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__5573___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ).
fof('$_lam_5602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__5602___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ).
fof('$_lam_5885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__5885___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_6074',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__6074___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6080___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__6)),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,cQuicksortComplexity_2eqs__definitions_2emon__det_2egt___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6),c_24__lam__6137___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)),c_24__lam__6275___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)) ).
fof('$_lam_6080',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__6080___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__5),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4))) ) ).
fof('$_lam_6137',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__6137___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,cCoq_2eInit_2eSpecif_2eexist___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6142___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__5602___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__1___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,c_24__lam__6171___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6))) ).
fof('$_lam_6142',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__6142___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__4),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ).
fof('$_lam_6171',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__6171___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6142___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__5)) ).
fof('$_lam_6275',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__6275___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__5602___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__6)),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6),c_24__lam__6336___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)),c_24__lam__6379___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5,Vv__CANONICAL__7)) ).
fof('$_lam_6336',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__6336___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,cCoq_2eInit_2eSpecif_2eexist___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6142___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__5602___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__2___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,c_24__lam__6369___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6))) ).
fof('$_lam_6369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__6369___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6142___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__5)) ).
fof('$_lam_6379',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__6379___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__1,Vv__CANONICAL__4,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5))) ).
fof('$_lam_6420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__6420___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))) ) ).
fof('$_lam_6441',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6441___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ).
fof('$_lam_6817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6817___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6823',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6823___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6848',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6848___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6854',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6854___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6879___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__6885___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_6894',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__6894___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3)) ) ).
fof('$_lam_6903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__6903___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3)) ) ).
fof('$_lam_6959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__6959___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eProgram_2eWf_2eFix__sub___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__6968___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__5)) ).
fof('$_lam_6968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__6968___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3)) ) ).
fof('$_lam_730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__730___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_lam_7828',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__7828___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__3,Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ).
fof('$_lam_7865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__7865___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5) ).
fof('$_lam_7940',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__7940___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__lam__7950___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_7950',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__7950___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__case__Coq_2eInit_2eDatatypes_2ebool_247955___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_7988',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__7988___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__lam__7950___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_8015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__8015___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_8018',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__8018___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cQuicksortComplexity_2emonads_2emon___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1)) ).
fof('$_lam_8039',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__8039___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2emonads_2ebind___24a5(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cQuicksortComplexity_2emonads_2efilterM___24a4(Vv__CANONICAL__1,Vv__CANONICAL__0,happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)),c_24__lam__8044___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5)) ).
fof('$_lam_8044',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__8044___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cQuicksortComplexity_2emonads_2eret___24a3(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),cCoq_2eInit_2eDatatypes_2eapp___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4))) ).
fof('$_lam_974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7] : c_24__lam__974___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),Vv__CANONICAL__6) ).
fof('$_prop_104829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__104829___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_104830',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__104830___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_186030',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__186030___24a2(V0__A,V1__B))
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V1__B,V4__x)) ) ) ).
fof('$_prop_186031',axiom,
! [V0__A,V2__C] :
( p(c_24__prop__186031___24a2(V0__A,V2__C))
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(V2__C,V4__x)) ) ) ).
fof('$_prop_186790',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__S__186768,Vvar__1__x__186769,Vvar__2__y__186770] :
( p(c_24__prop__186790___24a4(Vvar__0___24Anonymous__186766,Vvar__0__S__186768,Vvar__1__x__186769,Vvar__2__y__186770))
<=> Vvar__1__x__186769 = Vvar__2__y__186770 ) ).
fof('$_prop_186791',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__x__186771,Vvar__1__y__186772] :
( p(c_24__prop__186791___24a3(Vvar__0___24Anonymous__186766,Vvar__0__x__186771,Vvar__1__y__186772))
<=> Vvar__0__x__186771 = Vvar__1__y__186772 ) ).
fof('$_prop_186792',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__x__186773,Vvar__1__s__186774] :
( p(c_24__prop__186792___24a3(Vvar__0___24Anonymous__186766,Vvar__0__x__186773,Vvar__1__s__186774))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__186773,Vvar__1__s__186774) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_186793',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__P__186775,Vvar__1__Q__186776] :
( p(c_24__prop__186793___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186775,Vvar__1__Q__186776))
<=> ( p(Vvar__0__P__186775)
& p(Vvar__1__Q__186776) ) ) ).
fof('$_prop_186794',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__P__186779,Vvar__1__Q__186780] :
( p(c_24__prop__186794___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186779,Vvar__1__Q__186780))
<=> ( p(Vvar__0__P__186779)
| p(Vvar__1__Q__186780) ) ) ).
fof('$_prop_186795',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__P__186783,Vvar__1__Q__186784] :
( p(c_24__prop__186795___24a3(Vvar__0___24Anonymous__186766,Vvar__0__P__186783,Vvar__1__Q__186784))
<=> ( p(Vvar__0__P__186783)
=> p(Vvar__1__Q__186784) ) ) ).
fof('$_prop_186796',axiom,
! [Vvar__0___24Anonymous__186766,Vvar__0__P__186788] :
( p(c_24__prop__186796___24a2(Vvar__0___24Anonymous__186766,Vvar__0__P__186788))
<=> ~ p(Vvar__0__P__186788) ) ).
fof('$_prop_186797',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__186797___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_34811',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5] :
( p(c_24__prop__34811___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__5 ) ).
fof('$_prop_34812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5] :
( p(c_24__prop__34812___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__5 ) ).
fof('$_prop_34815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5] :
( p(c_24__prop__34815___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__5 ) ).
fof('$_prop_34816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5] :
( p(c_24__prop__34816___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__5 ) ).
fof('$_prop_42902',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__42902___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_44049',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__44049___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_44050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__44050___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_type_10168',axiom,
! [Vvar__10169] :
( c_24__type__10168___24t(Vvar__10169)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__10169,Vv__CANONICAL__0)) ) ) ).
fof('$_type_102',axiom,
! [Vv__CANONICAL__0,Vvar__103] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vvar__103)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__103,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10250',axiom,
! [Vvar__10251] :
( c_24__type__10250___24t(Vvar__10251)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__10251,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_10336',axiom,
! [Vvar__10337] :
( c_24__type__10336___24t(Vvar__10337)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10337,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10339',axiom,
! [Vv__CANONICAL__0,Vvar__10340] :
( c_24__type__10339___24t(Vv__CANONICAL__0,Vvar__10340)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__10340,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_10375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10376] :
( c_24__type__10375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10376)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__10376,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10379',axiom,
! [Vvar__10380] :
( c_24__type__10379___24t(Vvar__10380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10380,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10397',axiom,
! [Vvar__10398] :
( c_24__type__10397___24t(Vvar__10398)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___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__10398,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10410',axiom,
! [Vvar__10411] :
( c_24__type__10410___24t(Vvar__10411)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10411,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10433',axiom,
! [Vvar__10434] :
( c_24__type__10433___24t(Vvar__10434)
<=> ! [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__10434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10438',axiom,
! [Vvar__10439] :
( c_24__type__10438___24t(Vvar__10439)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__10439,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_10449',axiom,
! [Vvar__10450] :
( c_24__type__10449___24t(Vvar__10450)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10450,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10472',axiom,
! [Vvar__10473] :
( c_24__type__10472___24t(Vvar__10473)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__10473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10478',axiom,
! [Vvar__10479] :
( c_24__type__10478___24t(Vvar__10479)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10479,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_104827',axiom,
! [Vvar__104828] :
( c_24__type__104827___24t(Vvar__104828)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__104829___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__104830___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__104828,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10490',axiom,
! [Vvar__10491] :
( c_24__type__10490___24t(Vvar__10491)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6757___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__10491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10497',axiom,
! [Vv__CANONICAL__0,Vvar__10498] :
( c_24__type__10497___24t(Vv__CANONICAL__0,Vvar__10498)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__10498,Vv__CANONICAL__1)) ) ) ).
fof('$_type_105038',axiom,
! [Vvar__105039] :
( c_24__type__105038___24t(Vvar__105039)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__105039,Vv__CANONICAL__0)) ) ) ).
fof('$_type_105042',axiom,
! [Vvar__105043] :
( c_24__type__105042___24t(Vvar__105043)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__42124___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__42124___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__105043,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_105072',axiom,
! [Vvar__105073] :
( c_24__type__105072___24t(Vvar__105073)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6617___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__105073,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_105126',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105127] :
( c_24__type__105126___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__105127)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__105127,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_105193',axiom,
! [Vvar__105194] :
( c_24__type__105193___24t(Vvar__105194)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__105194,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1053',axiom,
! [Vv__CANONICAL__0,Vvar__1054] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vvar__1054)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1054,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10544',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__10545] :
( c_24__type__10544___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__10545)
<=> ! [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__10545,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_1060',axiom,
! [Vvar__1061] :
( c_24__type__1060___24t(Vvar__1061)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1061,Vv__CANONICAL__0)) ) ) ).
fof('$_type_106836',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__106837] :
( c_24__type__106836___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__106837)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__106837,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_106961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__106962] :
( c_24__type__106961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__106962)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__106962,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_107086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107087] :
( c_24__type__107086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107087)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__107087,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_107211',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107212] :
( c_24__type__107211___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107212)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__107212,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_107336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107337] :
( c_24__type__107336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107337)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__107337,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_107461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107462] :
( c_24__type__107461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107462)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__107462,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_107572',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107573] :
( c_24__type__107572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__107573)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__107573,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_107896',axiom,
! [Vvar__107897] :
( c_24__type__107896___24t(Vvar__107897)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8059___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(happ(happ(happ(Vvar__107897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_107908',axiom,
! [Vvar__107909] :
( c_24__type__107908___24t(Vvar__107909)
<=> ! [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__107909,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_107933',axiom,
! [Vvar__107934] :
( c_24__type__107933___24t(Vvar__107934)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__107934,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_108193',axiom,
! [Vvar__108194] :
( c_24__type__108193___24t(Vvar__108194)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__108194,Vv__CANONICAL__0)) ) ) ).
fof('$_type_108198',axiom,
! [Vvar__108199] :
( c_24__type__108198___24t(Vvar__108199)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__65587___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__65587___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__108199,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_108384',axiom,
! [Vvar__108385] :
( c_24__type__108384___24t(Vvar__108385)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3) = Vv__CANONICAL__3 )
=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__1) = Vv__CANONICAL__4 )
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> happ(happ(Vv__CANONICAL__2,happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6)),Vv__CANONICAL__7) = happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) )
=> cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(happ(happ(happ(Vvar__108385,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ).
fof('$_type_1088',axiom,
! [Vvar__1089] :
( c_24__type__1088___24t(Vvar__1089)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__1089,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1091',axiom,
! [Vvar__1092] :
( c_24__type__1091___24t(Vvar__1092)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled,Vv__CANONICAL__0,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__1092,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10931',axiom,
! [Vv__CANONICAL__0,Vvar__10932] :
( c_24__type__10931___24t(Vv__CANONICAL__0,Vvar__10932)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__10932,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1095',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1096] :
( c_24__type__1095___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1096)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled,Vv__CANONICAL__1,happ(Vvar__1096,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11050',axiom,
! [Vvar__11051] :
( c_24__type__11050___24t(Vvar__11051)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__11051,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11089',axiom,
! [Vvar__11090] :
( c_24__type__11089___24t(Vvar__11090)
<=> ! [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)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__11090,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11105',axiom,
! [Vvar__11106] :
( c_24__type__11105___24t(Vvar__11106)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__11106,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11115',axiom,
! [Vvar__11116] :
( c_24__type__11115___24t(Vvar__11116)
<=> ! [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__11116,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11146',axiom,
! [Vvar__11147] :
( c_24__type__11146___24t(Vvar__11147)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__11147,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_11163',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11164] :
( c_24__type__11163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11164)
<=> ! [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__11164,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11193',axiom,
! [Vvar__11194] :
( c_24__type__11193___24t(Vvar__11194)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__11194,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_11202',axiom,
! [Vvar__11203] :
( c_24__type__11202___24t(Vvar__11203)
<=> ! [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__11203,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11320',axiom,
! [Vvar__11321] :
( c_24__type__11320___24t(Vvar__11321)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__11321,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11324',axiom,
! [Vvar__11325] :
( c_24__type__11324___24t(Vvar__11325)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11325,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11340',axiom,
! [Vvar__11341] :
( c_24__type__11340___24t(Vvar__11341)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__11341,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11343',axiom,
! [Vvar__11344] :
( c_24__type__11343___24t(Vvar__11344)
<=> ! [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__11344,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11472',axiom,
! [Vvar__11473] :
( c_24__type__11472___24t(Vvar__11473)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2esig___24a2(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__11426___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)),happ(happ(happ(happ(happ(Vvar__11473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_11479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11480] :
( c_24__type__11479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__11480)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2ecomparison,happ(happ(Vvar__11480,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11494',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__11495] :
( c_24__type__11494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__11495)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)))
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(Vvar__11495,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_11801',axiom,
! [Vvar__11802] :
( c_24__type__11801___24t(Vvar__11802)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__11479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__11802,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_119',axiom,
! [Vvar__120] :
( c_24__type__119___24t(Vvar__120)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__120,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_12',axiom,
! [Vvar__13] :
( c_24__type__12___24t(Vvar__13)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__13,Vv__CANONICAL__0)) ) ) ).
fof('$_type_136',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__137] :
( c_24__type__136___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__137)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__137,Vv__CANONICAL__2)) ) ) ).
fof('$_type_13616',axiom,
! [Vvar__13617] :
( c_24__type__13616___24t(Vvar__13617)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__13617,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13623',axiom,
! [Vvar__13624] :
( c_24__type__13623___24t(Vvar__13624)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__13624,Vv__CANONICAL__0)) ) ) ).
fof('$_type_142',axiom,
! [Vvar__143] :
( c_24__type__142___24t(Vvar__143)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___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__143,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_176660',axiom,
! [Vvar__176661] :
( c_24__type__176660___24t(Vvar__176661)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(cM,cB,happ(Vvar__176661,Vv__CANONICAL__0)) ) ) ).
fof('$_type_176669',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176670] :
( c_24__type__176669___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176670)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__1,happ(happ(Vvar__176670,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_176677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176678] :
( c_24__type__176677___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176678)
<=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__1,happ(Vvar__176678,Vv__CANONICAL__2)) ) ) ).
fof('$_type_176714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176715] :
( c_24__type__176714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176715)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__176721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__176715,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__2) ) ) ) ) ).
fof('$_type_176721',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176722] :
( c_24__type__176721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176722)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__176722,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_176735',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176736] :
( c_24__type__176735___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__176736)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__176736,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_176762',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176763] :
( c_24__type__176762___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176763)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(Vvar__176763,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_type_176782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176783] :
( c_24__type__176782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__176783)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(Vvar__176783,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_176833',axiom,
! [Vvar__176834] :
( c_24__type__176833___24t(Vvar__176834)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__176834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_176906',axiom,
! [Vvar__176907] :
( c_24__type__176906___24t(Vvar__176907)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__5)
=> cType___24t(happ(happ(happ(happ(happ(happ(Vvar__176907,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_177004',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__177005] :
( c_24__type__177004___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__177005)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__177005,Vv__CANONICAL__6)) ) ) ).
fof('$_type_177017',axiom,
! [Vvar__177018] :
( c_24__type__177017___24t(Vvar__177018)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> cProp___24t(happ(happ(happ(happ(Vvar__177018,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_177021',axiom,
! [Vvar__177022] :
( c_24__type__177021___24t(Vvar__177022)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__177022,Vv__CANONICAL__0)) ) ) ).
fof('$_type_177101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177102] :
( c_24__type__177101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177102)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__177102) ) ) ).
fof('$_type_177117',axiom,
! [Vvar__177118] :
( c_24__type__177117___24t(Vvar__177118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__177118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_177122',axiom,
! [Vvar__177123] :
( c_24__type__177122___24t(Vvar__177123)
<=> ! [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__177123,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_177125',axiom,
! [Vvar__177126] :
( c_24__type__177125___24t(Vvar__177126)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__177126,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_177133',axiom,
! [Vvar__177134] :
( c_24__type__177133___24t(Vvar__177134)
<=> ! [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__177134,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_177574',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177575] :
( c_24__type__177574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177575)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177575,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177579',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177580] :
( c_24__type__177579___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177580)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177580,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177594] :
( c_24__type__177593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177594)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177594,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177599] :
( c_24__type__177598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177599)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177599,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177606',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177607] :
( c_24__type__177606___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177607)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177607,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177611',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177612] :
( c_24__type__177611___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__177612)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__177612,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_177944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__177945] :
( c_24__type__177944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__177945)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__177945,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_177963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__177964] :
( c_24__type__177963___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__177964)
<=> ! [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__177964,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_177983',axiom,
! [Vvar__177984] :
( c_24__type__177983___24t(Vvar__177984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__177984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_178086',axiom,
! [Vvar__178087] :
( c_24__type__178086___24t(Vvar__178087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__178087,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_178117',axiom,
! [Vvar__178118] :
( c_24__type__178117___24t(Vvar__178118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__178118,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_178148',axiom,
! [Vvar__178149] :
( c_24__type__178148___24t(Vvar__178149)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__178149,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_183723',axiom,
! [Vvar__183724] :
( c_24__type__183723___24t(Vvar__183724)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__183724,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_183793',axiom,
! [Vvar__183794] :
( c_24__type__183793___24t(Vvar__183794)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__183794,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_185665',axiom,
! [Vvar__185666] :
( c_24__type__185665___24t(Vvar__185666)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__185666,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_185672',axiom,
! [Vvar__185673] :
( c_24__type__185672___24t(Vvar__185673)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__177101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__185673,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_185684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__185685] :
( c_24__type__185684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__185685)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__185685,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_185689',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__185690] :
( c_24__type__185689___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__185690)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__185690,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_185692',axiom,
! [Vv__CANONICAL__0,Vvar__185693] :
( c_24__type__185692___24t(Vv__CANONICAL__0,Vvar__185693)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__185693,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_185700',axiom,
! [Vvar__185701] :
( c_24__type__185700___24t(Vvar__185701)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__185701,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_185705',axiom,
! [Vvar__185706] :
( c_24__type__185705___24t(Vvar__185706)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__185706,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_185872',axiom,
! [Vvar__185873] :
( c_24__type__185872___24t(Vvar__185873)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__185873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_185875',axiom,
! [Vvar__185876] :
( c_24__type__185875___24t(Vvar__185876)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__185876,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_185880',axiom,
! [Vvar__185881] :
( c_24__type__185880___24t(Vvar__185881)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__185881,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_185891',axiom,
! [Vvar__185892] :
( c_24__type__185891___24t(Vvar__185892)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__185892,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_185899',axiom,
! [Vvar__185900] :
( c_24__type__185899___24t(Vvar__185900)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__185900,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_185923',axiom,
! [Vvar__185924] :
( c_24__type__185923___24t(Vvar__185924)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__185924,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_185961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__185962] :
( c_24__type__185961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__185962)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__185962,Vv__CANONICAL__6)) ) ) ).
fof('$_type_185976',axiom,
! [Vvar__185977] :
( c_24__type__185976___24t(Vvar__185977)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(happ(happ(Vvar__185977,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_185980',axiom,
! [Vvar__185981] :
( c_24__type__185980___24t(Vvar__185981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__185981,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_185999',axiom,
! [Vvar__186000] :
( c_24__type__185999___24t(Vvar__186000)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__186000,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186036',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__186037] :
( c_24__type__186036___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__186037)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__186037,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_186061',axiom,
! [Vvar__186062] :
( c_24__type__186061___24t(Vvar__186062)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__186062,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186064',axiom,
! [Vv__CANONICAL__0,Vvar__186065] :
( c_24__type__186064___24t(Vv__CANONICAL__0,Vvar__186065)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__186065,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_186218',axiom,
! [Vvar__186219] :
( c_24__type__186218___24t(Vvar__186219)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__186219,Vv__CANONICAL__0)) ) ) ).
fof('$_type_186309',axiom,
! [Vvar__186310] :
( c_24__type__186309___24t(Vvar__186310)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(Vvar__186310,Vv__CANONICAL__0)) ) ) ).
fof('$_type_186380',axiom,
! [Vvar__186381] :
( c_24__type__186380___24t(Vvar__186381)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__186381,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_186391',axiom,
! [Vvar__186392] :
( c_24__type__186391___24t(Vvar__186392)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__186392,Vv__CANONICAL__0)) ) ) ).
fof('$_type_186394',axiom,
! [Vvar__186395] :
( c_24__type__186394___24t(Vvar__186395)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__186395,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186399',axiom,
! [Vvar__186400] :
( c_24__type__186399___24t(Vvar__186400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__186400,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_186487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186488] :
( c_24__type__186487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186488)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__186488,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_186510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186511] :
( c_24__type__186510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186511)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__186511,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_186533',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186534] :
( c_24__type__186533___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186534)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__186534,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_186556',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186557] :
( c_24__type__186556___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186557)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__186557,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_186574',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186575] :
( c_24__type__186574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186575)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__186575,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_186600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186601] :
( c_24__type__186600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186601)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__186601,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_186618',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186619] :
( c_24__type__186618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186619)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__186619,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_186701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186702] :
( c_24__type__186701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186702)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__186702,Vv__CANONICAL__4)) ) ) ).
fof('$_type_186710',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186711] :
( c_24__type__186710___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__186711)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__186711,Vv__CANONICAL__4)) ) ) ).
fof('$_type_186752',axiom,
! [Vvar__186753] :
( c_24__type__186752___24t(Vvar__186753)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__186753,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_186810',axiom,
! [Vvar__186811] :
( c_24__type__186810___24t(Vvar__186811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__186811,Vv__CANONICAL__0)) ) ) ).
fof('$_type_186830',axiom,
! [Vvar__186831] :
( c_24__type__186830___24t(Vvar__186831)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__186831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186836',axiom,
! [Vvar__186837] :
( c_24__type__186836___24t(Vvar__186837)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__186837,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186841',axiom,
! [Vvar__186842] :
( c_24__type__186841___24t(Vvar__186842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__186842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_186863',axiom,
! [Vvar__186864] :
( c_24__type__186863___24t(Vvar__186864)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__186864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_199',axiom,
! [Vvar__200] :
( c_24__type__199___24t(Vvar__200)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__200,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21011',axiom,
! [Vvar__21012] :
( c_24__type__21011___24t(Vvar__21012)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21012,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21172',axiom,
! [Vvar__21173] :
( c_24__type__21172___24t(Vvar__21173)
<=> ! [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__21173,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21419',axiom,
! [Vvar__21420] :
( c_24__type__21419___24t(Vvar__21420)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__21420,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21425',axiom,
! [Vvar__21426] :
( c_24__type__21425___24t(Vvar__21426)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_215',axiom,
! [Vv__CANONICAL__0,Vvar__216] :
( c_24__type__215___24t(Vv__CANONICAL__0,Vvar__216)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__216,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_2164',axiom,
! [Vvar__2165] :
( c_24__type__2164___24t(Vvar__2165)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2168___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1729___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)),happ(happ(happ(happ(Vvar__2165,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2168',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2169] :
( c_24__type__2168___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2169)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,happ(Vvar__2169,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2188',axiom,
! [Vvar__2189] :
( c_24__type__2188___24t(Vvar__2189)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,happ(happ(happ(happ(happ(Vvar__2189,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_2195',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2196] :
( c_24__type__2195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2196)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2ebool,happ(happ(Vvar__2196,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22',axiom,
! [Vvar__23] :
( c_24__type__22___24t(Vvar__23)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__23,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_220',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__221] :
( c_24__type__220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__221)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__221,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_225',axiom,
! [Vv__CANONICAL__0,Vvar__226] :
( c_24__type__225___24t(Vv__CANONICAL__0,Vvar__226)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__226,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22634',axiom,
! [Vvar__22635] :
( c_24__type__22634___24t(Vvar__22635)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__22635,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_22641',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22642] :
( c_24__type__22641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22642)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__22642,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22762',axiom,
! [Vvar__22763] :
( c_24__type__22762___24t(Vvar__22763)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__22763,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22817',axiom,
! [Vvar__22818] :
( c_24__type__22817___24t(Vvar__22818)
<=> ! [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__22818,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22829',axiom,
! [Vv__CANONICAL__0,Vvar__22830] :
( c_24__type__22829___24t(Vv__CANONICAL__0,Vvar__22830)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__22830,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22957',axiom,
! [Vvar__22958] :
( c_24__type__22957___24t(Vvar__22958)
<=> ! [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__22958,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22960',axiom,
! [Vvar__22961] :
( c_24__type__22960___24t(Vvar__22961)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22961,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22965',axiom,
! [Vvar__22966] :
( c_24__type__22965___24t(Vvar__22966)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__22966,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23683',axiom,
! [Vvar__23684] :
( c_24__type__23683___24t(Vvar__23684)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8059___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__23684,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24122',axiom,
! [Vvar__24123] :
( c_24__type__24122___24t(Vvar__24123)
<=> ! [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__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__6617___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__24136___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__24141___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__24150___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__24123,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__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('$_type_24136',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24137] :
( c_24__type__24136___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24137)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__24137,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_24141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24142] :
( c_24__type__24141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24142)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__24142,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_24150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24151] :
( c_24__type__24150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24151)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24151,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_244',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__245] :
( c_24__type__244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__245)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__245,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_24835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24836] :
( c_24__type__24835___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24836)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__24836,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_24849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24850] :
( c_24__type__24849___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24850)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__24850,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_24856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24857] :
( c_24__type__24856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24857)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__24857,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_2494',axiom,
! [Vvar__2495] :
( c_24__type__2494___24t(Vvar__2495)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__2495,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2505',axiom,
! [Vvar__2506] :
( c_24__type__2505___24t(Vvar__2506)
<=> ! [Vv__CANONICAL__0] :
( cqs__worst_2eT___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cqs__worst_2eT___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2506,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25161',axiom,
! [Vvar__25162] :
( c_24__type__25161___24t(Vvar__25162)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1053___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__25162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_25166',axiom,
! [Vvar__25167] :
( c_24__type__25166___24t(Vvar__25167)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__25167,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25186',axiom,
! [Vvar__25187] :
( c_24__type__25186___24t(Vvar__25187)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25187,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2519',axiom,
! [Vvar__2520] :
( c_24__type__2519___24t(Vvar__2520)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__2520,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_25197',axiom,
! [Vvar__25198] :
( c_24__type__25197___24t(Vvar__25198)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1053___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__25198,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_25289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25290] :
( c_24__type__25289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25290)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25290,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_25327',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25328] :
( c_24__type__25327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25328)
<=> ! [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__25328,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_25394',axiom,
! [Vvar__25395] :
( c_24__type__25394___24t(Vvar__25395)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6542___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__25395,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2542',axiom,
! [Vvar__2543] :
( c_24__type__2542___24t(Vvar__2543)
<=> ! [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__2543,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25424',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25425] :
( c_24__type__25424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25425)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25425,Vv__CANONICAL__3)) ) ) ).
fof('$_type_25432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25433] :
( c_24__type__25432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25433)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25433,Vv__CANONICAL__3)) ) ) ).
fof('$_type_25440',axiom,
! [Vvar__25441] :
( c_24__type__25440___24t(Vvar__25441)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__25441,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2545',axiom,
! [Vv__CANONICAL__0,Vvar__2546] :
( c_24__type__2545___24t(Vv__CANONICAL__0,Vvar__2546)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__2546,Vv__CANONICAL__1)) ) ) ).
fof('$_type_25627',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25628] :
( c_24__type__25627___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25628)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__25628,Vv__CANONICAL__2)) ) ) ).
fof('$_type_25633',axiom,
! [Vvar__25634] :
( c_24__type__25633___24t(Vvar__25634)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___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__25634,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_25650',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25651] :
( c_24__type__25650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__25651)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__25651,Vv__CANONICAL__2)) ) ) ).
fof('$_type_25656',axiom,
! [Vvar__25657] :
( c_24__type__25656___24t(Vvar__25657)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___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__25657,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('$_type_2573',axiom,
! [Vvar__2574] :
( c_24__type__2573___24t(Vvar__2574)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2576___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__2588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__2574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_2576',axiom,
! [Vv__CANONICAL__0,Vvar__2577] :
( c_24__type__2576___24t(Vv__CANONICAL__0,Vvar__2577)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__2577,Vv__CANONICAL__1)) ) ) ).
fof('$_type_2588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2589] :
( c_24__type__2588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2589)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__2589,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_2596',axiom,
! [Vvar__2597] :
( c_24__type__2596___24t(Vvar__2597)
<=> ! [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__2597,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2606',axiom,
! [Vvar__2607] :
( c_24__type__2606___24t(Vvar__2607)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2607,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2619',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2620] :
( c_24__type__2619___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2620)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__2620,Vv__CANONICAL__4)) ) ) ).
fof('$_type_2643',axiom,
! [Vvar__2644] :
( c_24__type__2643___24t(Vvar__2644)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2644,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2702',axiom,
! [Vvar__2703] :
( c_24__type__2702___24t(Vvar__2703)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2706___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__2703,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2706',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2707] :
( c_24__type__2706___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2707)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2ebool,happ(Vvar__2707,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2722',axiom,
! [Vvar__2723] :
( c_24__type__2722___24t(Vvar__2723)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__2723,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2726',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2727] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2727)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__2727,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_2739',axiom,
! [Vvar__2740] :
( c_24__type__2739___24t(Vvar__2740)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2743___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__2740,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2743',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2744] :
( c_24__type__2743___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2744)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(Vv__CANONICAL__1,happ(Vvar__2744,Vv__CANONICAL__2)) ) ) ).
fof('$_type_2746',axiom,
! [Vvar__2747] :
( c_24__type__2746___24t(Vvar__2747)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(Vv__CANONICAL__0,happ(happ(Vvar__2747,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28521',axiom,
! [Vvar__28522] :
( c_24__type__28521___24t(Vvar__28522)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__28522,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28544',axiom,
! [Vvar__28545] :
( c_24__type__28544___24t(Vvar__28545)
<=> ! [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__28545,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_28549',axiom,
! [Vvar__28550] :
( c_24__type__28549___24t(Vvar__28550)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__28550,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_29128',axiom,
! [Vvar__29129] :
( c_24__type__29128___24t(Vvar__29129)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__29129,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29133',axiom,
! [Vv__CANONICAL__0,Vvar__29134] :
( c_24__type__29133___24t(Vv__CANONICAL__0,Vvar__29134)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__29134,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_31189',axiom,
! [Vvar__31190] :
( c_24__type__31189___24t(Vvar__31190)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
=> cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S___24t(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__31190,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_33319',axiom,
! [Vvar__33320] :
( c_24__type__33319___24t(Vvar__33320)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
=> cQuicksortComplexity_2earith__lems_2eR__floor__log2__S___24t(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__33320,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_34750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34751] :
( c_24__type__34750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34751)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__34751,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34838',axiom,
! [Vvar__34839] :
( c_24__type__34838___24t(Vvar__34839)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__34597___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vv__CANONICAL__4)
=> cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__34845___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(happ(happ(happ(Vvar__34839,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34853',axiom,
! [Vvar__34854] :
( c_24__type__34853___24t(Vvar__34854)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(Vv__CANONICAL__0),c_24__lam__34856___24a1(Vv__CANONICAL__0),happ(Vvar__34854,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34862',axiom,
! [Vvar__34863] :
( c_24__type__34862___24t(Vvar__34863)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__34863,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38',axiom,
! [Vvar__39] :
( c_24__type__38___24t(Vvar__39)
<=> ! [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__39,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_38256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38257] :
( c_24__type__38256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38257)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__38257,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38511',axiom,
! [Vvar__38512] :
( c_24__type__38511___24t(Vvar__38512)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__199___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38527___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__38537___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__6] :
( c_24__type__38532___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__6)
=> happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__5)),Vv__CANONICAL__6) = happ(Vv__CANONICAL__6,Vv__CANONICAL__5) ) ) ) )
=> ( ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__0,Vv__CANONICAL__4))
=> happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) = Vv__CANONICAL__5 ) )
=> ( ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cType___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__0,Vv__CANONICAL__5))
=> ! [Vv__CANONICAL__9] :
( c_24__type__38532___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__38556___24t(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__10)
=> happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__8),Vv__CANONICAL__9)),Vv__CANONICAL__10) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__5),Vv__CANONICAL__7),Vv__CANONICAL__8),c_24__lam__38581___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)) ) ) ) ) ) )
=> cQuicksortComplexity_2emonads_2eMonad___24t(happ(happ(happ(Vvar__38512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ) ).
fof('$_type_38527',axiom,
! [Vv__CANONICAL__0,Vvar__38528] :
( c_24__type__38527___24t(Vv__CANONICAL__0,Vvar__38528)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__38532___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__38528,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_38532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38533] :
( c_24__type__38532___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38533)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__38533,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38537',axiom,
! [Vv__CANONICAL__0,Vvar__38538] :
( c_24__type__38537___24t(Vv__CANONICAL__0,Vvar__38538)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__38538,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38556',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38557] :
( c_24__type__38556___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38557)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__38557,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_38642',axiom,
! [Vv__CANONICAL__0,Vvar__38643] :
( c_24__type__38642___24t(Vv__CANONICAL__0,Vvar__38643)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__38643,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_38659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38660] :
( c_24__type__38659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38660)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__38660,Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ).
fof('$_type_38665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38666] :
( c_24__type__38665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38666)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(Vvar__38666,Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ).
fof('$_type_38758',axiom,
! [Vvar__38759] :
( c_24__type__38758___24t(Vvar__38759)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__199___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__38773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__2),c_24__lam__38779___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)) = c_24__lam__38782___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) )
=> ( ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__7] :
( c_24__type__38790___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__38796___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__8)
=> happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__5),cCoq_2eProgram_2eBasics_2ecompose___24a5(Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__7,Vv__CANONICAL__8)),Vv__CANONICAL__6) = happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__7),happ(happ(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__8),Vv__CANONICAL__6)) ) ) ) ) ) )
=> cQuicksortComplexity_2emonads_2eFunctor___24t(happ(happ(Vvar__38759,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_38773',axiom,
! [Vv__CANONICAL__0,Vvar__38774] :
( c_24__type__38773___24t(Vv__CANONICAL__0,Vvar__38774)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__38774,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_38790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38791] :
( c_24__type__38790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38791)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__38791,Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ).
fof('$_type_38796',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38797] :
( c_24__type__38796___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38797)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(Vvar__38797,Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ).
fof('$_type_38897',axiom,
! [Vv__CANONICAL__0,Vvar__38898] :
( c_24__type__38897___24t(Vv__CANONICAL__0,Vvar__38898)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(happ(happ(Vvar__38898,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_38914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38915] :
( c_24__type__38914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38915)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__38915,Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ).
fof('$_type_38920',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38921] :
( c_24__type__38920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38921)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(Vvar__38921,Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ).
fof('$_type_38931',axiom,
! [Vvar__38932] :
( c_24__type__38931___24t(Vvar__38932)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eFunctor___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__38932,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38949] :
( c_24__type__38948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__38949)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__38949,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_38959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38960] :
( c_24__type__38959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__38960)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(happ(Vvar__38960,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_39024',axiom,
! [Vvar__39025] :
( c_24__type__39024___24t(Vvar__39025)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___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__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__39025,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_39532',axiom,
! [Vvar__39533] :
( c_24__type__39532___24t(Vvar__39533)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ( ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,Vv__CANONICAL__5) )
=> Vv__CANONICAL__3 = Vv__CANONICAL__4 ) ) ) ) )
=> cQuicksortComplexity_2emonads_2eFunctor___24t(happ(Vvar__39533,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_39588',axiom,
! [Vvar__39589] :
( c_24__type__39588___24t(Vvar__39589)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___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__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2726___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = happ(Vv__CANONICAL__4,Vv__CANONICAL__5) )
=> Vv__CANONICAL__3 = Vv__CANONICAL__4 ) ) ) ) )
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2efunc___24t(cQuicksortComplexity_2emonads_2eMonadFunctor___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,happ(happ(happ(Vvar__39589,Vv__CANONICAL__0),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_39664',axiom,
! [Vvar__39665] :
( c_24__type__39664___24t(Vvar__39665)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__4,Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__4,Vv__CANONICAL__1,Vv__CANONICAL__6)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__4,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(happ(Vvar__39665,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_39673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39674] :
( c_24__type__39673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39674)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__39674,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_39718',axiom,
! [Vvar__39719] :
( c_24__type__39718___24t(Vvar__39719)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__39727___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__39719,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_39727',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39728] :
( c_24__type__39727___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__39728)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,happ(happ(Vvar__39728,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_39762',axiom,
! [Vvar__39763] :
( c_24__type__39762___24t(Vvar__39763)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2eMonad___24t(happ(Vvar__39763,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_39774',axiom,
! [Vv__CANONICAL__0,Vvar__39775] :
( c_24__type__39774___24t(Vv__CANONICAL__0,Vvar__39775)
<=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(Vvar__39775,Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ).
fof('$_type_39792',axiom,
! [Vvar__39793] :
( c_24__type__39792___24t(Vvar__39793)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__39762___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__39805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2eMonadTrans___24t(happ(happ(Vvar__39793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_39805',axiom,
! [Vv__CANONICAL__0,Vvar__39806] :
( c_24__type__39805___24t(Vv__CANONICAL__0,Vvar__39806)
<=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(Vvar__39806,Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ).
fof('$_type_39835',axiom,
! [Vv__CANONICAL__0,Vvar__39836] :
( c_24__type__39835___24t(Vv__CANONICAL__0,Vvar__39836)
<=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(Vvar__39836,Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ).
fof('$_type_39840',axiom,
! [Vvar__39841] :
( c_24__type__39840___24t(Vvar__39841)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2eMonad___24t(happ(happ(Vvar__39841,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_39870',axiom,
! [Vv__CANONICAL__0,Vvar__39871] :
( c_24__type__39870___24t(Vv__CANONICAL__0,Vvar__39871)
<=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(Vvar__39871,Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ).
fof('$_type_39882',axiom,
! [Vvar__39883] :
( c_24__type__39882___24t(Vvar__39883)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonads_2etransMonad___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__39883,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_39994',axiom,
! [Vvar__39995] :
( c_24__type__39994___24t(Vvar__39995)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(Vv__CANONICAL__0,happ(Vvar__39995,Vv__CANONICAL__0)) ) ) ).
fof('$_type_40068',axiom,
! [Vvar__40069] :
( c_24__type__40068___24t(Vvar__40069)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__40069,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40080',axiom,
! [Vvar__40081] :
( c_24__type__40080___24t(Vvar__40081)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__40081,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_40082',axiom,
! [Vvar__40083] :
( c_24__type__40082___24t(Vvar__40083)
<=> ! [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__40083,Vv__CANONICAL__0)) ) ) ).
fof('$_type_40091',axiom,
! [Vvar__40092] :
( c_24__type__40091___24t(Vvar__40092)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(happ(Vvar__40092,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_40108',axiom,
! [Vvar__40109] :
( c_24__type__40108___24t(Vvar__40109)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,happ(happ(Vvar__40109,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_40113',axiom,
! [Vvar__40114] :
( c_24__type__40113___24t(Vvar__40114)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__40114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40149',axiom,
! [Vvar__40150] :
( c_24__type__40149___24t(Vvar__40150)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cQuicksortComplexity_2ene__list_2eL___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__40150,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_40214',axiom,
! [Vv__CANONICAL__0,Vvar__40215] :
( c_24__type__40214___24t(Vv__CANONICAL__0,Vvar__40215)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__40215,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_40352',axiom,
! [Vvar__40353] :
( c_24__type__40352___24t(Vvar__40353)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2esort__order_2eE___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__40353,Vv__CANONICAL__0)) ) ) ).
fof('$_type_41913',axiom,
! [Vvar__41914] :
( c_24__type__41913___24t(Vvar__41914)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eM,Vv__CANONICAL__0,happ(happ(Vvar__41914,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_41935',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41936] :
( c_24__type__41935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__41936)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,happ(Vvar__41936,Vv__CANONICAL__4)) ) ) ).
fof('$_type_42087',axiom,
! [Vvar__42088] :
( c_24__type__42087___24t(Vvar__42088)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__42088,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_42096',axiom,
! [Vvar__42097] :
( c_24__type__42096___24t(Vvar__42097)
<=> ! [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__42097,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42109',axiom,
! [Vvar__42110] :
( c_24__type__42109___24t(Vvar__42110)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__42110,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42124',axiom,
! [Vvar__42125] :
( c_24__type__42124___24t(Vvar__42125)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__42125,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42134',axiom,
! [Vvar__42135] :
( c_24__type__42134___24t(Vvar__42135)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__42135,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42140',axiom,
! [Vvar__42141] :
( c_24__type__42140___24t(Vvar__42141)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__42141,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42162',axiom,
! [Vvar__42163] :
( c_24__type__42162___24t(Vvar__42163)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__42163,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42301',axiom,
! [Vvar__42302] :
( c_24__type__42301___24t(Vvar__42302)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__42302,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42307',axiom,
! [Vvar__42308] :
( c_24__type__42307___24t(Vvar__42308)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__42308,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42311',axiom,
! [Vvar__42312] :
( c_24__type__42311___24t(Vvar__42312)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__42312,Vv__CANONICAL__0)) ) ) ).
fof('$_type_42330',axiom,
! [Vvar__42331] :
( c_24__type__42330___24t(Vvar__42331)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__42331,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_42379',axiom,
! [Vvar__42380] :
( c_24__type__42379___24t(Vvar__42380)
<=> ! [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__42380,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42442',axiom,
! [Vvar__42443] :
( c_24__type__42442___24t(Vvar__42443)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__42443,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_42451',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42452] :
( c_24__type__42451___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__42452)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(Vvar__42452,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_42469',axiom,
! [Vvar__42470] :
( c_24__type__42469___24t(Vvar__42470)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__42470,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43231',axiom,
! [Vvar__43232] :
( c_24__type__43231___24t(Vvar__43232)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__43232,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43945] :
( c_24__type__43944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43945)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__43945,Vv__CANONICAL__3)) ) ) ).
fof('$_type_43946',axiom,
! [Vvar__43947] :
( c_24__type__43946___24t(Vvar__43947)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__43947,Vv__CANONICAL__0)) ) ) ).
fof('$_type_43960',axiom,
! [Vvar__43961] :
( c_24__type__43960___24t(Vvar__43961)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__43961,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43988',axiom,
! [Vvar__43989] :
( c_24__type__43988___24t(Vvar__43989)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__43989,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44047',axiom,
! [Vv__CANONICAL__0,Vvar__44048] :
( c_24__type__44047___24t(Vv__CANONICAL__0,Vvar__44048)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__44049___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__44050___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__44048,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_44094',axiom,
! [Vvar__44095] :
( c_24__type__44094___24t(Vvar__44095)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__44101___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__44095,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_44101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44102] :
( c_24__type__44101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44102)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__44102,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_44201',axiom,
! [Vvar__44202] :
( c_24__type__44201___24t(Vvar__44202)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__44202,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44205',axiom,
! [Vvar__44206] :
( c_24__type__44205___24t(Vvar__44206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__44206,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44208',axiom,
! [Vvar__44209] :
( c_24__type__44208___24t(Vvar__44209)
<=> ! [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__44209,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44213',axiom,
! [Vvar__44214] :
( c_24__type__44213___24t(Vvar__44214)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__44214,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_44224',axiom,
! [Vvar__44225] :
( c_24__type__44224___24t(Vvar__44225)
<=> ! [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__44225,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44244',axiom,
! [Vvar__44245] :
( c_24__type__44244___24t(Vvar__44245)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__44254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__44245,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_44254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44255] :
( c_24__type__44254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44255)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__44255,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_44294',axiom,
! [Vvar__44295] :
( c_24__type__44294___24t(Vvar__44295)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__44304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__44254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__44295,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_44304',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44305] :
( c_24__type__44304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44305)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__44305,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_44321',axiom,
! [Vvar__44322] :
( c_24__type__44321___24t(Vvar__44322)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__44322,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44375',axiom,
! [Vvar__44376] :
( c_24__type__44375___24t(Vvar__44376)
<=> ! [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__44376,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_44400',axiom,
! [Vvar__44401] :
( c_24__type__44400___24t(Vvar__44401)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__1,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__44401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_44531',axiom,
! [Vvar__44532] :
( c_24__type__44531___24t(Vvar__44532)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__42162___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__42162___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__44532,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44567',axiom,
! [Vvar__44568] :
( c_24__type__44567___24t(Vvar__44568)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__44568,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44579',axiom,
! [Vvar__44580] :
( c_24__type__44579___24t(Vvar__44580)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__44580,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44593',axiom,
! [Vvar__44594] :
( c_24__type__44593___24t(Vvar__44594)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__44594,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_44604',axiom,
! [Vvar__44605] :
( c_24__type__44604___24t(Vvar__44605)
<=> ! [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__44605,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44696',axiom,
! [Vvar__44697] :
( c_24__type__44696___24t(Vvar__44697)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__44697,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_44702',axiom,
! [Vvar__44703] :
( c_24__type__44702___24t(Vvar__44703)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__44703,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44776',axiom,
! [Vvar__44777] :
( c_24__type__44776___24t(Vvar__44777)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__44777,Vv__CANONICAL__0)) ) ) ).
fof('$_type_450',axiom,
! [Vv__CANONICAL__0,Vvar__451] :
( c_24__type__450___24t(Vv__CANONICAL__0,Vvar__451)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__451,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__456] :
( c_24__type__455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__456)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__456,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_460',axiom,
! [Vv__CANONICAL__0,Vvar__461] :
( c_24__type__460___24t(Vv__CANONICAL__0,Vvar__461)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__461,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_46155',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46156] :
( c_24__type__46155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46156)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__46156,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__46257] :
( c_24__type__46256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__46257)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__46257,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46357',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46358] :
( c_24__type__46357___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46358)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__46358,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__46448] :
( c_24__type__46447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__46448)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__46448,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_46548',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46549] :
( c_24__type__46548___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46549)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__46549,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_46649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__46650] :
( c_24__type__46649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__46650)
<=> ! [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__46650,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_46750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46751] :
( c_24__type__46750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__46751)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__46751,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_47497',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47498] :
( c_24__type__47497___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__47498)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__47498,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_47843',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47844] :
( c_24__type__47843___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__47844)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__47844,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__480] :
( c_24__type__479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__480)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__480,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_48189',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48190] :
( c_24__type__48189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48190)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__48190,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_48512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48513] :
( c_24__type__48512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__48513)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__48513,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_48858',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48859] :
( c_24__type__48858___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__48859)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__48859,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_49204',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49205] :
( c_24__type__49204___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49205)
<=> ! [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__49205,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_49550',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__49551] :
( c_24__type__49550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__49551)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__49551,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_49896',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49897] :
( c_24__type__49896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__49897)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__49897,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_50',axiom,
! [Vvar__51] :
( c_24__type__50___24t(Vvar__51)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__51,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_50242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__50243] :
( c_24__type__50242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__50243)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__50243,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_50565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__50566] :
( c_24__type__50565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__50566)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__50566,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_50911',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__50912] :
( c_24__type__50911___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__50912)
<=> ! [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__50912,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_51257',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__51258] :
( c_24__type__51257___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__51258)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__51258,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_515',axiom,
! [Vvar__516] :
( c_24__type__515___24t(Vvar__516)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__516,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51580',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__51581] :
( c_24__type__51580___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__51581)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__51581,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_51903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__51904] :
( c_24__type__51903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__51904)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__51904,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_52',axiom,
! [Vvar__53] :
( c_24__type__52___24t(Vvar__53)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__53,Vv__CANONICAL__0)) ) ) ).
fof('$_type_52249',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__52250] :
( c_24__type__52249___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__52250)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__52250,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_52873',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__52874] :
( c_24__type__52873___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__52874)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__52874,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53087] :
( c_24__type__53086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53087)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53087,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__53300] :
( c_24__type__53299___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__53300)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__53300,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_53494',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53495] :
( c_24__type__53494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53495)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__53495,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_53707',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__53708] :
( c_24__type__53707___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__53708)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__53708,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_53920',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53921] :
( c_24__type__53920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__53921)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__53921,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_54133',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54134] :
( c_24__type__54133___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54134)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__54134,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_54346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54347] :
( c_24__type__54346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54347)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__54347,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_54541',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54542] :
( c_24__type__54541___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54542)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__54542,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_54754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54755] :
( c_24__type__54754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__54755)
<=> ! [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__54755,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_54949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54950] :
( c_24__type__54949___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__54950)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__54950,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_55063',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55064] :
( c_24__type__55063___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55064)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__55064,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_55107',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55108] :
( c_24__type__55107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55108)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__55108,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_55143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55144] :
( c_24__type__55143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55144)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__55144,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_55187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55188] :
( c_24__type__55187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__55188)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__55188,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_55209',axiom,
! [Vvar__55210] :
( c_24__type__55209___24t(Vvar__55210)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__55210,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_55237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55238] :
( c_24__type__55237___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55238)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__55238,Vv__CANONICAL__3)) ) ) ).
fof('$_type_55245',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55246] :
( c_24__type__55245___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__55246)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__55246,Vv__CANONICAL__3)) ) ) ).
fof('$_type_55253',axiom,
! [Vvar__55254] :
( c_24__type__55253___24t(Vvar__55254)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__55254,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_55287',axiom,
! [Vvar__55288] :
( c_24__type__55287___24t(Vvar__55288)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__55288,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_5548',axiom,
! [Vvar__5549] :
( c_24__type__5548___24t(Vvar__5549)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__1)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2eMonad___24t(happ(happ(Vvar__5549,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_5555',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5556] :
( c_24__type__5555___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5556)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vvar__5556,Vv__CANONICAL__3)) ) ) ).
fof('$_type_5565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__5566] :
( c_24__type__5565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__5566)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__1105___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,happ(Vvar__5566,Vv__CANONICAL__4)) ) ) ).
fof('$_type_5596',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5597] :
( c_24__type__5596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5597)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3),cCoq_2eInit_2eDatatypes_2elength___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2)))
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(Vvar__5597,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_62',axiom,
! [Vvar__63] :
( c_24__type__62___24t(Vvar__63)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__63,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6403',axiom,
! [Vvar__6404] :
( c_24__type__6403___24t(Vvar__6404)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2195___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] :
( c_24__type__6416___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(happ(happ(Vvar__6404,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_6416',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6417] :
( c_24__type__6416___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6417)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),c_24__lam__6420___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(Vvar__6417,Vv__CANONICAL__3)) ) ) ).
fof('$_type_64164',axiom,
! [Vvar__64165] :
( c_24__type__64164___24t(Vvar__64165)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__64165,Vv__CANONICAL__0)) ) ) ).
fof('$_type_64215',axiom,
! [Vvar__64216] :
( c_24__type__64215___24t(Vvar__64216)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__6617___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__64216,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_6452',axiom,
! [Vvar__6453] :
( c_24__type__6452___24t(Vvar__6453)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__6453,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6454',axiom,
! [Vvar__6455] :
( c_24__type__6454___24t(Vvar__6455)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6455,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6473',axiom,
! [Vvar__6474] :
( c_24__type__6473___24t(Vvar__6474)
<=> ! [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__6474,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6475',axiom,
! [Vvar__6476] :
( c_24__type__6475___24t(Vvar__6476)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__6476,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6487',axiom,
! [Vvar__6488] :
( c_24__type__6487___24t(Vvar__6488)
<=> ! [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__6488,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6526',axiom,
! [Vvar__6527] :
( c_24__type__6526___24t(Vvar__6527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__6527,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_65398',axiom,
! [Vvar__65399] :
( c_24__type__65398___24t(Vvar__65399)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__65399,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6542',axiom,
! [Vv__CANONICAL__0,Vvar__6543] :
( c_24__type__6542___24t(Vv__CANONICAL__0,Vvar__6543)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__6543,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6548',axiom,
! [Vvar__6549] :
( c_24__type__6548___24t(Vvar__6549)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6542___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__6549,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_65587',axiom,
! [Vvar__65588] :
( c_24__type__65587___24t(Vvar__65588)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__65588,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65612',axiom,
! [Vvar__65613] :
( c_24__type__65612___24t(Vvar__65613)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__65613,Vv__CANONICAL__0)) ) ) ).
fof('$_type_65663',axiom,
! [Vvar__65664] :
( c_24__type__65663___24t(Vvar__65664)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__65664,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_65859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__65860] :
( c_24__type__65859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__65860)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__65860,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_65952',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__65953] :
( c_24__type__65952___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__65953)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__65953,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_66045',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__66046] :
( c_24__type__66045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__66046)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__66046,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_66127',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__66128] :
( c_24__type__66127___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__66128)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__66128,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6614',axiom,
! [Vvar__6615] :
( c_24__type__6614___24t(Vvar__6615)
<=> ! [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__6617___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__6615,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_6617',axiom,
! [Vv__CANONICAL__0,Vvar__6618] :
( c_24__type__6617___24t(Vv__CANONICAL__0,Vvar__6618)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__6618,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_66220',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__66221] :
( c_24__type__66220___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__66221)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__66221,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6628',axiom,
! [Vvar__6629] :
( c_24__type__6628___24t(Vvar__6629)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__6629,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_66302',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__66303] :
( c_24__type__66302___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__66303)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__66303,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_66395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__66396] :
( c_24__type__66395___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__66396)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__66396,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_67265',axiom,
! [Vvar__67266] :
( c_24__type__67265___24t(Vvar__67266)
<=> ! [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__67266,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_67285',axiom,
! [Vvar__67286] :
( c_24__type__67285___24t(Vvar__67286)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__67286,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6747',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6748] :
( c_24__type__6747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6748)
<=> ! [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__6748,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_6754',axiom,
! [Vv__CANONICAL__0,Vvar__6755] :
( c_24__type__6754___24t(Vv__CANONICAL__0,Vvar__6755)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__6755,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_6757',axiom,
! [Vv__CANONICAL__0,Vvar__6758] :
( c_24__type__6757___24t(Vv__CANONICAL__0,Vvar__6758)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__6758,Vv__CANONICAL__1)) ) ) ).
fof('$_type_676',axiom,
! [Vv__CANONICAL__0,Vvar__677] :
( c_24__type__676___24t(Vv__CANONICAL__0,Vvar__677)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__677,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_6765',axiom,
! [Vv__CANONICAL__0,Vvar__6766] :
( c_24__type__6765___24t(Vv__CANONICAL__0,Vvar__6766)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6766,Vv__CANONICAL__1)) ) ) ).
fof('$_type_6791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6792] :
( c_24__type__6791___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__6792)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( c_24__type__6810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__6792,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__682] :
( c_24__type__681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__682)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__682,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6811] :
( c_24__type__6810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6811)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__6817___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(Vvar__6811,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__6823___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))) ) ) ).
fof('$_type_6841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6842] :
( c_24__type__6841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6842)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__6848___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(Vvar__6842,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__6854___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))) ) ) ).
fof('$_type_686',axiom,
! [Vv__CANONICAL__0,Vvar__687] :
( c_24__type__686___24t(Vv__CANONICAL__0,Vvar__687)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__687,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6873] :
( c_24__type__6872___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__6873)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__6879___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)
=> t(happ(Vvar__6873,Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(Vv__CANONICAL__0,c_24__lam__6885___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))) ) ) ).
fof('$_type_68787',axiom,
! [Vvar__68788] :
( c_24__type__68787___24t(Vvar__68788)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__68792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__68788,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_68792',axiom,
! [Vv__CANONICAL__0,Vvar__68793] :
( c_24__type__68792___24t(Vv__CANONICAL__0,Vvar__68793)
<=> ! [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__68793,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_68826',axiom,
! [Vvar__68827] :
( c_24__type__68826___24t(Vvar__68827)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__68827,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_68859',axiom,
! [Vvar__68860] :
( c_24__type__68859___24t(Vvar__68860)
<=> ! [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__8059___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__68860,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_68929',axiom,
! [Vvar__68930] :
( c_24__type__68929___24t(Vvar__68930)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__68930,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_69018',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69019] :
( c_24__type__69018___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__69019)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__69019,Vv__CANONICAL__3)) ) ) ).
fof('$_type_69064',axiom,
! [Vvar__69065] :
( c_24__type__69064___24t(Vvar__69065)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__69065,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_69260',axiom,
! [Vvar__69261] :
( c_24__type__69260___24t(Vvar__69261)
<=> ! [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__69261,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_69265',axiom,
! [Vvar__69266] :
( c_24__type__69265___24t(Vvar__69266)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__69266,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_69273',axiom,
! [Vvar__69274] :
( c_24__type__69273___24t(Vvar__69274)
<=> ! [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__69274,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_69437',axiom,
! [Vvar__69438] :
( c_24__type__69437___24t(Vvar__69438)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1053___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__69438,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_69691',axiom,
! [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__69692] :
( c_24__type__69691___24t(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__69692)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__69692,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_69754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__69755] :
( c_24__type__69754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__69755)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__69755,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_69817',axiom,
! [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__69818] :
( c_24__type__69817___24t(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__69818)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__69818,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6983',axiom,
! [Vvar__6984] :
( c_24__type__6983___24t(Vvar__6984)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__6542___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__6984,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_69871',axiom,
! [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__69872] :
( c_24__type__69871___24t(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__69872)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__69872,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_69934',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__69935] :
( c_24__type__69934___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__69935)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__69935,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_70141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70142] :
( c_24__type__70141___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70142)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__70142,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_70171',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70172] :
( c_24__type__70171___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70172)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__70172,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_70195',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70196] :
( c_24__type__70195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70196)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__70196,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_70225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70226] :
( c_24__type__70225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70226)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__70226,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_70255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70256] :
( c_24__type__70255___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70256)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__70256,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_70279',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70280] :
( c_24__type__70279___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70280)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__70280,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_70312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70313] :
( c_24__type__70312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70313)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__70313,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_70336',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70337] :
( c_24__type__70336___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70337)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__70337,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_70363',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70364] :
( c_24__type__70363___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__70364)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__70364,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_705',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__706] :
( c_24__type__705___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__706)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__706,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_70681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70682] :
( c_24__type__70681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70682)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__70682,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_70700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70701] :
( c_24__type__70700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70701)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__70701,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_70714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70715] :
( c_24__type__70714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__70715)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__70715,Vv__CANONICAL__4)) ) ) ).
fof('$_type_70859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70860] :
( c_24__type__70859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70860)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__70860,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_70909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70910] :
( c_24__type__70909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70910)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__70910,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_70959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70960] :
( c_24__type__70959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__70960)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__70960,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_71001',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__71002] :
( c_24__type__71001___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__71002)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__71002,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_71051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__71052] :
( c_24__type__71051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__71052)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__71052,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_71127',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__71128] :
( c_24__type__71127___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__71128)
<=> ! [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__71128,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_71330',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71331] :
( c_24__type__71330___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__71331)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__71331,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_71333',axiom,
! [Vvar__71334] :
( c_24__type__71333___24t(Vvar__71334)
<=> ! [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__71334,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_71389',axiom,
! [Vvar__71390] :
( c_24__type__71389___24t(Vvar__71390)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__71390,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_74',axiom,
! [Vvar__75] :
( c_24__type__74___24t(Vvar__75)
<=> ! [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__75,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_754',axiom,
! [Vvar__755] :
( c_24__type__754___24t(Vvar__755)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__759___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(happ(happ(happ(happ(Vvar__755,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_759',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__760] :
( c_24__type__759___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__760)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vvar__760,Vv__CANONICAL__3)) ) ) ).
fof('$_type_7841',axiom,
! [Vvar__7842] :
( c_24__type__7841___24t(Vvar__7842)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2726___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__3,Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__3,Vv__CANONICAL__1,happ(happ(happ(happ(happ(Vvar__7842,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_7888',axiom,
! [Vvar__7889] :
( c_24__type__7888___24t(Vvar__7889)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7897___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_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__7889,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_7897',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7898] :
( c_24__type__7897___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__7898)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__2,Vv__CANONICAL__0,happ(happ(Vvar__7898,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_79',axiom,
! [Vvar__80] :
( c_24__type__79___24t(Vvar__80)
<=> ! [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__80,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7900',axiom,
! [Vv__CANONICAL__0,Vvar__7901] :
( c_24__type__7900___24t(Vv__CANONICAL__0,Vvar__7901)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eM,cCoq_2eInit_2eDatatypes_2ebool,happ(Vvar__7901,Vv__CANONICAL__1)) ) ) ).
fof('$_type_7908',axiom,
! [Vv__CANONICAL__0,Vvar__7909] :
( c_24__type__7908___24t(Vv__CANONICAL__0,Vvar__7909)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eM,cCoq_2eInit_2eDatatypes_2ebool,happ(happ(Vvar__7909,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_7964',axiom,
! [Vvar__7965] :
( c_24__type__7964___24t(Vvar__7965)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2168___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__7965,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8054',axiom,
! [Vvar__8055] :
( c_24__type__8054___24t(Vvar__8055)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8059___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__8055,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8059',axiom,
! [Vv__CANONICAL__0,Vvar__8060] :
( c_24__type__8059___24t(Vv__CANONICAL__0,Vvar__8060)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8060,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_920',axiom,
! [Vv__CANONICAL__0,Vvar__921] :
( c_24__type__920___24t(Vv__CANONICAL__0,Vvar__921)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__4] :
( c_24__type__925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(Vvar__921,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_925',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__926] :
( c_24__type__925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__926)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__926,Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__2)) ) ) ).
fof('$_type_930',axiom,
! [Vv__CANONICAL__0,Vvar__931] :
( c_24__type__930___24t(Vv__CANONICAL__0,Vvar__931)
<=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__931,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__950] :
( c_24__type__949___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__950)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(Vvar__950,Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ).
fof('$_type_95',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__96] :
( c_24__type__95___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__96)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__96,Vv__CANONICAL__2)) ) ) ).
fof('$_type_987',axiom,
! [Vvar__988] :
( c_24__type__987___24t(Vvar__988)
<=> ! [Vv__CANONICAL__0] :
( cQuicksortComplexity_2emonads_2eMonad___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cQuicksortComplexity_2emonads_2emon___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__988,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_99',axiom,
! [Vvar__100] :
( c_24__type__99___24t(Vvar__100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__102___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__100,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__2606___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__42301___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__2606___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__44531___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__10490___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__64164___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__21011___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__43960___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__42162___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__44696___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__42442___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__42330___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__44696___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__44696___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__42379___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__186836___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Byte.xc6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).
fof('$_typeof_Coq.Init.Byte.xc7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).
fof('$_typeof_Coq.Init.Byte.xc8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).
fof('$_typeof_Coq.Init.Byte.xc9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).
fof('$_typeof_Coq.Init.Byte.xca',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).
fof('$_typeof_Coq.Init.Byte.xcb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).
fof('$_typeof_Coq.Init.Byte.xcc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__65612___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompSpecT',axiom,
c_24__type__176906___24t(cCoq_2eInit_2eDatatypes_2eCompSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__176833___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__6475___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__12___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__6473___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__21011___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__74___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__2542___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__50___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__62___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__199___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__2573___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__6452___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__52___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__199___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__21011___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__38___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__22___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__2519___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__22___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__21011___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__22762___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__12___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__12___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__2596___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__42162___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__2596___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__42162___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__12___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__12___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__79___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__2596___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__2606___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__2606___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__2606___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__119___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.exist2',axiom,
c_24__type__55209___24t(cCoq_2eInit_2eSpecif_2eexist2) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__10397___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.existT2',axiom,
c_24__type__55287___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__10433___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__10438___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__28544___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__142___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__25633___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__25656___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__28549___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__99___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__25440___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__10379___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__55253___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__28521___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__10410___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__10478___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__6487___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__6548___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__22634___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__44094___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__68929___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__6526___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__10250___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_bool',axiom,
c_24__type__25394___24t(cCoq_2eLists_2eSetoidList_2ecompat__bool) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__44294___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__44244___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__43988___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__185976___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__177021___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
c_24__type__177017___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__185672___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_',axiom,
c_24__type__177021___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__185665___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
c_24__type__185980___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__) ).
fof('$_typeof_Coq.Logic.FinFun.Bijective',axiom,
c_24__type__21419___24t(cCoq_2eLogic_2eFinFun_2eBijective) ).
fof('$_typeof_Coq.Logic.FinFun.Injective',axiom,
c_24__type__21419___24t(cCoq_2eLogic_2eFinFun_2eInjective) ).
fof('$_typeof_Coq.Logic.FinFun.Surjective',axiom,
c_24__type__21419___24t(cCoq_2eLogic_2eFinFun_2eSurjective) ).
fof('$_typeof_Coq.Logic.FinFun.bInjective',axiom,
c_24__type__21425___24t(cCoq_2eLogic_2eFinFun_2ebInjective) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__105038___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__42140___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__105042___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__42140___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__42140___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__42109___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__22817___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__42124___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__42124___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sqrt',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__42096___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__25166___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__22817___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__42134___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__13623___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__10168___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__10168___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__13616___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__13616___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__44604___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__44604___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__186830___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__186810___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__44567___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__44579___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__105072___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__44593___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__44567___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__44567___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__44567___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__42311___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__42311___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__13616___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__44567___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__13616___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__42307___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__186061___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__44201___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__22965___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__22957___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__22960___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__22960___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__44201___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__22960___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__22960___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__22957___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__22957___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__44201___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__22957___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__186218___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__183723___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__186309___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__44224___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__107908___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__199___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__107908___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__107908___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__107908___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__71333___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__177983___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedType.EQ',axiom,
c_24__type__178117___24t(cCoq_2eStructures_2eOrderedType_2eEQ) ).
fof('$_typeof_Coq.Structures.OrderedType.GT',axiom,
c_24__type__178148___24t(cCoq_2eStructures_2eOrderedType_2eGT) ).
fof('$_typeof_Coq.Structures.OrderedType.LT',axiom,
c_24__type__178086___24t(cCoq_2eStructures_2eOrderedType_2eLT) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__42140___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__42140___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__2606___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__2606___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__44604___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__104827___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__44604___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__44604___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__186841___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__186841___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__11343___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__11343___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.F1',axiom,
c_24__type__21172___24t(cCoq_2eVectors_2eFin_2eF1) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__11050___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__10472___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__29128___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__10449___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Bezout',axiom,
c_24__type__186863___24t(cCoq_2eZArith_2eBinInt_2eZ_2eBezout) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__105193___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__108198___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__42469___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__44321___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__44321___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__44702___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__11340___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__11320___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__11324___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__108193___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__44321___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__11343___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__183723___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__183793___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.funind.Recdef.iter',axiom,
c_24__type__6614___24t(cCoq_2efunind_2eRecdef_2eiter) ).
fof('$_typeof_Coq.funind.Recdef.max_type',axiom,
c_24__type__6628___24t(cCoq_2efunind_2eRecdef_2emax__type) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.Env.jump',axiom,
c_24__type__185700___24t(cCoq_2emicromega_2eEnv_2ejump) ).
fof('$_typeof_Coq.micromega.Env.nth',axiom,
c_24__type__185705___24t(cCoq_2emicromega_2eEnv_2enth) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__185875___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEadd',axiom,
c_24__type__185880___24t(cCoq_2emicromega_2eEnvRing_2ePEadd) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__185872___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEmul',axiom,
c_24__type__185880___24t(cCoq_2emicromega_2eEnvRing_2ePEmul) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__185880___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__185899___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__65663___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__185891___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__185923___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__185923___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__69064___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__186380___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__107933___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__71389___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__199___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__65398___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__177117___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__185999___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__177125___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__177122___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__199___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__68787___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__67285___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__67265___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__199___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__177133___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__67265___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__199___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__25166___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__68826___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__64215___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__68859___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__21011___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__186391___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__186391___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__44208___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__44213___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__44205___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__24122___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__44213___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__186394___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__186399___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__44213___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__199___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__69273___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__69260___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__23683___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__69265___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__199___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Computational',axiom,
c_24__type__107896___24t(cCoq_2esetoid__ring_2eRing__theory_2eComputational) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__25186___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__25186___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__25197___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.get_sign_None',axiom,
c_24__type__6473___24t(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__25166___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__25161___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__69437___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_M',axiom,
cQuicksortComplexity_2emonads_2eMonad___24t(cM) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_ceil_log2_S',axiom,
c_24__type__6628___24t(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_ceil_log2_S_0',axiom,
c_24__type__31189___24t(cQuicksortComplexity_2earith__lems_2eR__ceil__log2__S__0) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_floor_log2_S',axiom,
c_24__type__6628___24t(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S) ).
fof('$_typeof_QuicksortComplexity.arith_lems.R_floor_log2_S_0',axiom,
c_24__type__33319___24t(cQuicksortComplexity_2earith__lems_2eR__floor__log2__S__0) ).
fof('$_typeof_QuicksortComplexity.arith_lems.geb',axiom,
c_24__type__2596___24t(cQuicksortComplexity_2earith__lems_2egeb) ).
fof('$_typeof_QuicksortComplexity.fix_measure_utils.MR',axiom,
c_24__type__186752___24t(cQuicksortComplexity_2efix__measure__utils_2eMR) ).
fof('$_typeof_QuicksortComplexity.list_utils.Partitioning',axiom,
c_24__type__199___24t(cQuicksortComplexity_2elist__utils_2ePartitioning) ).
fof('$_typeof_QuicksortComplexity.list_utils.addToPartitioning',axiom,
c_24__type__34838___24t(cQuicksortComplexity_2elist__utils_2eaddToPartitioning) ).
fof('$_typeof_QuicksortComplexity.list_utils.count',axiom,
c_24__type__6983___24t(cQuicksortComplexity_2elist__utils_2ecount) ).
fof('$_typeof_QuicksortComplexity.list_utils.emp',axiom,
c_24__type__34853___24t(cQuicksortComplexity_2elist__utils_2eemp) ).
fof('$_typeof_QuicksortComplexity.list_utils.repeat',axiom,
c_24__type__34862___24t(cQuicksortComplexity_2elist__utils_2erepeat) ).
fof('$_typeof_QuicksortComplexity.monads.Build_Functor',axiom,
c_24__type__38758___24t(cQuicksortComplexity_2emonads_2eBuild__Functor) ).
fof('$_typeof_QuicksortComplexity.monads.Build_Monad',axiom,
c_24__type__38511___24t(cQuicksortComplexity_2emonads_2eBuild__Monad) ).
fof('$_typeof_QuicksortComplexity.monads.Build_MonadTrans',axiom,
c_24__type__39792___24t(cQuicksortComplexity_2emonads_2eBuild__MonadTrans) ).
fof('$_typeof_QuicksortComplexity.monads.Functor',axiom,
cType___24t(cQuicksortComplexity_2emonads_2eFunctor) ).
fof('$_typeof_QuicksortComplexity.monads.IdMonad.C',axiom,
c_24__type__199___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eC) ).
fof('$_typeof_QuicksortComplexity.monads.IdMonad.M',axiom,
cQuicksortComplexity_2emonads_2eMonad___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eM) ).
fof('$_typeof_QuicksortComplexity.monads.IdMonad.bind',axiom,
c_24__type__2739___24t(cQuicksortComplexity_2emonads_2eIdMonad_2ebind) ).
fof('$_typeof_QuicksortComplexity.monads.IdMonad.id_isa_monad',axiom,
c_24__type__41913___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eid__isa__monad) ).
fof('$_typeof_QuicksortComplexity.monads.IdMonad.ret',axiom,
c_24__type__2746___24t(cQuicksortComplexity_2emonads_2eIdMonad_2eret) ).
fof('$_typeof_QuicksortComplexity.monads.Monad',axiom,
cType___24t(cQuicksortComplexity_2emonads_2eMonad) ).
fof('$_typeof_QuicksortComplexity.monads.MonadFunctor',axiom,
c_24__type__39532___24t(cQuicksortComplexity_2emonads_2eMonadFunctor) ).
fof('$_typeof_QuicksortComplexity.monads.MonadTrans',axiom,
cType___24t(cQuicksortComplexity_2emonads_2eMonadTrans) ).
fof('$_typeof_QuicksortComplexity.monads.a_monad_isa_functor',axiom,
c_24__type__39588___24t(cQuicksortComplexity_2emonads_2ea__monad__isa__functor) ).
fof('$_typeof_QuicksortComplexity.monads.bind',axiom,
c_24__type__754___24t(cQuicksortComplexity_2emonads_2ebind) ).
fof('$_typeof_QuicksortComplexity.monads.bind_map',axiom,
c_24__type__39024___24t(cQuicksortComplexity_2emonads_2ebind__map) ).
fof('$_typeof_QuicksortComplexity.monads.extMonad',axiom,
c_24__type__2643___24t(cQuicksortComplexity_2emonads_2eextMonad) ).
fof('$_typeof_QuicksortComplexity.monads.filterM',axiom,
c_24__type__2702___24t(cQuicksortComplexity_2emonads_2efilterM) ).
fof('$_typeof_QuicksortComplexity.monads.foldlM',axiom,
c_24__type__39718___24t(cQuicksortComplexity_2emonads_2efoldlM) ).
fof('$_typeof_QuicksortComplexity.monads.foldrM',axiom,
c_24__type__7888___24t(cQuicksortComplexity_2emonads_2efoldrM) ).
fof('$_typeof_QuicksortComplexity.monads.func',axiom,
c_24__type__38931___24t(cQuicksortComplexity_2emonads_2efunc) ).
fof('$_typeof_QuicksortComplexity.monads.lift',axiom,
c_24__type__39882___24t(cQuicksortComplexity_2emonads_2elift) ).
fof('$_typeof_QuicksortComplexity.monads.liftM',axiom,
c_24__type__7841___24t(cQuicksortComplexity_2emonads_2eliftM) ).
fof('$_typeof_QuicksortComplexity.monads.liftM2',axiom,
c_24__type__39664___24t(cQuicksortComplexity_2emonads_2eliftM2) ).
fof('$_typeof_QuicksortComplexity.monads.mon',axiom,
c_24__type__515___24t(cQuicksortComplexity_2emonads_2emon) ).
fof('$_typeof_QuicksortComplexity.monads.ret',axiom,
c_24__type__987___24t(cQuicksortComplexity_2emonads_2eret) ).
fof('$_typeof_QuicksortComplexity.monads.transMonad',axiom,
c_24__type__39840___24t(cQuicksortComplexity_2emonads_2etransMonad) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.Build_Monoid',axiom,
c_24__type__108384___24t(cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.Monoid',axiom,
cType___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoid) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.M',axiom,
c_24__type__5548___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.lift',axiom,
c_24__type__42087___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2elift) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.NatAddMonoid',axiom,
cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(cQuicksortComplexity_2emonoid__monad__trans_2eNatAddMonoid) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.SimplyProfiled',axiom,
cQuicksortComplexity_2emonads_2eMonad___24t(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.cost',axiom,
c_24__type__1088___24t(cQuicksortComplexity_2emonoid__monad__trans_2ecost) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.monoid_mult',axiom,
c_24__type__40068___24t(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.monoid_type',axiom,
c_24__type__1060___24t(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.monoid_zero',axiom,
c_24__type__39994___24t(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero) ).
fof('$_typeof_QuicksortComplexity.monoid_monad_trans.result',axiom,
c_24__type__1091___24t(cQuicksortComplexity_2emonoid__monad__trans_2eresult) ).
fof('$_typeof_QuicksortComplexity.nat_below.Snb',axiom,
c_24__type__40091___24t(cQuicksortComplexity_2enat__below_2eSnb) ).
fof('$_typeof_QuicksortComplexity.nat_below.natBelow',axiom,
c_24__type__11050___24t(cQuicksortComplexity_2enat__below_2enatBelow) ).
fof('$_typeof_QuicksortComplexity.nat_below.nb0',axiom,
c_24__type__40082___24t(cQuicksortComplexity_2enat__below_2enb0) ).
fof('$_typeof_QuicksortComplexity.nat_below.nb_val',axiom,
c_24__type__40080___24t(cQuicksortComplexity_2enat__below_2enb__val) ).
fof('$_typeof_QuicksortComplexity.ne_list.L',axiom,
c_24__type__199___24t(cQuicksortComplexity_2ene__list_2eL) ).
fof('$_typeof_QuicksortComplexity.ne_list.cons',axiom,
c_24__type__40113___24t(cQuicksortComplexity_2ene__list_2econs) ).
fof('$_typeof_QuicksortComplexity.ne_list.from_vec',axiom,
c_24__type__11089___24t(cQuicksortComplexity_2ene__list_2efrom__vec) ).
fof('$_typeof_QuicksortComplexity.ne_list.map',axiom,
c_24__type__40149___24t(cQuicksortComplexity_2ene__list_2emap) ).
fof('$_typeof_QuicksortComplexity.ne_list.one',axiom,
c_24__type__40108___24t(cQuicksortComplexity_2ene__list_2eone) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.body',axiom,
c_24__type__6403___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.filter',axiom,
c_24__type__2164___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.fold_filter',axiom,
c_24__type__7964___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.gt',axiom,
c_24__type__2188___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2egt) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.qs',axiom,
c_24__type__2494___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det.simple_filter',axiom,
c_24__type__7964___24t(cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det_partition.partition',axiom,
c_24__type__11472___24t(cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_det_partition.qs',axiom,
c_24__type__11801___24t(cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.mon_nondet.partition',axiom,
c_24__type__11472___24t(cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.nonmonadic.gt',axiom,
c_24__type__8054___24t(cQuicksortComplexity_2eqs__definitions_2enonmonadic_2egt) ).
fof('$_typeof_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs',axiom,
c_24__type__43231___24t(cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs) ).
fof('$_typeof_QuicksortComplexity.sort_order.E',axiom,
cType___24t(cQuicksortComplexity_2esort__order_2eE) ).
fof('$_typeof_QuicksortComplexity.sort_order.Ec',axiom,
c_24__type__40352___24t(cQuicksortComplexity_2esort__order_2eEc) ).
fof('$_typeof_QuicksortComplexity.util.ext_eq',axiom,
c_24__type__2722___24t(cQuicksortComplexity_2eutil_2eext__eq) ).
fof('$_typeof_QuicksortComplexity.util.id',axiom,
c_24__type__25186___24t(cQuicksortComplexity_2eutil_2eid) ).
fof('$_typeof_QuicksortComplexity.vec.from_list',axiom,
c_24__type__11115___24t(cQuicksortComplexity_2evec_2efrom__list) ).
fof('$_typeof_QuicksortComplexity.vec.map',axiom,
c_24__type__44400___24t(cQuicksortComplexity_2evec_2emap) ).
fof('$_typeof_QuicksortComplexity.vec.nats',axiom,
c_24__type__11202___24t(cQuicksortComplexity_2evec_2enats) ).
fof('$_typeof_QuicksortComplexity.vec.nth',axiom,
c_24__type__11146___24t(cQuicksortComplexity_2evec_2enth) ).
fof('$_typeof_QuicksortComplexity.vec.remove',axiom,
c_24__type__11193___24t(cQuicksortComplexity_2evec_2eremove) ).
fof('$_typeof_QuicksortComplexity.vec.tail',axiom,
c_24__type__44375___24t(cQuicksortComplexity_2evec_2etail) ).
fof('$_typeof_QuicksortComplexity.vec.to_list',axiom,
c_24__type__11105___24t(cQuicksortComplexity_2evec_2eto__list) ).
fof('$_typeof_f',axiom,
c_24__type__176660___24t(cf) ).
fof('$_typeof_g',axiom,
c_24__type__176660___24t(cg) ).
fof('$_typeof_m',axiom,
cQuicksortComplexity_2emonads_2emon___24t(cM,cA,cm) ).
fof('$_typeof_n',axiom,
cQuicksortComplexity_2emonads_2emon___24t(cM,cA,cn) ).
fof('$_typeof_qs_worst.T',axiom,
cType___24t(cqs__worst_2eT) ).
fof('$_typeof_qs_worst.cmp',axiom,
c_24__type__2505___24t(cqs__worst_2ecmp) ).
fof('Coq.Arith.Between.bet_eq',axiom,
! [V0__P] :
( c_24__type__6454___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( V2__l = V1__k
=> cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V2__l) ) ) ) ) ).
fof('Coq.Arith.Compare_dec.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_eq',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_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
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.EqNat.eq_eq_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.EqNat.eq_nat_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).
fof('Coq.Arith.Lt.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_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.nat_total_order',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( 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.Private_OrderTac.IsTotal.lt_total',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.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( 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_neq_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(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ 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.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ 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.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( 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_neq_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(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ 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.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__79,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__12,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2eadd) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> 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.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2egcd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2egcd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
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_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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( 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__2606,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__6454,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_eq_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(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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_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)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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.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.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2606,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__6454,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eNat_2emul___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( V2__p != cCoq_2eInit_2eDatatypes_2eO
=> ( cCoq_2eInit_2eNat_2emul___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__79,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__12,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2emul) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
fof('Coq.Arith.PeanoNat.Nat.two_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Bool.Bool.andb_true_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.eq_iff_eq_true',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = V1__b2
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_false_abs',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
=> p(c_24False) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.Bool.Bool.not_false_is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2efalse
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.not_true_is_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2etrue
=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.orb_true_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
| V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('Coq.Bool.Bool.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Init.Datatypes.comparison_eq_stable',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ~ ( V0__c != V1__c_27 )
=> V0__c = V1__c_27 ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2545___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__6454___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.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.f_equal2_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__22829___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__10339___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( 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_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.not_eq_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__102___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Init.Wf.Acc_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__6754___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V3__y) ) )
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x) ) ) ) ) ).
fof('Coq.Init.Wf.Acc_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__6754___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V4__y),V2__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__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.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Eqdep.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__177101___24t(V0__U,V1__x,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.UIP_refl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__6765___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_rec_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__6765___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__42451___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
=> V2__y = V1__x ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__177101___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__P] :
( c_24__type__177101___24t(V0__A,V1__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ( V1__x = V1__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.UIP_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__44047___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_dep_eq_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__44047___24t(V0__A,V1___24Anonymous)
=> ! [V2__P] :
( c_24__type__6765___24t(V0__A,V2__P)
=> ! [V3__p] :
( t(V3__p,V0__A)
=> ! [V4__x] :
( t(V4__x,happ(V2__P,V3__p))
=> ! [V5__y] :
( t(V5__y,happ(V2__P,V3__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__A,V2__P,V3__p,V4__x,V3__p,V5__y)
=> V4__x = V5__y ) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V1__x = V3__y
=> ( V1__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6765___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__185684___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__185689___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__186052___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6765___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__186036___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__186044___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6765___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__6765___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__type__177593___24a2(V0__A,V1__B) = c_24__type__177598___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionalityP',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__102___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__102___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__prop__186030___24a2(V0__A,V1__B) = c_24__prop__186031___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.forall_extensionalityS',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6765___24t(V0__A,V1__B)
=> ! [V2__C] :
( c_24__type__6765___24t(V0__A,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__B,V3__x) = happ(V2__C,V3__x) )
=> c_24__type__177606___24a2(V0__A,V1__B) = c_24__type__177611___24a2(V0__A,V2__C) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__6765___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__177574___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__177579___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.JMeq.JMeq_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(V0__A,V1__x,V0__A,V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.PI.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__177101___24t(V0__U,V1__x,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP_refl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__6765___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_rec_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__6765___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__42451___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.le_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__42140,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__44776,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eN0
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__43946___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__105126___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__24849___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_total',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q)
| V0__p = V1__q
| cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p) ) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)
=> V0__p = V1__q ) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.Reals.DiscrR.IZR_eq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 = V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( V0__r1 = V1__r2
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V3__r4)
=> ( V3__r4 = V2__r3
=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V2__r3) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ! [V3__r4] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__r4)
=> ( V0__r1 = V1__r2
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V3__r4)
=> ( V3__r4 = V2__r3
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rmult_eq_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r) ) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_eq_compat',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V2__r2,V0__r) ) ) ) ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.f_equal_R',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__186064___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Sorting.Permutation.Permutation_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V0__A,V1__l,V1__l) ) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_sym',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Vectors.VectorDef.t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__29133___24t(V0__A,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
=> ( ! [V3__h] :
( t(V3__h,V0__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> ( p(happ(happ(V1__P,V4__n),V5__t))
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__t] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
=> p(happ(happ(V1__P,V4__n),V5__t)) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.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__42902___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.le_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__11343,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__10336,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.BinInt.Z.opp_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj_wd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_null',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z_eq_mult',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zeq_minus',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Zplus_eq_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( V0__n = V1__m
=> ( V2__p = V3__q
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zpos_eq',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( V0__p = V1__q
=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V1__q) ) ) ) ).
fof('Coq.ZArith.BinInt.Zsucc_eq_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.Zcompare.Zcompare_eq_case',axiom,
! [V0__c1] :
( cProp___24t(V0__c1)
=> ! [V1__c2] :
( cProp___24t(V1__c2)
=> ! [V2__c3] :
( cProp___24t(V2__c3)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__m)
=> ( p(V0__c1)
=> ( V3__n = V4__m
=> c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717___24a5(V0__c1,V1__c2,V2__c3,V3__n,V4__m) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.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_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.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.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.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.EnvRing.Mphi_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__1053___24t(V0__R,V2__rmul)
=> ! [V3__M] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V3__M)
=> ! [V4__e1] :
( c_24__type__185692___24t(V0__R,V4__e1)
=> ! [V5__e2] :
( c_24__type__185692___24t(V0__R,V5__e2)
=> ( ! [V6__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__x)
=> happ(V4__e1,V6__x) = happ(V5__e2,V6__x) )
=> cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V4__e1,V3__M) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V5__e2,V3__M) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.In_eq_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__y)
=> ( V1__x = V2__y
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__x,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__186797___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_refl_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( V0__x = V0__x
<=> p(c_24True) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA7',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__10336___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_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__10336___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__10336___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_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__10336___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__10336___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__10336___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__10336___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_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__10336___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__10336___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__10336___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_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__10336___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__10336___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.omega.PreOmega.Z.div_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.mod_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.quot_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.omega.PreOmega.Z.rem_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__1053___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1053___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__6617___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__1053___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__1053___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___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__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V11__cadd,V18__x),V19__y))),happ(happ(V3__radd,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_mul',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V12__cmul,V18__x),V19__y))),happ(happ(V4__rmul,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V18__x))),happ(V6__ropp,happ(V16__phi,V18__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_sub',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__1053___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1053___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1053___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__6617___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__6754___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__24835___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__24835___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__24835___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__24849___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__24856___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__24136___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> ! [V19__y] :
( t(V19__y,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(happ(V13__csub,V18__x),V19__y))),happ(happ(V5__rsub,happ(V16__phi,V18__x)),happ(V16__phi,V19__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Req_le_trans',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( V0__x = V1__y
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__y,V2__z)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Rle_eq_trans',axiom,
! [V0__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__z)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.Rmult_eq_compat_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r1,V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V2__r2,V0__r) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.le_ne_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(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('QuicksortComplexity.arith_lems.ne_le_impl_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('QuicksortComplexity.fix_measure_utils.unfold',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__6754___24t(V0__A,V1__R)
=> ( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
=> ! [V3__P] :
( c_24__type__6765___24t(V0__A,V3__P)
=> ! [V4__f] :
( c_24__type__6791___24t(V0__A,V1__R,V3__P,V4__f)
=> ( ! [V5__x0] :
( t(V5__x0,V0__A)
=> ! [V6__g] :
( c_24__type__6841___24t(V0__A,V1__R,V3__P,V5__x0,V6__g)
=> ! [V7__h] :
( c_24__type__6872___24t(V0__A,V1__R,V3__P,V5__x0,V7__h)
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ( p(happ(happ(V1__R,V8__x),V5__x0))
=> ( p(happ(happ(V1__R,V8__x),V5__x0))
=> happ(V6__g,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,c_24__lam__6894___24a4(V0__A,V1__R,V3__P,V5__x0),V8__x)) = happ(V7__h,cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,c_24__lam__6903___24a4(V0__A,V1__R,V3__P,V5__x0),V8__x)) ) ) )
=> happ(happ(V4__f,V5__x0),V6__g) = happ(happ(V4__f,V5__x0),V7__h) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> cCoq_2eProgram_2eWf_2eFix__sub___24a5(V0__A,V1__R,V3__P,V4__f,V6__x) = happ(happ(V4__f,V6__x),c_24__lam__6959___24a5(V0__A,V1__R,V3__P,V4__f,V6__x)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.list_utils.Permutation_length_morphism',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__10931___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.Reflexive_Symmetric',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V0__T)) ) ).
fof('QuicksortComplexity.list_utils.map_ext_eq_mor',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176782___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__2726___24a2(V0__A,V1__B),c_24__type__38256___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__B))),cCoq_2eLists_2eList_2emap___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.monads.IdMonad.ext',axiom,
cQuicksortComplexity_2emonads_2eextMonad___24a1(cQuicksortComplexity_2emonads_2eIdMonad_2eM) ).
fof('QuicksortComplexity.monads.bind_eqq',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> ! [V2__A] :
( cType___24t(V2__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__m] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__M,V2__A,V4__m)
=> ! [V5__n] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__M,V2__A,V5__n)
=> ! [V6__f] :
( c_24__type__759___24t(V0__M,V2__A,V3__B,V6__f)
=> ! [V7__g] :
( c_24__type__759___24t(V0__M,V2__A,V3__B,V7__g)
=> ( V4__m = V5__n
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V2__A,cQuicksortComplexity_2emonads_2emon___24a2(V0__M,V3__B),V6__f,V7__g)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V2__A,V3__B,V4__m,V6__f) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V2__A,V3__B,V5__n,V7__g) ) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.eta',axiom,
( ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) )
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__2726___24t(V1__A,V2__B,V3__f)
=> c_24__lam__39048___24a3(V1__A,V2__B,V3__f) = V3__f ) ) ) ) ).
fof('QuicksortComplexity.monads.extFlipped',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> ! [V2__A] :
( cType___24t(V2__A)
=> ! [V3__x] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__M,V2__A,V3__x)
=> ! [V4__B] :
( cType___24t(V4__B)
=> ! [V5__f] :
( c_24__type__759___24t(V0__M,V2__A,V4__B,V5__f)
=> ! [V6__g] :
( c_24__type__759___24t(V0__M,V2__A,V4__B,V6__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V2__A,cQuicksortComplexity_2emonads_2emon___24a2(V0__M,V4__B),V5__f,V6__g)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V2__A,V4__B,V3__x,V5__f) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V2__A,V4__B,V3__x,V6__g) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.filterM_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__p] :
( c_24__type__7900___24t(V0__A,V1__p)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__p,V2__l) = cQuicksortComplexity_2emonads_2efilterM___24a4(V0__A,cQuicksortComplexity_2emonads_2eIdMonad_2eM,V1__p,V2__l) ) ) ) ).
fof('QuicksortComplexity.monads.foldlM_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V2__M)
=> ! [V3__f] :
( c_24__type__39727___24t(V0__A,V1__B,V2__M,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__h] :
( t(V5__h,V1__B)
=> ! [V6__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V6__t)
=> cQuicksortComplexity_2emonads_2efoldlM___24a6(V0__A,V1__B,V2__M,V3__f,V4__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,V5__h,V6__t)) = cQuicksortComplexity_2emonads_2ebind___24a5(V2__M,V0__A,V0__A,happ(happ(V3__f,V4__x),V5__h),c_24__lam__39747___24a5(V0__A,V1__B,V2__M,V3__f,V6__t)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.mon_assoc',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__b] :
( cType___24t(V2__b)
=> ! [V3__c] :
( cType___24t(V3__c)
=> ! [V4__n] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__m,V1__a,V4__n)
=> ! [V5__f] :
( c_24__type__759___24t(V0__m,V1__a,V2__b,V5__f)
=> ! [V6__g] :
( c_24__type__2619___24t(V0__m,V1__a,V2__b,V3__c,V6__g)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__m,V2__b,V3__c,cQuicksortComplexity_2emonads_2ebind___24a5(V0__m,V1__a,V2__b,V4__n,V5__f),V6__g) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__m,V1__a,V3__c,V4__n,c_24__lam__2636___24a6(V0__m,V1__a,V2__b,V3__c,V5__f,V6__g)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.mon_lunit',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__b] :
( cType___24t(V2__b)
=> ! [V3__x] :
( t(V3__x,V1__a)
=> ! [V4__f] :
( c_24__type__759___24t(V0__m,V1__a,V2__b,V4__f)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__m,V1__a,V2__b,cQuicksortComplexity_2emonads_2eret___24a3(V0__m,V1__a,V3__x),V4__f) = happ(V4__f,V3__x) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.mon_lunit_under_bind',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__C] :
( cType___24t(V3__C)
=> ! [V4__a] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__M,V1__A,V4__a)
=> ! [V5__b] :
( c_24__type__38948___24t(V0__M,V1__A,V2__B,V5__b)
=> ! [V6__f] :
( c_24__type__38959___24t(V0__M,V1__A,V2__B,V3__C,V6__f)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V1__A,V3__C,V4__a,c_24__lam__38981___24a6(V0__M,V1__A,V2__B,V3__C,V5__b,V6__f)) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,V1__A,V3__C,V4__a,c_24__lam__39002___24a6(V0__M,V1__A,V2__B,V3__C,V5__b,V6__f)) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monads.mon_runit',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__m)
=> ! [V1__a] :
( cType___24t(V1__a)
=> ! [V2__f] :
( cQuicksortComplexity_2emonads_2emon___24t(V0__m,V1__a,V2__f)
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__m,V1__a,V1__a,V2__f,cQuicksortComplexity_2emonads_2eret___24a2(V0__m,V1__a)) = V2__f ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.Mext',axiom,
! [V0__monoid] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__monoid)
=> ! [V1__monad] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__monad)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V1__monad)
=> cQuicksortComplexity_2emonads_2eextMonad___24a1(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad)) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.bind_toLower',axiom,
! [V0__monoid] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__monoid)
=> ! [V1__monad] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__monad)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V1__monad)
=> ! [V3__X] :
( cType___24t(V3__X)
=> ! [V4__V] :
( cType___24t(V4__V)
=> ! [V5__f] :
( cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V4__V,V5__f)
=> ! [V6__g] :
( c_24__type__41935___24t(V0__monoid,V1__monad,V3__X,V4__V,V6__g)
=> cQuicksortComplexity_2emonads_2ebind___24a5(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V4__V,V3__X,V5__f,V6__g) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V4__V),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__X),c_24__cast__41965___24a5(V0__monoid,V1__monad,V3__X,V4__V,V5__f),c_24__lam__41981___24a5(V0__monoid,V1__monad,V3__X,V4__V,V6__g)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.bind_toLower\'',axiom,
! [V0__monoid] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__monoid)
=> ! [V1__monad] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__monad)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V1__monad)
=> ! [V3__X] :
( cType___24t(V3__X)
=> ! [V4__V] :
( cType___24t(V4__V)
=> ! [V5__f] :
( cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V4__V,V5__f)
=> ! [V6__g] :
( c_24__type__41935___24t(V0__monoid,V1__monad,V3__X,V4__V,V6__g)
=> cQuicksortComplexity_2emonads_2ebind___24a5(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V4__V,V3__X,V5__f,V6__g) = cQuicksortComplexity_2emonads_2ebind___24a5(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V4__V),cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__X),c_24__cast__41937___24a5(V0__monoid,V1__monad,V3__X,V4__V,V5__f),c_24__lam__41953___24a5(V0__monoid,V1__monad,V3__X,V4__V,V6__g)) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.mon_toLower',axiom,
! [V0__monoid] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__monoid)
=> ! [V1__monad] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__monad)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V1__monad)
=> ! [V3__X] :
( cType___24t(V3__X)
=> cQuicksortComplexity_2emonads_2emon___24a2(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V3__X) = cQuicksortComplexity_2emonads_2emon___24a2(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__X)) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.ret_toLower',axiom,
! [V0__monoid] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__monoid)
=> ! [V1__monad] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__monad)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V1__monad)
=> ! [V3__X] :
( cType___24t(V3__X)
=> ! [V4__x] :
( t(V4__x,V3__X)
=> cQuicksortComplexity_2emonads_2eret___24a3(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V0__monoid,V1__monad),V3__X,V4__x) = cQuicksortComplexity_2emonads_2eret___24a3(V1__monad,cCoq_2eInit_2eDatatypes_2eprod___24a2(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__X),cCoq_2eInit_2eDatatypes_2epair___24a4(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V0__monoid),V3__X,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__monoid),V4__x)) ) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.SimplyProfiled_ext',axiom,
cQuicksortComplexity_2emonads_2eextMonad___24a1(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled) ).
fof('QuicksortComplexity.monoid_monad_trans.bind_cost',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__a] :
( cQuicksortComplexity_2emonads_2emon___24t(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled,V0__T,V2__a)
=> ! [V3__b] :
( c_24__type__1095___24t(V0__T,V1__U,V3__b)
=> cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a2(V1__U,cQuicksortComplexity_2emonads_2ebind___24a5(cQuicksortComplexity_2emonoid__monad__trans_2eSimplyProfiled,V0__T,V1__U,V2__a,V3__b)) = cCoq_2eInit_2eNat_2eadd___24a2(cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a2(V0__T,V2__a),cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a2(V1__U,happ(V3__b,cQuicksortComplexity_2emonoid__monad__trans_2eresult___24a2(V0__T,V2__a)))) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.monoid_assoc',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ! [V1__x] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V0__m,V1__x)
=> ! [V2__y] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V0__m,V2__y)
=> ! [V3__z] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V0__m,V3__z)
=> cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,V1__x,V2__y),V3__z) = cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,V1__x,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,V2__y,V3__z)) ) ) ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.monoid_lunit',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ! [V1__x] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V0__m,V1__x)
=> cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__m),V1__x) = V1__x ) ) ).
fof('QuicksortComplexity.monoid_monad_trans.monoid_runit',axiom,
! [V0__m] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V0__m)
=> ! [V1__x] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V0__m,V1__x)
=> cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V0__m,V1__x,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V0__m)) = V1__x ) ) ).
fof('QuicksortComplexity.ne_list.map_ext',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__U] :
( cType___24t(V1__U)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__T,V1__U,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__T,V1__U,V3__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__T,V1__U,V2__f,V3__g)
=> ! [V5__l] :
( cQuicksortComplexity_2ene__list_2eL___24t(V0__T,V5__l)
=> cQuicksortComplexity_2ene__list_2emap___24a4(V0__T,V1__U,V2__f,V5__l) = cQuicksortComplexity_2ene__list_2emap___24a4(V0__T,V1__U,V3__g,V5__l) ) ) ) ) ) ) ).
fof('QuicksortComplexity.ne_list.ne_list_map_ext_eq_morph',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__2726___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__2726___24t(V0__A,V1__B,V3__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__x,V3__y)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(cQuicksortComplexity_2ene__list_2eL___24a1(V0__A),cQuicksortComplexity_2ene__list_2eL___24a1(V1__B),cQuicksortComplexity_2ene__list_2emap___24a3(V0__A,V1__B,V2__x),cQuicksortComplexity_2ene__list_2emap___24a3(V0__A,V1__B,V3__y)) ) ) ) ) ) ).
fof('QuicksortComplexity.ne_list.ne_list_map_ext_eq_morph_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176669___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__2726___24a2(V0__A,V1__B),c_24__type__176677___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(cQuicksortComplexity_2ene__list_2eL___24a1(V0__A),cQuicksortComplexity_2ene__list_2eL___24a1(V1__B))),cQuicksortComplexity_2ene__list_2emap___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.body_eq',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__le] :
( c_24__type__2195___24t(V0__M,V1__T,V2__le)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> ! [V4__x0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V4__x0)
=> ! [V5__g] :
( c_24__type__6416___24t(V0__M,V1__T,V4__x0,V5__g)
=> ! [V6__h] :
( c_24__type__6416___24t(V0__M,V1__T,V4__x0,V6__h)
=> ( ! [V7__x1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V7__x1)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V7__x1),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V4__x0)))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V7__x1),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V4__x0)))
=> happ(V5__g,cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__6441___24a3(V0__M,V1__T,V4__x0),V7__x1)) = happ(V6__h,cCoq_2eInit_2eSpecif_2eexist___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__6441___24a3(V0__M,V1__T,V4__x0),V7__x1)) ) ) )
=> cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a5(V0__M,V1__T,V2__le,V4__x0,V5__g) = cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a5(V0__M,V1__T,V2__le,V4__x0,V6__h) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.hm',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> ! [V3__c] :
( c_24__type__2168___24t(V0__M,V1__T,V3__c)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V4__l)
=> ! [V5__U] :
( cType___24t(V5__U)
=> ! [V6__f] :
( c_24__type__5555___24t(V0__M,V1__T,V5__U,V6__f)
=> ! [V7__g] :
( c_24__type__5565___24t(V0__M,V1__T,V4__l,V5__U,V7__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5573___24a4(V0__M,V1__T,V4__l,V5__U)),cQuicksortComplexity_2emonads_2emon___24a2(V0__M,V5__U),V7__g,cCoq_2eProgram_2eBasics_2ecompose___24a5(cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5573___24a4(V0__M,V1__T,V4__l,V5__U)),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cQuicksortComplexity_2emonads_2emon___24a2(V0__M,V5__U),V6__f,cCoq_2eInit_2eSpecif_2eproj1__sig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5573___24a4(V0__M,V1__T,V4__l,V5__U))))
=> cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5573___24a4(V0__M,V1__T,V4__l,V5__U)),V5__U,cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter___24a4(V0__M,V1__T,V3__c,V4__l),V7__g) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),V5__U,cQuicksortComplexity_2emonads_2efilterM___24a4(V1__T,V0__M,V3__c,V4__l),V6__f) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.qs_obligation_1',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__l0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V2__l0)
=> ! [V3__qs] :
( c_24__type__5596___24t(V0__M,V1__T,V2__l0,V3__qs)
=> ! [V4__pivot] :
( t(V4__pivot,V1__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V4__pivot,V5__t) = V2__l0
=> ! [V7__l] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5602___24a4(V0__M,V1__T,V2__l0,V5__t),V7__l)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5602___24a4(V0__M,V1__T,V2__l0,V5__t),V7__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V2__l0))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.qs_obligation_2',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__l0] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V2__l0)
=> ! [V3__qs] :
( c_24__type__5596___24t(V0__M,V1__T,V2__l0,V3__qs)
=> ! [V4__pivot] :
( t(V4__pivot,V1__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V4__pivot,V5__t) = V2__l0
=> ! [V7__l] :
( cCoq_2eInit_2eSpecif_2esig___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5602___24a4(V0__M,V1__T,V2__l0,V5__t),V7__l)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),c_24__lam__5602___24a4(V0__M,V1__T,V2__l0,V5__t),V7__l)),cCoq_2eInit_2eDatatypes_2elength___24a2(V1__T,V2__l0))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.qs_obligation_3',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__2200___24a1(V0__T))) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.simple_fold_filter',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__c] :
( c_24__type__2168___24t(V0__M,V1__T,V2__c)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V3__l)
=> cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter___24a4(V0__M,V1__T,V2__c,V3__l) = cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter___24a4(V0__M,V1__T,V2__c,V3__l) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.unfold',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__le] :
( c_24__type__2195___24t(V0__M,V1__T,V2__le)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V3__l)
=> cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a4(V0__M,V1__T,V2__le,V3__l) = cCoq_2eProgram_2eWf_2eFix__sub___24a6(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__8015___24a2(V0__M,V1__T)),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__3___24a1(V1__T),c_24__lam__8018___24a2(V0__M,V1__T),cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a3(V0__M,V1__T,V2__le),V3__l) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det.unfold\'',axiom,
! [V0__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V0__M)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__le] :
( c_24__type__2195___24t(V0__M,V1__T,V2__le)
=> ( cQuicksortComplexity_2emonads_2eextMonad___24a1(V0__M)
=> ! [V4__pivot] :
( t(V4__pivot,V1__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__T,V5__t)
=> cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a4(V0__M,V1__T,V2__le,cCoq_2eInit_2eDatatypes_2econs___24a3(V1__T,V4__pivot,V5__t)) = cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cQuicksortComplexity_2emonads_2ebind___24a5(V0__M,cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cCoq_2eInit_2eDatatypes_2elist___24a1(V1__T),cQuicksortComplexity_2emonads_2efilterM___24a4(V1__T,V0__M,cQuicksortComplexity_2eqs__definitions_2emon__det_2egt___24a4(V0__M,V1__T,V2__le,V4__pivot),V5__t),cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a3(V0__M,V1__T,V2__le)),c_24__lam__8039___24a5(V0__M,V1__T,V2__le,V4__pivot,V5__t)) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det_nonmonadic_eq',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Xle] :
( c_24__type__6754___24t(V0__X,V1__Xle)
=> ! [V2__leb] :
( c_24__type__7908___24t(V0__X,V2__leb)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V3__l)
=> cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a4(cQuicksortComplexity_2emonads_2eIdMonad_2eM,V0__X,V2__leb,V3__l) = cQuicksortComplexity_2eqs__definitions_2enonmonadic_2eqs___24a3(V0__X,V2__leb,V3__l) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det_partition.qs_obligation_1',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__qs] :
( c_24__type__11494___24t(V0__T,V1__M,V2__l,V3__qs)
=> ! [V4__h] :
( t(V4__h,V0__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t) = V2__l
=> ! [V7__part] :
( cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11500___24a4(V0__T,V1__M,V2__l,V5__t),V7__part)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11500___24a4(V0__T,V1__M,V2__l,V5__t),V7__part,cCoq_2eInit_2eDatatypes_2eLt)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det_partition.qs_obligation_2',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__qs] :
( c_24__type__11494___24t(V0__T,V1__M,V2__l,V3__qs)
=> ! [V4__h] :
( t(V4__h,V0__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t) = V2__l
=> ! [V7__part] :
( cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11500___24a4(V0__T,V1__M,V2__l,V5__t),V7__part)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__11500___24a4(V0__T,V1__M,V2__l,V5__t),V7__part,cCoq_2eInit_2eDatatypes_2eGt)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_det_partition.qs_obligation_3',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__2200___24a1(V0__T))) ) ).
fof('QuicksortComplexity.qs_definitions.mon_nondet.qs_obligation_1',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__qs] :
( c_24__type__11494___24t(V0__T,V1__M,V2__l,V3__qs)
=> ! [V4__h] :
( t(V4__h,V0__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t) = V2__l
=> ! [V7__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t))),V7__i)
=> ! [V8__part] :
( cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__12041___24a6(V0__T,V1__M,V2__l,V4__h,V5__t,V7__i),V8__part)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__12041___24a6(V0__T,V1__M,V2__l,V4__h,V5__t,V7__i),V8__part,cCoq_2eInit_2eDatatypes_2eLt)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_nondet.qs_obligation_2',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__M] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V1__M)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V2__l)
=> ! [V3__qs] :
( c_24__type__11494___24t(V0__T,V1__M,V2__l,V3__qs)
=> ! [V4__h] :
( t(V4__h,V0__T)
=> ! [V5__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__T,V5__t)
=> ( cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t) = V2__l
=> ! [V7__i] :
( cQuicksortComplexity_2enat__below_2enatBelow___24t(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__T,V4__h,V5__t))),V7__i)
=> ! [V8__part] :
( cCoq_2eInit_2eSpecif_2esig___24t(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__12041___24a6(V0__T,V1__M,V2__l,V4__h,V5__t,V7__i),V8__part)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(cQuicksortComplexity_2elist__utils_2ePartitioning___24a1(V0__T),c_24__lam__12041___24a6(V0__T,V1__M,V2__l,V4__h,V5__t,V7__i),V8__part,cCoq_2eInit_2eDatatypes_2eGt)),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__T,V2__l))) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.qs_definitions.mon_nondet.qs_obligation_3',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eProgram_2eWf_2eMR___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__T),cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2elt,c_24__lam__2200___24a1(V0__T))) ) ).
fof('QuicksortComplexity.util.compose_ext_eq_morph',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> ! [V3__x] :
( c_24__type__2726___24t(V1__Y,V2__Z,V3__x)
=> ! [V4__y] :
( c_24__type__2726___24t(V1__Y,V2__Z,V4__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V1__Y,V2__Z,V3__x,V4__y)
=> ! [V6__x] :
( c_24__type__176721___24t(V0__X,V1__Y,V2__Z,V6__x)
=> ! [V7__y] :
( c_24__type__176721___24t(V0__X,V1__Y,V2__Z,V7__y)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__X,V1__Y,V6__x,V7__y)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__X,V2__Z,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,V1__Y,V2__Z,V3__x,V6__x),cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__X,V1__Y,V2__Z,V4__y,V7__y)) ) ) ) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.compose_ext_eq_morph_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176714___24a3(V0__X,V1__Y,V2__Z),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__2726___24a2(V1__Y,V2__Z),c_24__type__176735___24a3(V0__X,V1__Y,V2__Z),cQuicksortComplexity_2eutil_2eext__eq___24a2(V1__Y,V2__Z),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__2726___24a2(V0__X,V1__Y),c_24__type__2726___24a2(V0__X,V2__Z),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V2__Z))),cCoq_2eProgram_2eBasics_2ecompose___24a3(V0__X,V1__Y,V2__Z)) ) ) ) ).
fof('QuicksortComplexity.util.compose_lunit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V1__B,cQuicksortComplexity_2eutil_2eid___24a1(V1__B),V2__f),V2__f) ) ) ) ).
fof('QuicksortComplexity.util.compose_runit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V0__A,V1__B,V2__f,cQuicksortComplexity_2eutil_2eid___24a1(V0__A)),V2__f) ) ) ) ).
fof('QuicksortComplexity.util.eq_trans',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__a] :
( t(V1__a,V0__X)
=> ! [V2__b] :
( t(V2__b,V0__X)
=> ! [V3__c] :
( t(V3__c,V0__X)
=> ( V1__a = V2__b
=> ( V2__b = V3__c
=> V1__a = V3__c ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.ext_eq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__2726___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Reflexive',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(c_24__type__2726___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Symmetric',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(c_24__type__2726___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_Transitive',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(c_24__type__2726___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rel_relation',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(c_24__type__2726___24a2(V0__X,V1__Y),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__X,V1__Y)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_rw',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__2726___24t(V0__A,V1__B,V3__g)
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(V0__A,V1__B,V2__f,V3__g)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('QuicksortComplexity.util.ext_eq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(c_24__type__2726___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.util.ext_eq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(c_24__type__2726___24a2(V0__A,V1__B),cQuicksortComplexity_2eutil_2eext__eq___24a2(V0__A,V1__B)) ) ) ).
fof('QuicksortComplexity.vec.double_rect',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__P] :
( c_24__type__176762___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.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.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.map_ext',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__2726___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__2726___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.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(e,axiom,
cQuicksortComplexity_2emonads_2eextMonad___24a1(cM) ).
fof('$adef_$_lam_6171_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6171,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6171___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_6336_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6336,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6336___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('$adef_QuicksortComplexity.qs_definitions.mon_det_partition.qs_obligation_3_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs__obligation__3,V_24X1) = cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs__obligation__3___24a1(V_24X1) ).
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('$adef_$_lam_6142_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__6142,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__6142___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_QuicksortComplexity.qs_definitions.mon_det.fold_filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_39747_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39747,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39747___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_$_lam_11375_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__11375,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__11375___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_1444_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1444,V_24X1),V_24X2),V_24X3) = c_24__lam__1444___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8039_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__8039,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__8039___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2636_$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__2636,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__2636___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_$_lam_2688_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2688,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2688___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_1955_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1955,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1955___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_11167_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11167,V_24X1),V_24X2),V_24X3) = c_24__lam__11167___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.monads.func_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2efunc,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2efunc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Permutation.perm_nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2eperm__nil,V_24X1) = cCoq_2eSorting_2ePermutation_2eperm__nil___24a1(V_24X1) ).
fof('$adef_$_lam_38981_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__38981,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__38981___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.fix_measure_utils.MR_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2efix__measure__utils_2eMR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cQuicksortComplexity_2efix__measure__utils_2eMR___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_prop_104829_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__104829,V_24X1),V_24X2) = c_24__prop__104829___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.get_sign_None_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eget__sign__None___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_34815_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34815,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34815___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.Program.Wf.Fix_sub_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eProgram_2eWf_2eFix__sub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eProgram_2eWf_2eFix__sub___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_6885_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6885,V_24X1),V_24X2),V_24X3) = c_24__lam__6885___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_186052_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__186052,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__186052___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1102_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1102,V_24X1),V_24X2) = c_24__lam__1102___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8015_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__8015,V_24X1),V_24X2) = c_24__lam__8015___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.ne_list.map_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2ene__list_2emap,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2ene__list_2emap___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_7950_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7950,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7950___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_6848_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6848,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6848___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_4357_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4357,V_24X1),V_24X2) = c_24__lam__4357___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_$_lam_269_$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__269,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__269___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_$_lam_7865_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7865,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7865___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_186044_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__186044,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__186044___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.result_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonoid__monad__trans_2eresult,V_24X1) = cQuicksortComplexity_2emonoid__monad__trans_2eresult___24a1(V_24X1) ).
fof('$adef_$_lam_34800_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__34800,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__34800___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_6879_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6879,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6879___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Logic.JMeq.JMeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eJMeq_2eJMeq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eJMeq_2eJMeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.vec.map_$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('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_$_lam_38581_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__38581,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__38581___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8018_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__8018,V_24X1),V_24X2) = c_24__lam__8018___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_186031_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__186031,V_24X1),V_24X2) = c_24__prop__186031___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_186343_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__186343,V_24X1),V_24X2) = c_24__lam__186343___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('$adef_$_lam_186343_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__186343,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__186343___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_186335_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__186335,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__186335___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.ne_list.map_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2ene__list_2emap,V_24X1),V_24X2) = cQuicksortComplexity_2ene__list_2emap___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6137_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__6137,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__6137___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_Coq.NArith.BinNatDef.N.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.body_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_QuicksortComplexity.qs_definitions.mon_det.qs_obligation_1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_186794_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__186794,V_24X1),V_24X2),V_24X3) = c_24__prop__186794___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_34812_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34812,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34812___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_11788_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11788,V_24X1),V_24X2),V_24X3) = c_24__lam__11788___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_5602_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__5602,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__5602___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6441_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6441,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6441___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('$adef_$_lam_34856_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34856,V_24X1) = c_24__lam__34856___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.eq_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.util.ext_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eutil_2eext__eq,V_24X1),V_24X2) = cQuicksortComplexity_2eutil_2eext__eq___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2803_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2803,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2803___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_186327_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__186327,V_24X1),V_24X2) = c_24__lam__186327___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34758_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__34758,V_24X1),V_24X2),V_24X3) = c_24__lam__34758___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_6894_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__6894,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__6894___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ediv,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_39502_$a1',axiom,
! [V_24X1] : happ(c_24__lam__39502,V_24X1) = c_24__lam__39502___24a1(V_24X1) ).
fof('$adef_$_lam_7940_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7940,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7940___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Program.Wf.Fix_sub_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eProgram_2eWf_2eFix__sub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eProgram_2eWf_2eFix__sub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_$_lam_6369_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6369,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6369___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_34851_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34851,V_24X1),V_24X2) = c_24__lam__34851___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_6854_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6854,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6854___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5885_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__5885,V_24X1),V_24X2),V_24X3) = c_24__lam__5885___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7988_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7988,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7988___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_5538_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__5538,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__5538___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.monads.bind_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2ebind,V_24X1) = cQuicksortComplexity_2emonads_2ebind___24a1(V_24X1) ).
fof('$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_$_let_5_ret_MMT_42049_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__ret__MMT__42049,V_24X1),V_24X2),V_24X3) = c_24__let__5__ret__MMT__42049___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_cast_41954_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__cast__41954,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__cast__41954___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_QuicksortComplexity.monads.liftM_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2eliftM,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2emonads_2eliftM___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_prop_186796_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__186796,V_24X1),V_24X2) = c_24__prop__186796___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$7955_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_247955,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_247955___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.arith_lems.geb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2earith__lems_2egeb,V_24X1),V_24X2) = cQuicksortComplexity_2earith__lems_2egeb___24a2(V_24X1,V_24X2) ).
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_11881_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__11881,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__11881___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).
fof('$adef_$_prop_186797_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__186797,V_24X1),V_24X2) = c_24__prop__186797___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_186795_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__186795,V_24X1),V_24X2),V_24X3) = c_24__prop__186795___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP__$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V_24X1) ) ).
fof('$adef_$_prop_44050_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__44050,V_24X1),V_24X2),V_24X3) = c_24__prop__44050___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_186319_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__186319,V_24X1),V_24X2) = c_24__lam__186319___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_11447_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__11447,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__11447___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_12041_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__12041,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__12041___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.monads.IdMonad.C_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2eIdMonad_2eC,V_24X1) = cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(V_24X1) ).
fof('$adef_$_lam_11788_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__11788,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__11788___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_v_CANONICAL_5_11789_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__v__CANONICAL__5__11789,V_24X1),V_24X2),V_24X3) = c_24__let__v__CANONICAL__5__11789___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_6137_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6137,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6137___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_v_CANONICAL_5_2482_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__v__CANONICAL__5__2482,V_24X1),V_24X2),V_24X3) = c_24__let__v__CANONICAL__5__2482___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_186030_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__186030,V_24X1),V_24X2) = c_24__prop__186030___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_1449_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__1449,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__1449___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_34856_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__34856,V_24X1),V_24X2))
<=> c_24__lam__34856___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_269_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__269,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__269___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_QuicksortComplexity.util.id_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eutil_2eid,V_24X1) = cQuicksortComplexity_2eutil_2eid___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.RewriteRelation_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eRewriteRelation,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_39622_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39622,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39622___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.monads.extMonad_$a1',axiom,
! [V_24X1] :
( p(happ(cQuicksortComplexity_2emonads_2eextMonad,V_24X1))
<=> cQuicksortComplexity_2emonads_2eextMonad___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.Build_Monoid_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1063_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1063,V_24X1) = c_24__lam__1063___24a1(V_24X1) ).
fof('$adef_$_lam_6275_$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__6275,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__6275___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_$_lam_11186_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11186,V_24X1),V_24X2) = c_24__lam__11186___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11422_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__11422,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__11422___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_11370_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__11370,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__11370___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_11133_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11133,V_24X1),V_24X2) = c_24__lam__11133___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_34845_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__34845,V_24X1),V_24X2),V_24X3) = c_24__lam__34845___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_QuicksortComplexity.monoid_monad_trans.Build_Monoid_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2emonoid__monad__trans_2eBuild__Monoid___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_2678_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2678,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2678___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_11200_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11200,V_24X1),V_24X2) = c_24__lam__11200___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_34597_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34597,V_24X1),V_24X2) = c_24__lam__34597___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_504_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__504,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__504___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$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.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_974_$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__974,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__974___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_1_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_34845_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__34845,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__34845___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_6968_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__6968,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__6968___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_7742_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__7742__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__7742__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6080_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__6080,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__6080___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6903_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__6903,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__6903___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34597_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__34597,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__34597___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Env.jump_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_12041_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(c_24__lam__12041,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> c_24__lam__12041___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_11167_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11167,V_24X1),V_24X2) = c_24__lam__11167___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$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('$adef_Coq.setoid_ring.Field_theory.condition_$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('$adef_$_lam_6885_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6885,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6885___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$7499_$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_247499,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__case__Coq_2eInit_2eDatatypes_2elist_247499___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_prop_44049_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__44049,V_24X1),V_24X2),V_24X3) = c_24__prop__44049___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.list_utils.count_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2elist__utils_2ecount,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2elist__utils_2ecount___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_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_$_lam_39157_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__39157,V_24X1),V_24X2) = c_24__lam__39157___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.qs_obligation_2_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
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('$adef_QuicksortComplexity.monads.a_monad_isa_functor_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonads_2ea__monad__isa__functor,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonads_2ea__monad__isa__functor___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_$_fix_44537_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__44537__1__add__carry,V_24X1),V_24X2) = c_24__fix__44537__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_$_cast_41965_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__cast__41965,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__cast__41965___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Init.Datatypes.nat_rect_$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('$adef_$_lam_7950_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7950,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7950___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs,V_24X1),V_24X2) = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.monoid_mult_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult,V_24X1) = cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Logic.FinFun.Bijective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eFinFun_2eBijective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eFinFun_2eBijective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.monoid_type_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type,V_24X1) = cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.gt_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2egt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eqs__definitions_2emon__det_2egt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_6817_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6817,V_24X1),V_24X2),V_24X3) = c_24__lam__6817___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('$adef_QuicksortComplexity.monads.IdMonad.bind_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2emonads_2eIdMonad_2ebind,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2emonads_2eIdMonad_2ebind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6968_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__6968,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__6968___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_1729_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1729,V_24X1),V_24X2),V_24X3) = c_24__lam__1729___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('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_186044_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__186044,V_24X1),V_24X2),V_24X3) = c_24__lam__186044___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.monoid_mult_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonoid__monad__trans_2emonoid__mult___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2757_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2757,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2757___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38648_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38648,V_24X1),V_24X2) = c_24__lam__38648___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.mon_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2emon,V_24X1) = cQuicksortComplexity_2emonads_2emon___24a1(V_24X1) ).
fof('$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_$_fix_185366_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__185366__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__185366__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6823_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6823,V_24X1),V_24X2),V_24X3) = c_24__lam__6823___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_39002_$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__39002,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__39002___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_1069_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1069,V_24X1),V_24X2),V_24X3) = c_24__lam__1069___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2258_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2258,V_24X1),V_24X2),V_24X3) = c_24__lam__2258___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_5573_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__5573,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__5573___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38906_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38906,V_24X1),V_24X2),V_24X3) = c_24__lam__38906___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1) = cCoq_2eSorting_2ePermutation_2ePermutation___24a1(V_24X1) ).
fof('$adef_$_lam_11370_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11370,V_24X1),V_24X2) = c_24__lam__11370___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_QuicksortComplexity.qs_definitions.mon_det.qs_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_41960_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41960,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41960___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_$_lam_4461_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__4461,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__4461___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_$_lam_730_$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__730,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__730___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_$_lam_41988_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41988,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41988___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.monads.lift_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2elift,V_24X1) = cQuicksortComplexity_2emonads_2elift___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.util.cmp_cmp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eutil_2ecmp__cmp,V_24X1),V_24X2) = cQuicksortComplexity_2eutil_2ecmp__cmp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.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.ne_list.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2ene__list_2econs,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2ene__list_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$185329_$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_24185329,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24185329___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_QuicksortComplexity.ne_list.one_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2ene__list_2eone,V_24X1),V_24X2) = cQuicksortComplexity_2ene__list_2eone___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$186248_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24186248,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24186248___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2803_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2803,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2803___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_34800_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__34800,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__34800___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_2200_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2200,V_24X1),V_24X2) = c_24__lam__2200___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_22801_$a1',axiom,
! [V_24X1] : happ(c_24__lam__22801,V_24X1) = c_24__lam__22801___24a1(V_24X1) ).
fof('$adef_$_lam_39635_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39635,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39635___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_11085_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11085,V_24X1),V_24X2) = c_24__lam__11085___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_39048_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__39048,V_24X1),V_24X2),V_24X3) = c_24__lam__39048___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38779_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38779,V_24X1),V_24X2) = c_24__lam__38779___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_3_C_MMT_4200_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__3__C__MMT__4200,V_24X1),V_24X2),V_24X3) = c_24__let__3__C__MMT__4200___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$7606_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_247606,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_247606___24a3(V_24X1,V_24X2,V_24X3) ).
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_8044_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__8044,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__8044___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6142_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__6142,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__6142___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_11160_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__11160,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__11160___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_6336_$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__6336,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__6336___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_1108_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1108,V_24X1),V_24X2) = c_24__lam__1108___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$11029_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2411029,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2411029___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11500_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__11500,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__11500___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_5_ret_MMT_4202_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__5__ret__MMT__4202,V_24X1),V_24X2) = c_24__let__5__ret__MMT__4202___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1062_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1062,V_24X1) = c_24__lam__1062___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.ne_list.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2ene__list_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2ene__list_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$186270_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24186270___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('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5573_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__5573,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__5573___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.fst_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2efst___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Nat.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esqrt,V_24X1) = cCoq_2eInit_2eNat_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.qs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.CompSpecT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompSpecT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Program.Basics.compose_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3) = cCoq_2eProgram_2eBasics_2ecompose___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.gt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2egt,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2emon__det_2egt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs_0_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0,V_24X1) = cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs__0___24a1(V_24X1) ).
fof('$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_QuicksortComplexity.monads.transMonad_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2etransMonad,V_24X1) = cQuicksortComplexity_2emonads_2etransMonad___24a1(V_24X1) ).
fof('$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_$_lam_2258_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2258,V_24X1),V_24X2) = c_24__lam__2258___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39157_$a1',axiom,
! [V_24X1] : happ(c_24__lam__39157,V_24X1) = c_24__lam__39157___24a1(V_24X1) ).
fof('$adef_$_lam_1725_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1725,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1725___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_504_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__504,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__504___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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.monads.Build_Functor_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2emonads_2eBuild__Functor,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2emonads_2eBuild__Functor___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1725_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1725,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1725___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_4_bind_MMT_4201_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__bind__MMT__4201,V_24X1),V_24X2) = c_24__let__4__bind__MMT__4201___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_7828_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7828,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7828___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_11451_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11451,V_24X1),V_24X2),V_24X3) = c_24__lam__11451___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5521_$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__5521,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__5521___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
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('$adef_$_lam_41981_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41981,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41981___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.list_utils.merges_spec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2emerges__spec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cQuicksortComplexity_2elist__utils_2emerges__spec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.exist_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_let_5_ret_MMT_4202_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__ret__MMT__4202,V_24X1),V_24X2),V_24X3) = c_24__let__5__ret__MMT__4202___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_$_lam_974_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__974,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__974___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_6903_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__6903,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__6903___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_lam_11575_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11575,V_24X1),V_24X2),V_24X3) = c_24__lam__11575___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_44151_$a1',axiom,
! [V_24X1] : happ(c_24__lam__44151,V_24X1) = c_24__lam__44151___24a1(V_24X1) ).
fof('$adef_$_lam_1105_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1105,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1105___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_8015_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__8015,V_24X1),V_24X2),V_24X3) = c_24__lam__8015___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_7988_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7988,V_24X1),V_24X2),V_24X3) = c_24__lam__7988___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_QuicksortComplexity.monads.func_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2efunc,V_24X1) = cQuicksortComplexity_2emonads_2efunc___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_69423_69426_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__69423__69426,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__69423__69426___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_1449_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1449,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1449___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_38779_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38779,V_24X1),V_24X2),V_24X3) = c_24__lam__38779___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4357_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__4357,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__4357___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.vec.tail_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2evec_2etail,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2evec_2etail___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_38782_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38782,V_24X1),V_24X2) = c_24__lam__38782___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39502_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__39502,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__39502___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_38903_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38903,V_24X1),V_24X2),V_24X3) = c_24__lam__38903___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_7828_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__7828,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__7828___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_v_CANONICAL_3_2259_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__v__CANONICAL__3__2259,V_24X1),V_24X2) = c_24__let__v__CANONICAL__3__2259___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11422_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__11422,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__11422___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.list_utils.addToPartitioning_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eaddToPartitioning,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2elist__utils_2eaddToPartitioning___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.list_utils.partition_oblig_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2epartition__oblig,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2elist__utils_2epartition__oblig___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_41960_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41960,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41960___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_11447_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__11447,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__11447___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.util.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2eutil_2eid,V_24X1),V_24X2) = cQuicksortComplexity_2eutil_2eid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_$_lam_6848_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6848,V_24X1),V_24X2),V_24X3) = c_24__lam__6848___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_3_C_MMT_4200_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__C__MMT__4200,V_24X1),V_24X2) = c_24__let__3__C__MMT__4200___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6379_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6379,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6379___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_34811_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34811,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34811___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.ne_list.from_vec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2ene__list_2efrom__vec,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2ene__list_2efrom__vec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_186792_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__186792,V_24X1),V_24X2),V_24X3) = c_24__prop__186792___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_186791_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__186791,V_24X1),V_24X2),V_24X3) = c_24__prop__186791___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Program.Wf.MR_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eProgram_2eWf_2eMR,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eProgram_2eWf_2eMR___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.ne_list.from_vec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2ene__list_2efrom__vec,V_24X1),V_24X2) = cQuicksortComplexity_2ene__list_2efrom__vec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_42055_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__42055,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__42055___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_11375_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__11375,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__11375___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_186319_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__186319,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__186319___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.monads.ret_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2eret,V_24X1) = cQuicksortComplexity_2emonads_2eret___24a1(V_24X1) ).
fof('$adef_$_lam_186335_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__186335,V_24X1),V_24X2) = c_24__lam__186335___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.list_utils.elemsR_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cQuicksortComplexity_2elist__utils_2eelemsR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cQuicksortComplexity_2elist__utils_2eelemsR___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_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_$_lam_2200_$a1',axiom,
! [V_24X1] : happ(c_24__lam__2200,V_24X1) = c_24__lam__2200___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('$adef_$_lam_39747_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__39747,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__39747___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_5521_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__5521,V_24X1),V_24X2) = c_24__lam__5521___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.foldlM_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2efoldlM,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2emonads_2efoldlM___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_38981_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__38981,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__38981___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_fix_11048_v_CANONICAL_0_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__11048__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__11048__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$186265_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24186265___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.ret_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonads_2eret,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonads_2eret___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11426_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11426,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11426___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.monads.transMonad_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2etransMonad,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2etransMonad___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_nondet.partition_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eqs__definitions_2emon__nondet_2epartition___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.monads.ret_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2eret,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2eret___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5602_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__5602,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__5602___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_lam_39695_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__39695,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__39695___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.Env.nth_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2enth,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2enth___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6441_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6441,V_24X1),V_24X2),V_24X3) = c_24__lam__6441___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_v_CANONICAL_3_11576_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__v__CANONICAL__3__11576,V_24X1),V_24X2) = c_24__let__v__CANONICAL__3__11576___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.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_QuicksortComplexity.monads.bind_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2ebind,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2emonads_2ebind___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$2693_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242693,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242693___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.gcd_$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_39695_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39695,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39695___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.arith_lems.geb_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2egeb,V_24X1) = cQuicksortComplexity_2earith__lems_2egeb___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_$_lam_6080_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6080,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6080___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.monads.liftM2_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2eliftM2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cQuicksortComplexity_2emonads_2eliftM2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_QuicksortComplexity.monads.Build_Functor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2eBuild__Functor,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2eBuild__Functor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_38782_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38782,V_24X1),V_24X2),V_24X3) = c_24__lam__38782___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_38581_$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__38581,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = c_24__lam__38581___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_$_lam_186327_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__186327,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__186327___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_lam_11139_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__11139,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__11139___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_11082_$a1',axiom,
! [V_24X1] : happ(c_24__lam__11082,V_24X1) = c_24__lam__11082___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.Mphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2eMphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.nat_below.nb0_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2enat__below_2enb0,V_24X1) = cQuicksortComplexity_2enat__below_2enb0___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2481_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2481,V_24X1),V_24X2),V_24X3) = c_24__lam__2481___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6275_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__6275,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__6275___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_1105_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1105,V_24X1),V_24X2) = c_24__lam__1105___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.MonadFunctor_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2eMonadFunctor,V_24X1) = cQuicksortComplexity_2emonads_2eMonadFunctor___24a1(V_24X1) ).
fof('$adef_$_lam_2688_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2688,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2688___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_$_prop_104830_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__104830,V_24X1),V_24X2) = c_24__prop__104830___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_7645_v_CANONICAL_2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__7645__v__CANONICAL__2,V_24X1),V_24X2),V_24X3) = c_24__fix__7645__v__CANONICAL__2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_186052_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__186052,V_24X1),V_24X2),V_24X3) = c_24__lam__186052___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_39622_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__39622,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__39622___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_refl_on__$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$5837_$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_245837,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_245837___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_2759_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2759,V_24X1),V_24X2) = c_24__lam__2759___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.qs_definitions.mon_det_partition.partition_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2epartition___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$71114_$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_2471114,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_2471114___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_$_prop_186790_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__186790,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__186790___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.monads.IdMonad.id_isa_monad_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2eIdMonad_2eid__isa__monad,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2eIdMonad_2eid__isa__monad___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6074_$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__6074,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__6074___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_lam_39002_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__39002,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__39002___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_cast_41982_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__cast__41982,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__cast__41982___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_6420_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__6420,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__6420___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_38651_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38651,V_24X1),V_24X2) = c_24__lam__38651___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.monads.foldrM_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2efoldrM,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2emonads_2efoldrM___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$5837_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_245837,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2elist_245837___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_4_bind_MMT_42048_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__4__bind__MMT__42048,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__4__bind__MMT__42048___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39010_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__39010,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__39010___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('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11426_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11426,V_24X1),V_24X2),V_24X3) = c_24__lam__11426___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$2139_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_242139,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_242139___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_39010_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__39010,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__39010___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_v_CANONICAL_2_2201_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__v__CANONICAL__2__2201,V_24X1),V_24X2) = c_24__let__v__CANONICAL__2__2201___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_41988_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41988,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41988___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_lam_2636_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2636,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2636___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_case_Coq.Init.Datatypes.comparison$186717_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__case__Coq_2eInit_2eDatatypes_2ecomparison_24186717___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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_5544_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__5544,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__5544___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_6959_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6959,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6959___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2481_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__2481,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__2481___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.lift_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2elift,V_24X1),V_24X2) = cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2elift___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11160_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11160,V_24X1),V_24X2) = c_24__lam__11160___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6879_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6879,V_24X1),V_24X2),V_24X3) = c_24__lam__6879___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_let_var_6_p_69425_69427_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__69425__69427,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__69425__69427___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rec___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_11200_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11200,V_24X1),V_24X2),V_24X3) = c_24__lam__11200___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_6379_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6379,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6379___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_186793_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__186793,V_24X1),V_24X2),V_24X3) = c_24__prop__186793___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_fix_12068_v_CANONICAL_3_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__12068__v__CANONICAL__3,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__12068__v__CANONICAL__3___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.cost_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2ecost,V_24X1),V_24X2) = cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a2(V_24X1,V_24X2) ).
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_6420_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__6420,V_24X1),V_24X2) = c_24__lam__6420___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.qs_definitions.nonmonadic.gt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2enonmonadic_2egt,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2enonmonadic_2egt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_34849_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34849,V_24X1) = c_24__lam__34849___24a1(V_24X1) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.M_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.fold_filter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2emon__det_2efold__filter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Arith.Wf_nat.ltof_$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('$adef_QuicksortComplexity.list_utils.emp_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2elist__utils_2eemp,V_24X1) = cQuicksortComplexity_2elist__utils_2eemp___24a1(V_24X1) ).
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('$adef_QuicksortComplexity.qs_definitions.mon_det.qs_obligation_3_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__3,V_24X1) = cQuicksortComplexity_2eqs__definitions_2emon__det_2eqs__obligation__3___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38651_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38651,V_24X1),V_24X2),V_24X3) = c_24__lam__38651___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esnd___24a2(V_24X1,V_24X2) ).
fof('$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_QuicksortComplexity.ne_list.L_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2ene__list_2eL,V_24X1) = cQuicksortComplexity_2ene__list_2eL___24a1(V_24X1) ).
fof('$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_$_lam_11082_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11082,V_24X1),V_24X2) = c_24__lam__11082___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_38906_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38906,V_24X1),V_24X2) = c_24__lam__38906___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_8044_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__8044,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__8044___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_$_lam_2790_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2790,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2790___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_5544_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__5544,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__5544___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_$_lam_1959_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1959,V_24X1),V_24X2),V_24X3) = c_24__lam__1959___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.monads.Build_MonadTrans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2eBuild__MonadTrans,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2eBuild__MonadTrans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_4_bind_MMT_4201_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__4__bind__MMT__4201,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__4__bind__MMT__4201___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_41953_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41953,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41953___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_QuicksortComplexity.monads.bind_map_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonads_2ebind__map,V_24X1) = cQuicksortComplexity_2emonads_2ebind__map___24a1(V_24X1) ).
fof('$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.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1955_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1955,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1955___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_$_lam_730_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__730,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__730___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$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_$_lam_8018_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__8018,V_24X1),V_24X2),V_24X3) = c_24__lam__8018___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_6854_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__6854,V_24X1),V_24X2),V_24X3) = c_24__lam__6854___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.sqrt_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_$_lam_38648_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__38648,V_24X1),V_24X2),V_24X3) = c_24__lam__38648___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.monads.IdMonad.ret_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2eIdMonad_2eret,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2eIdMonad_2eret___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11186_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__11186,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__11186___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_lam_6817_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6817,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6817___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_41981_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__41981,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__41981___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det_partition.qs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eqs__definitions_2emon__det__partition_2eqs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_$_lam_8039_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__8039,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__8039___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.arith_lems.ltb_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2earith__lems_2eltb,V_24X1) = cQuicksortComplexity_2earith__lems_2eltb___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('$adef_Coq.Init.Datatypes.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1) = cCoq_2eInit_2eDatatypes_2elength___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_42902_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__42902,V_24X1),V_24X2) = c_24__prop__42902___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6823_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__6823,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__6823___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_42055_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__42055,V_24X1),V_24X2) = c_24__lam__42055___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.foldrM_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2efoldrM,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2emonads_2efoldrM___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.map_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2) = cCoq_2eLists_2eList_2emap___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.Build_Monad_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2eBuild__Monad,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cQuicksortComplexity_2emonads_2eBuild__Monad___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_cast_41937_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__cast__41937,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__cast__41937___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_QuicksortComplexity.arith_lems.R_floor_log2_S_1_$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('$adef_$_lam_38903_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__38903,V_24X1),V_24X2) = c_24__lam__38903___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_6894_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__6894,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__6894___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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_6171_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6171,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6171___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_7865_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__7865,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__7865___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34758_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__34758,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__34758___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.filter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2emon__det_2efilter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.MonoidMonadTrans.M_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM,V_24X1),V_24X2) = cQuicksortComplexity_2emonoid__monad__trans_2eMonoidMonadTrans_2eM___24a2(V_24X1,V_24X2) ).
fof('$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_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_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_$_lam_6369_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__6369,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__6369___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_11139_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__11139,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__11139___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_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_QuicksortComplexity.monoid_monad_trans.result_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonoid__monad__trans_2eresult,V_24X1),V_24X2) = cQuicksortComplexity_2emonoid__monad__trans_2eresult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1729_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1729,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1729___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1108_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1108,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1108___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_lam_11575_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__11575,V_24X1),V_24X2) = c_24__lam__11575___24a2(V_24X1,V_24X2) ).
fof('$adef_QuicksortComplexity.monads.Build_Monad_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2emonads_2eBuild__Monad,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2emonads_2eBuild__Monad___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11451_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__11451,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__11451___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_$_lam_6959_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__6959,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__6959___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_34849_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__34849,V_24X1),V_24X2))
<=> c_24__lam__34849___24a2(V_24X1,V_24X2) ) ).
fof('$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.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_$_lam_4461_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4461,V_24X1),V_24X2) = c_24__lam__4461___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_5538_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__5538,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__5538___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.cost_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonoid__monad__trans_2ecost,V_24X1) = cQuicksortComplexity_2emonoid__monad__trans_2ecost___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.simple_filter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2eqs__definitions_2emon__det_2esimple__filter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_$_let_3_C_MMT_42047_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__3__C__MMT__42047,V_24X1),V_24X2),V_24X3) = c_24__let__3__C__MMT__42047___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_7940_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__7940,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__7940___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_11133_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11133,V_24X1),V_24X2),V_24X3) = c_24__lam__11133___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.eq_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__sym,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eLogic_2eeq__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Lists.SetoidList.compat_bool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__bool,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_42071_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__42071,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__42071___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_QuicksortComplexity.qs_definitions.mon_det.body_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eqs__definitions_2emon__det_2ebody___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11085_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__11085,V_24X1),V_24X2),V_24X3) = c_24__lam__11085___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_11500_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__11500,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__11500___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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_$_lam_34851_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34851,V_24X1) = c_24__lam__34851___24a1(V_24X1) ).
fof('$adef_$_lam_39635_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(c_24__lam__39635,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__39635___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_34816_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__34816,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__34816___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$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_41953_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__41953,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__41953___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_QuicksortComplexity.monoid_monad_trans.monoid_zero_$a1',axiom,
! [V_24X1] : happ(cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero,V_24X1) = cQuicksortComplexity_2emonoid__monad__trans_2emonoid__zero___24a1(V_24X1) ).
fof('$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_QuicksortComplexity.qs_definitions.nonmonadic.qs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuicksortComplexity_2eqs__definitions_2enonmonadic_2eqs,V_24X1),V_24X2),V_24X3) = cQuicksortComplexity_2eqs__definitions_2enonmonadic_2eqs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1444_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__1444,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__1444___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_QuicksortComplexity.vec.trans_plus_n_Sm_$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('$adef_$_lam_1102_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1102,V_24X1),V_24X2),V_24X3) = c_24__lam__1102___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_42071_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__42071,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__42071___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_QuicksortComplexity.monads.mon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuicksortComplexity_2emonads_2emon,V_24X1),V_24X2) = cQuicksortComplexity_2emonads_2emon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_11881_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__11881,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__11881___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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_$_lam_39048_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__39048,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__39048___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2678_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__2678,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__2678___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_1959_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1959,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1959___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_QuicksortComplexity.monads.filterM_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cQuicksortComplexity_2emonads_2efilterM,V_24X1),V_24X2),V_24X3),V_24X4) = cQuicksortComplexity_2emonads_2efilterM___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_QuicksortComplexity.monads.bind_map_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuicksortComplexity_2emonads_2ebind__map,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuicksortComplexity_2emonads_2ebind__map___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_24122',axiom,
! [V_24Y] :
( c_24__type__24122___24t(V_24Y)
<=> t(V_24Y,c_24__type__24122) ) ).
fof('$tdef_$_type_176721',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__176721___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__176721___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_54133',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__54133___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__54133___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_40149',axiom,
! [V_24Y] :
( c_24__type__40149___24t(V_24Y)
<=> t(V_24Y,c_24__type__40149) ) ).
fof('$tdef_$_type_70171',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70171___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70171___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_38790',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38790___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38790___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_40108',axiom,
! [V_24Y] :
( c_24__type__40108___24t(V_24Y)
<=> t(V_24Y,c_24__type__40108) ) ).
fof('$tdef_$_type_2542',axiom,
! [V_24Y] :
( c_24__type__2542___24t(V_24Y)
<=> t(V_24Y,c_24__type__2542) ) ).
fof('$tdef_$_type_225',axiom,
! [V_24X1,V_24Y] :
( c_24__type__225___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__225___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6617',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6617___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6617___24a1(V_24X1)) ) ).
fof('$tdef_$_type_455',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__455___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__455___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6416',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6416___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6416___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38959___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_70959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__70959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__70959___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_183793',axiom,
! [V_24Y] :
( c_24__type__183793___24t(V_24Y)
<=> t(V_24Y,c_24__type__183793) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_69437',axiom,
! [V_24Y] :
( c_24__type__69437___24t(V_24Y)
<=> t(V_24Y,c_24__type__69437) ) ).
fof('$tdef_$_type_176906',axiom,
! [V_24Y] :
( c_24__type__176906___24t(V_24Y)
<=> t(V_24Y,c_24__type__176906) ) ).
fof('$tdef_$_type_28544',axiom,
! [V_24Y] :
( c_24__type__28544___24t(V_24Y)
<=> t(V_24Y,c_24__type__28544) ) ).
fof('$tdef_$_type_107086',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__107086___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__107086___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_2706',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2706___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2706___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10250',axiom,
! [V_24Y] :
( c_24__type__10250___24t(V_24Y)
<=> t(V_24Y,c_24__type__10250) ) ).
fof('$tdef_$_type_68792',axiom,
! [V_24X1,V_24Y] :
( c_24__type__68792___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__68792___24a1(V_24X1)) ) ).
fof('$tdef_$_type_65952',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__65952___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__65952___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_10168',axiom,
! [V_24Y] :
( c_24__type__10168___24t(V_24Y)
<=> t(V_24Y,c_24__type__10168) ) ).
fof('$tdef_$_type_10336',axiom,
! [V_24Y] :
( c_24__type__10336___24t(V_24Y)
<=> t(V_24Y,c_24__type__10336) ) ).
fof('$tdef_$_type_38665',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38665___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38665___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_QuicksortComplexity.monads.IdMonad.C',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2emonads_2eIdMonad_2eC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2eIdMonad_2eC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11050',axiom,
! [V_24Y] :
( c_24__type__11050___24t(V_24Y)
<=> t(V_24Y,c_24__type__11050) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_38931',axiom,
! [V_24Y] :
( c_24__type__38931___24t(V_24Y)
<=> t(V_24Y,c_24__type__38931) ) ).
fof('$tdef_$_type_7964',axiom,
! [V_24Y] :
( c_24__type__7964___24t(V_24Y)
<=> t(V_24Y,c_24__type__7964) ) ).
fof('$tdef_$_type_44579',axiom,
! [V_24Y] :
( c_24__type__44579___24t(V_24Y)
<=> t(V_24Y,c_24__type__44579) ) ).
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_$_type_25650',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25650___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25650___24a2(V_24X1,V_24X2)) ) ).
fof('$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_42311',axiom,
! [V_24Y] :
( c_24__type__42311___24t(V_24Y)
<=> t(V_24Y,c_24__type__42311) ) ).
fof('$tdef_$_type_40091',axiom,
! [V_24Y] :
( c_24__type__40091___24t(V_24Y)
<=> t(V_24Y,c_24__type__40091) ) ).
fof('$tdef_$_type_10375',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10375___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10375___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11494',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__11494___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__11494___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_176677',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__176677___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__176677___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11472',axiom,
! [V_24Y] :
( c_24__type__11472___24t(V_24Y)
<=> t(V_24Y,c_24__type__11472) ) ).
fof('$tdef_$_type_11479',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11479___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11479___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$tdef_$_type_55287',axiom,
! [V_24Y] :
( c_24__type__55287___24t(V_24Y)
<=> t(V_24Y,c_24__type__55287) ) ).
fof('$tdef_$_type_185684',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__185684___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__185684___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_65398',axiom,
! [V_24Y] :
( c_24__type__65398___24t(V_24Y)
<=> t(V_24Y,c_24__type__65398) ) ).
fof('$tdef_$_type_22965',axiom,
! [V_24Y] :
( c_24__type__22965___24t(V_24Y)
<=> t(V_24Y,c_24__type__22965) ) ).
fof('$tdef_$_type_21172',axiom,
! [V_24Y] :
( c_24__type__21172___24t(V_24Y)
<=> t(V_24Y,c_24__type__21172) ) ).
fof('$tdef_$_type_47497',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__47497___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__47497___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_48512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48512___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48512___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_5555',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__5555___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__5555___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_QuicksortComplexity.qs_definitions.nonmonadic_using_Function.R_qs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2eqs__definitions_2enonmonadic__using__Function_2eR__qs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11801',axiom,
! [V_24Y] :
( c_24__type__11801___24t(V_24Y)
<=> t(V_24Y,c_24__type__11801) ) ).
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_8054',axiom,
! [V_24Y] :
( c_24__type__8054___24t(V_24Y)
<=> t(V_24Y,c_24__type__8054) ) ).
fof('$tdef_$_type_44304',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44304___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44304___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10931',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10931___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10931___24a1(V_24X1)) ) ).
fof('$tdef_QuicksortComplexity.monoid_monad_trans.Monoid',axiom,
! [V_24Y] :
( cQuicksortComplexity_2emonoid__monad__trans_2eMonoid___24t(V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonoid__monad__trans_2eMonoid) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22',axiom,
! [V_24Y] :
( c_24__type__22___24t(V_24Y)
<=> t(V_24Y,c_24__type__22) ) ).
fof('$tdef_$_type_186061',axiom,
! [V_24Y] :
( c_24__type__186061___24t(V_24Y)
<=> t(V_24Y,c_24__type__186061) ) ).
fof('$tdef_$_type_104827',axiom,
! [V_24Y] :
( c_24__type__104827___24t(V_24Y)
<=> t(V_24Y,c_24__type__104827) ) ).
fof('$tdef_$_type_54541',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__54541___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__54541___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.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_38537',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38537___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38537___24a1(V_24X1)) ) ).
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_$_type_39024',axiom,
! [V_24Y] :
( c_24__type__39024___24t(V_24Y)
<=> t(V_24Y,c_24__type__39024) ) ).
fof('$tdef_$_type_43231',axiom,
! [V_24Y] :
( c_24__type__43231___24t(V_24Y)
<=> t(V_24Y,c_24__type__43231) ) ).
fof('$tdef_$_type_42096',axiom,
! [V_24Y] :
( c_24__type__42096___24t(V_24Y)
<=> t(V_24Y,c_24__type__42096) ) ).
fof('$tdef_$_type_177117',axiom,
! [V_24Y] :
( c_24__type__177117___24t(V_24Y)
<=> t(V_24Y,c_24__type__177117) ) ).
fof('$tdef_$_type_10472',axiom,
! [V_24Y] :
( c_24__type__10472___24t(V_24Y)
<=> t(V_24Y,c_24__type__10472) ) ).
fof('$tdef_$_type_987',axiom,
! [V_24Y] :
( c_24__type__987___24t(V_24Y)
<=> t(V_24Y,c_24__type__987) ) ).
fof('$tdef_$_type_44702',axiom,
! [V_24Y] :
( c_24__type__44702___24t(V_24Y)
<=> t(V_24Y,c_24__type__44702) ) ).
fof('$tdef_$_type_2643',axiom,
! [V_24Y] :
( c_24__type__2643___24t(V_24Y)
<=> t(V_24Y,c_24__type__2643) ) ).
fof('$tdef_$_type_177606',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177606___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177606___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55209',axiom,
! [V_24Y] :
( c_24__type__55209___24t(V_24Y)
<=> t(V_24Y,c_24__type__55209) ) ).
fof('$tdef_$_type_2164',axiom,
! [V_24Y] :
( c_24__type__2164___24t(V_24Y)
<=> t(V_24Y,c_24__type__2164) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6473',axiom,
! [V_24Y] :
( c_24__type__6473___24t(V_24Y)
<=> t(V_24Y,c_24__type__6473) ) ).
fof('$tdef_$_type_11089',axiom,
! [V_24Y] :
( c_24__type__11089___24t(V_24Y)
<=> t(V_24Y,c_24__type__11089) ) ).
fof('$tdef_$_type_44593',axiom,
! [V_24Y] :
( c_24__type__44593___24t(V_24Y)
<=> t(V_24Y,c_24__type__44593) ) ).
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_$_type_2739',axiom,
! [V_24Y] :
( c_24__type__2739___24t(V_24Y)
<=> t(V_24Y,c_24__type__2739) ) ).
fof('$tdef_$_type_186391',axiom,
! [V_24Y] :
( c_24__type__186391___24t(V_24Y)
<=> t(V_24Y,c_24__type__186391) ) ).
fof('$tdef_$_type_178148',axiom,
! [V_24Y] :
( c_24__type__178148___24t(V_24Y)
<=> t(V_24Y,c_24__type__178148) ) ).
fof('$tdef_$_type_186830',axiom,
! [V_24Y] :
( c_24__type__186830___24t(V_24Y)
<=> t(V_24Y,c_24__type__186830) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_71389',axiom,
! [V_24Y] :
( c_24__type__71389___24t(V_24Y)
<=> t(V_24Y,c_24__type__71389) ) ).
fof('$tdef_$_type_6791',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6791___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6791___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_185665',axiom,
! [V_24Y] :
( c_24__type__185665___24t(V_24Y)
<=> t(V_24Y,c_24__type__185665) ) ).
fof('$tdef_$_type_24849',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24849___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24849___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11193',axiom,
! [V_24Y] :
( c_24__type__11193___24t(V_24Y)
<=> t(V_24Y,c_24__type__11193) ) ).
fof('$tdef_$_type_53299',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__53299___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__53299___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('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_50',axiom,
! [V_24Y] :
( c_24__type__50___24t(V_24Y)
<=> t(V_24Y,c_24__type__50) ) ).
fof('$tdef_$_type_6754',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6754___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6754___24a1(V_24X1)) ) ).
fof('$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_186618',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186618___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186618___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11163',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__11163___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__11163___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5596',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__5596___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__5596___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_38796',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38796___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38796___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10497',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10497___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10497___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21419',axiom,
! [V_24Y] :
( c_24__type__21419___24t(V_24Y)
<=> t(V_24Y,c_24__type__21419) ) ).
fof('$tdef_$_type_70225',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70225___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70225___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_44244',axiom,
! [V_24Y] :
( c_24__type__44244___24t(V_24Y)
<=> t(V_24Y,c_24__type__44244) ) ).
fof('$tdef_$_type_46357',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__46357___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__46357___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_44400',axiom,
! [V_24Y] :
( c_24__type__44400___24t(V_24Y)
<=> t(V_24Y,c_24__type__44400) ) ).
fof('$tdef_$_type_186574',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186574___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186574___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_176782',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__176782___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__176782___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39774',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39774___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39774___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25633',axiom,
! [V_24Y] :
( c_24__type__25633___24t(V_24Y)
<=> t(V_24Y,c_24__type__25633) ) ).
fof('$tdef_$_type_68859',axiom,
! [V_24Y] :
( c_24__type__68859___24t(V_24Y)
<=> t(V_24Y,c_24__type__68859) ) ).
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_$_type_108193',axiom,
! [V_24Y] :
( c_24__type__108193___24t(V_24Y)
<=> t(V_24Y,c_24__type__108193) ) ).
fof('$tdef_$_type_13616',axiom,
! [V_24Y] :
( c_24__type__13616___24t(V_24Y)
<=> t(V_24Y,c_24__type__13616) ) ).
fof('$tdef_$_type_11146',axiom,
! [V_24Y] :
( c_24__type__11146___24t(V_24Y)
<=> t(V_24Y,c_24__type__11146) ) ).
fof('$tdef_$_type_177122',axiom,
! [V_24Y] :
( c_24__type__177122___24t(V_24Y)
<=> t(V_24Y,c_24__type__177122) ) ).
fof('$tdef_$_type_41935',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__41935___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__41935___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_11115',axiom,
! [V_24Y] :
( c_24__type__11115___24t(V_24Y)
<=> t(V_24Y,c_24__type__11115) ) ).
fof('$tdef_$_type_107933',axiom,
! [V_24Y] :
( c_24__type__107933___24t(V_24Y)
<=> t(V_24Y,c_24__type__107933) ) ).
fof('$tdef_$_type_54346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__54346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__54346___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_52249',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__52249___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__52249___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_51580',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__51580___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__51580___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_185999',axiom,
! [V_24Y] :
( c_24__type__185999___24t(V_24Y)
<=> t(V_24Y,c_24__type__185999) ) ).
fof('$tdef_$_type_2702',axiom,
! [V_24Y] :
( c_24__type__2702___24t(V_24Y)
<=> t(V_24Y,c_24__type__2702) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_39994',axiom,
! [V_24Y] :
( c_24__type__39994___24t(V_24Y)
<=> t(V_24Y,c_24__type__39994) ) ).
fof('$tdef_$_type_2573',axiom,
! [V_24Y] :
( c_24__type__2573___24t(V_24Y)
<=> t(V_24Y,c_24__type__2573) ) ).
fof('$tdef_$_type_48858',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__48858___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__48858___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_69934',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__69934___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__69934___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_50911',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__50911___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__50911___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('$tdef_QuicksortComplexity.monoid_monad_trans.monoid_type',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonoid__monad__trans_2emonoid__type___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25166',axiom,
! [V_24Y] :
( c_24__type__25166___24t(V_24Y)
<=> t(V_24Y,c_24__type__25166) ) ).
fof('$tdef_$_type_1088',axiom,
! [V_24Y] :
( c_24__type__1088___24t(V_24Y)
<=> t(V_24Y,c_24__type__1088) ) ).
fof('$tdef_$_type_107461',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__107461___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__107461___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_33319',axiom,
! [V_24Y] :
( c_24__type__33319___24t(V_24Y)
<=> t(V_24Y,c_24__type__33319) ) ).
fof('$tdef_$_type_67285',axiom,
! [V_24Y] :
( c_24__type__67285___24t(V_24Y)
<=> t(V_24Y,c_24__type__67285) ) ).
fof('$tdef_$_type_105038',axiom,
! [V_24Y] :
( c_24__type__105038___24t(V_24Y)
<=> t(V_24Y,c_24__type__105038) ) ).
fof('$tdef_$_type_43944',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__43944___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__43944___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_42162',axiom,
! [V_24Y] :
( c_24__type__42162___24t(V_24Y)
<=> t(V_24Y,c_24__type__42162) ) ).
fof('$tdef_qs_worst.T',axiom,
! [V_24Y] :
( cqs__worst_2eT___24t(V_24Y)
<=> t(V_24Y,cqs__worst_2eT) ) ).
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_$_type_7897',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__7897___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__7897___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_69018',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__69018___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__69018___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1060',axiom,
! [V_24Y] :
( c_24__type__1060___24t(V_24Y)
<=> t(V_24Y,c_24__type__1060) ) ).
fof('$tdef_$_type_40082',axiom,
! [V_24Y] :
( c_24__type__40082___24t(V_24Y)
<=> t(V_24Y,c_24__type__40082) ) ).
fof('$tdef_$_type_46256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46256___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46256___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_39835',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39835___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39835___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55063',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__55063___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__55063___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_64164',axiom,
! [V_24Y] :
( c_24__type__64164___24t(V_24Y)
<=> t(V_24Y,c_24__type__64164) ) ).
fof('$tdef_$_type_46155',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46155___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46155___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_185672',axiom,
! [V_24Y] :
( c_24__type__185672___24t(V_24Y)
<=> t(V_24Y,c_24__type__185672) ) ).
fof('$tdef_$_type_39792',axiom,
! [V_24Y] :
( c_24__type__39792___24t(V_24Y)
<=> t(V_24Y,c_24__type__39792) ) ).
fof('$tdef_$_type_185891',axiom,
! [V_24Y] :
( c_24__type__185891___24t(V_24Y)
<=> t(V_24Y,c_24__type__185891) ) ).
fof('$tdef_$_type_42442',axiom,
! [V_24Y] :
( c_24__type__42442___24t(V_24Y)
<=> t(V_24Y,c_24__type__42442) ) ).
fof('$tdef_$_type_244',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__244___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__244___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1053',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1053___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1053___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38758',axiom,
! [V_24Y] :
( c_24__type__38758___24t(V_24Y)
<=> t(V_24Y,c_24__type__38758) ) ).
fof('$tdef_$_type_44201',axiom,
! [V_24Y] :
( c_24__type__44201___24t(V_24Y)
<=> t(V_24Y,c_24__type__44201) ) ).
fof('$tdef_$_type_65859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__65859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__65859___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_70909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__70909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__70909___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_70363',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70363___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70363___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_177101',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177101___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177101___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_176735',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__176735___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__176735___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6872',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__6872___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__6872___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_25432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25432___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25432___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_185875',axiom,
! [V_24Y] :
( c_24__type__185875___24t(V_24Y)
<=> t(V_24Y,c_24__type__185875) ) ).
fof('$tdef_$_type_6628',axiom,
! [V_24Y] :
( c_24__type__6628___24t(V_24Y)
<=> t(V_24Y,c_24__type__6628) ) ).
fof('$tdef_$_type_34853',axiom,
! [V_24Y] :
( c_24__type__34853___24t(V_24Y)
<=> t(V_24Y,c_24__type__34853) ) ).
fof('$tdef_$_type_185923',axiom,
! [V_24Y] :
( c_24__type__185923___24t(V_24Y)
<=> t(V_24Y,c_24__type__185923) ) ).
fof('$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_$_type_186380',axiom,
! [V_24Y] :
( c_24__type__186380___24t(V_24Y)
<=> t(V_24Y,c_24__type__186380) ) ).
fof('$tdef_$_type_177133',axiom,
! [V_24Y] :
( c_24__type__177133___24t(V_24Y)
<=> t(V_24Y,c_24__type__177133) ) ).
fof('$tdef_$_type_930',axiom,
! [V_24X1,V_24Y] :
( c_24__type__930___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__930___24a1(V_24X1)) ) ).
fof('$tdef_QuicksortComplexity.monads.Functor',axiom,
! [V_24Y] :
( cQuicksortComplexity_2emonads_2eFunctor___24t(V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2eFunctor) ) ).
fof('$tdef_$_type_38773',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38773___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38773___24a1(V_24X1)) ) ).
fof('$tdef_$_type_99',axiom,
! [V_24Y] :
( c_24__type__99___24t(V_24Y)
<=> t(V_24Y,c_24__type__99) ) ).
fof('$tdef_$_type_186752',axiom,
! [V_24Y] :
( c_24__type__186752___24t(V_24Y)
<=> t(V_24Y,c_24__type__186752) ) ).
fof('$tdef_$_type_10478',axiom,
! [V_24Y] :
( c_24__type__10478___24t(V_24Y)
<=> t(V_24Y,c_24__type__10478) ) ).
fof('$tdef_$_type_22960',axiom,
! [V_24Y] :
( c_24__type__22960___24t(V_24Y)
<=> t(V_24Y,c_24__type__22960) ) ).
fof('$tdef_QuicksortComplexity.monads.MonadTrans',axiom,
! [V_24Y] :
( cQuicksortComplexity_2emonads_2eMonadTrans___24t(V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2eMonadTrans) ) ).
fof('$tdef_$_type_68929',axiom,
! [V_24Y] :
( c_24__type__68929___24t(V_24Y)
<=> t(V_24Y,c_24__type__68929) ) ).
fof('$tdef_$_type_70312',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70312___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70312___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_185880',axiom,
! [V_24Y] :
( c_24__type__185880___24t(V_24Y)
<=> t(V_24Y,c_24__type__185880) ) ).
fof('$tdef_$_type_40080',axiom,
! [V_24Y] :
( c_24__type__40080___24t(V_24Y)
<=> t(V_24Y,c_24__type__40080) ) ).
fof('$tdef_$_type_185980',axiom,
! [V_24Y] :
( c_24__type__185980___24t(V_24Y)
<=> t(V_24Y,c_24__type__185980) ) ).
fof('$tdef_$_type_6983',axiom,
! [V_24Y] :
( c_24__type__6983___24t(V_24Y)
<=> t(V_24Y,c_24__type__6983) ) ).
fof('$tdef_$_type_49896',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__49896___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__49896___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_186556',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186556___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186556___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_38920',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38920___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38920___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_38948',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__38948___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__38948___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_44696',axiom,
! [V_24Y] :
( c_24__type__44696___24t(V_24Y)
<=> t(V_24Y,c_24__type__44696) ) ).
fof('$tdef_$_type_2505',axiom,
! [V_24Y] :
( c_24__type__2505___24t(V_24Y)
<=> t(V_24Y,c_24__type__2505) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_25327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25327___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25327___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2596',axiom,
! [V_24Y] :
( c_24__type__2596___24t(V_24Y)
<=> t(V_24Y,c_24__type__2596) ) ).
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_QuicksortComplexity.monads.func',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuicksortComplexity_2emonads_2efunc___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2efunc___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_676',axiom,
! [V_24X1,V_24Y] :
( c_24__type__676___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__676___24a1(V_24X1)) ) ).
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_$_type_6403',axiom,
! [V_24Y] :
( c_24__type__6403___24t(V_24Y)
<=> t(V_24Y,c_24__type__6403) ) ).
fof('$tdef_$_type_52',axiom,
! [V_24Y] :
( c_24__type__52___24t(V_24Y)
<=> t(V_24Y,c_24__type__52) ) ).
fof('$tdef_$_type_2519',axiom,
! [V_24Y] :
( c_24__type__2519___24t(V_24Y)
<=> t(V_24Y,c_24__type__2519) ) ).
fof('$tdef_QuicksortComplexity.monads.mon',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuicksortComplexity_2emonads_2emon___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2emon___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25424',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25424___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25424___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_55245',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55245___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55245___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_754',axiom,
! [V_24Y] :
( c_24__type__754___24t(V_24Y)
<=> t(V_24Y,c_24__type__754) ) ).
fof('$tdef_$_type_25161',axiom,
! [V_24Y] :
( c_24__type__25161___24t(V_24Y)
<=> t(V_24Y,c_24__type__25161) ) ).
fof('$tdef_$_type_185976',axiom,
! [V_24Y] :
( c_24__type__185976___24t(V_24Y)
<=> t(V_24Y,c_24__type__185976) ) ).
fof('$tdef_$_type_71127',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__71127___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__71127___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_79',axiom,
! [V_24Y] :
( c_24__type__79___24t(V_24Y)
<=> t(V_24Y,c_24__type__79) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_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_28521',axiom,
! [V_24Y] :
( c_24__type__28521___24t(V_24Y)
<=> t(V_24Y,c_24__type__28521) ) ).
fof('$tdef_$_type_107908',axiom,
! [V_24Y] :
( c_24__type__107908___24t(V_24Y)
<=> t(V_24Y,c_24__type__107908) ) ).
fof('$tdef_$_type_107336',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__107336___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__107336___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_177944',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__177944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__177944___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_34862',axiom,
! [V_24Y] :
( c_24__type__34862___24t(V_24Y)
<=> t(V_24Y,c_24__type__34862) ) ).
fof('$tdef_$_type_39673',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39673___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39673___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_25289',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25289___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25289___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_44567',axiom,
! [V_24Y] :
( c_24__type__44567___24t(V_24Y)
<=> t(V_24Y,c_24__type__44567) ) ).
fof('$tdef_$_type_25440',axiom,
! [V_24Y] :
( c_24__type__25440___24t(V_24Y)
<=> t(V_24Y,c_24__type__25440) ) ).
fof('$tdef_$_type_10339',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10339___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10339___24a1(V_24X1)) ) ).
fof('$tdef_$_type_70714',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__70714___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__70714___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_177579',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177579___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177579___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5548',axiom,
! [V_24Y] :
( c_24__type__5548___24t(V_24Y)
<=> t(V_24Y,c_24__type__5548) ) ).
fof('$tdef_$_type_64215',axiom,
! [V_24Y] :
( c_24__type__64215___24t(V_24Y)
<=> t(V_24Y,c_24__type__64215) ) ).
fof('$tdef_$_type_42379',axiom,
! [V_24Y] :
( c_24__type__42379___24t(V_24Y)
<=> t(V_24Y,c_24__type__42379) ) ).
fof('$tdef_$_type_34838',axiom,
! [V_24Y] :
( c_24__type__34838___24t(V_24Y)
<=> t(V_24Y,c_24__type__34838) ) ).
fof('$tdef_$_type_186810',axiom,
! [V_24Y] :
( c_24__type__186810___24t(V_24Y)
<=> t(V_24Y,c_24__type__186810) ) ).
fof('$tdef_$_type_51257',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__51257___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__51257___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('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_43946',axiom,
! [V_24Y] :
( c_24__type__43946___24t(V_24Y)
<=> t(V_24Y,c_24__type__43946) ) ).
fof('$tdef_$_type_55187',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__55187___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__55187___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_69064',axiom,
! [V_24Y] :
( c_24__type__69064___24t(V_24Y)
<=> t(V_24Y,c_24__type__69064) ) ).
fof('$tdef_$_type_6526',axiom,
! [V_24Y] :
( c_24__type__6526___24t(V_24Y)
<=> t(V_24Y,c_24__type__6526) ) ).
fof('$tdef_$_type_39718',axiom,
! [V_24Y] :
( c_24__type__39718___24t(V_24Y)
<=> t(V_24Y,c_24__type__39718) ) ).
fof('$tdef_$_type_176714',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__176714___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__176714___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_70859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__70859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__70859___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_44254',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44254___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44254___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_70700',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__70700___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__70700___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_46548',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46548___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46548___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_11105',axiom,
! [V_24Y] :
( c_24__type__11105___24t(V_24Y)
<=> t(V_24Y,c_24__type__11105) ) ).
fof('$tdef_$_type_66127',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__66127___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__66127___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25656',axiom,
! [V_24Y] :
( c_24__type__25656___24t(V_24Y)
<=> t(V_24Y,c_24__type__25656) ) ).
fof('$tdef_$_type_54949',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__54949___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__54949___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_46447',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46447___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46447___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_69273',axiom,
! [V_24Y] :
( c_24__type__69273___24t(V_24Y)
<=> t(V_24Y,c_24__type__69273) ) ).
fof('$tdef_$_type_44531',axiom,
! [V_24Y] :
( c_24__type__44531___24t(V_24Y)
<=> t(V_24Y,c_24__type__44531) ) ).
fof('$tdef_$_type_38511',axiom,
! [V_24Y] :
( c_24__type__38511___24t(V_24Y)
<=> t(V_24Y,c_24__type__38511) ) ).
fof('$tdef_$_type_185689',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__185689___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__185689___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_71001',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__71001___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__71001___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_22762',axiom,
! [V_24Y] :
( c_24__type__22762___24t(V_24Y)
<=> t(V_24Y,c_24__type__22762) ) ).
fof('$tdef_$_type_39882',axiom,
! [V_24Y] :
( c_24__type__39882___24t(V_24Y)
<=> t(V_24Y,c_24__type__39882) ) ).
fof('$tdef_Coq.micromega.Env.Env',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_39805',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39805___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39805___24a1(V_24X1)) ) ).
fof('$tdef_$_type_55237',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__55237___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__55237___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_186710',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186710___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186710___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_6548',axiom,
! [V_24Y] :
( c_24__type__6548___24t(V_24Y)
<=> t(V_24Y,c_24__type__6548) ) ).
fof('$tdef_$_type_21425',axiom,
! [V_24Y] :
( c_24__type__21425___24t(V_24Y)
<=> t(V_24Y,c_24__type__21425) ) ).
fof('$tdef_$_type_186533',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186533___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186533___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_136',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__136___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__136___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12',axiom,
! [V_24Y] :
( c_24__type__12___24t(V_24Y)
<=> t(V_24Y,c_24__type__12) ) ).
fof('$tdef_$_type_25627',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__25627___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__25627___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_70255',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70255___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70255___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_186036',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__186036___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__186036___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7841',axiom,
! [V_24Y] :
( c_24__type__7841___24t(V_24Y)
<=> t(V_24Y,c_24__type__7841) ) ).
fof('$tdef_$_type_460',axiom,
! [V_24X1,V_24Y] :
( c_24__type__460___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__460___24a1(V_24X1)) ) ).
fof('$tdef_$_type_108198',axiom,
! [V_24Y] :
( c_24__type__108198___24t(V_24Y)
<=> t(V_24Y,c_24__type__108198) ) ).
fof('$tdef_$_type_11343',axiom,
! [V_24Y] :
( c_24__type__11343___24t(V_24Y)
<=> t(V_24Y,c_24__type__11343) ) ).
fof('$tdef_$_type_186841',axiom,
! [V_24Y] :
( c_24__type__186841___24t(V_24Y)
<=> t(V_24Y,c_24__type__186841) ) ).
fof('$tdef_$_type_6747',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__6747___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__6747___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_39762',axiom,
! [V_24Y] :
( c_24__type__39762___24t(V_24Y)
<=> t(V_24Y,c_24__type__39762) ) ).
fof('$tdef_$_type_42301',axiom,
! [V_24Y] :
( c_24__type__42301___24t(V_24Y)
<=> t(V_24Y,c_24__type__42301) ) ).
fof('$tdef_$_type_185872',axiom,
! [V_24Y] :
( c_24__type__185872___24t(V_24Y)
<=> t(V_24Y,c_24__type__185872) ) ).
fof('$tdef_$_type_53086',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__53086___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__53086___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_70195',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70195___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70195___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_QuicksortComplexity.ne_list.L',axiom,
! [V_24X1,V_24Y] :
( cQuicksortComplexity_2ene__list_2eL___24t(V_24X1,V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2ene__list_2eL___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_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_70141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70141___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70141___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_177983',axiom,
! [V_24Y] :
( c_24__type__177983___24t(V_24Y)
<=> t(V_24Y,c_24__type__177983) ) ).
fof('$tdef_$_type_185705',axiom,
! [V_24Y] :
( c_24__type__185705___24t(V_24Y)
<=> t(V_24Y,c_24__type__185705) ) ).
fof('$tdef_$_type_55253',axiom,
! [V_24Y] :
( c_24__type__55253___24t(V_24Y)
<=> t(V_24Y,c_24__type__55253) ) ).
fof('$tdef_$_type_11340',axiom,
! [V_24Y] :
( c_24__type__11340___24t(V_24Y)
<=> t(V_24Y,c_24__type__11340) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_39588',axiom,
! [V_24Y] :
( c_24__type__39588___24t(V_24Y)
<=> t(V_24Y,c_24__type__39588) ) ).
fof('$tdef_$_type_2746',axiom,
! [V_24Y] :
( c_24__type__2746___24t(V_24Y)
<=> t(V_24Y,c_24__type__2746) ) ).
fof('$tdef_$_type_42469',axiom,
! [V_24Y] :
( c_24__type__42469___24t(V_24Y)
<=> t(V_24Y,c_24__type__42469) ) ).
fof('$tdef_$_type_66302',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__66302___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__66302___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_177017',axiom,
! [V_24Y] :
( c_24__type__177017___24t(V_24Y)
<=> t(V_24Y,c_24__type__177017) ) ).
fof('$tdef_$_type_920',axiom,
! [V_24X1,V_24Y] :
( c_24__type__920___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__920___24a1(V_24X1)) ) ).
fof('$tdef_$_type_183723',axiom,
! [V_24Y] :
( c_24__type__183723___24t(V_24Y)
<=> t(V_24Y,c_24__type__183723) ) ).
fof('$tdef_$_type_10410',axiom,
! [V_24Y] :
( c_24__type__10410___24t(V_24Y)
<=> t(V_24Y,c_24__type__10410) ) ).
fof('$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_44213',axiom,
! [V_24Y] :
( c_24__type__44213___24t(V_24Y)
<=> t(V_24Y,c_24__type__44213) ) ).
fof('$tdef_$_type_450',axiom,
! [V_24X1,V_24Y] :
( c_24__type__450___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__450___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22957',axiom,
! [V_24Y] :
( c_24__type__22957___24t(V_24Y)
<=> t(V_24Y,c_24__type__22957) ) ).
fof('$tdef_$_type_67265',axiom,
! [V_24Y] :
( c_24__type__67265___24t(V_24Y)
<=> t(V_24Y,c_24__type__67265) ) ).
fof('$tdef_$_type_10438',axiom,
! [V_24Y] :
( c_24__type__10438___24t(V_24Y)
<=> t(V_24Y,c_24__type__10438) ) ).
fof('$tdef_$_type_24150',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24150___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24150___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_71333',axiom,
! [V_24Y] :
( c_24__type__71333___24t(V_24Y)
<=> t(V_24Y,c_24__type__71333) ) ).
fof('$tdef_$_type_42307',axiom,
! [V_24Y] :
( c_24__type__42307___24t(V_24Y)
<=> t(V_24Y,c_24__type__42307) ) ).
fof('$tdef_$_type_66220',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__66220___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__66220___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_71330',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__71330___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__71330___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_44776',axiom,
! [V_24Y] :
( c_24__type__44776___24t(V_24Y)
<=> t(V_24Y,c_24__type__44776) ) ).
fof('$tdef_$_type_39664',axiom,
! [V_24Y] :
( c_24__type__39664___24t(V_24Y)
<=> t(V_24Y,c_24__type__39664) ) ).
fof('$tdef_$_type_2722',axiom,
! [V_24Y] :
( c_24__type__2722___24t(V_24Y)
<=> t(V_24Y,c_24__type__2722) ) ).
fof('$tdef_$_type_178086',axiom,
! [V_24Y] :
( c_24__type__178086___24t(V_24Y)
<=> t(V_24Y,c_24__type__178086) ) ).
fof('$tdef_$_type_10490',axiom,
! [V_24Y] :
( c_24__type__10490___24t(V_24Y)
<=> t(V_24Y,c_24__type__10490) ) ).
fof('$tdef_$_type_47843',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__47843___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__47843___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_69817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__69817___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__69817___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6542',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6542___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6542___24a1(V_24X1)) ) ).
fof('$tdef_$_type_39727',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__39727___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__39727___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_65587',axiom,
! [V_24Y] :
( c_24__type__65587___24t(V_24Y)
<=> t(V_24Y,c_24__type__65587) ) ).
fof('$tdef_$_type_70681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__70681___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__70681___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_106836',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__106836___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__106836___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_44375',axiom,
! [V_24Y] :
( c_24__type__44375___24t(V_24Y)
<=> t(V_24Y,c_24__type__44375) ) ).
fof('$tdef_$_type_13623',axiom,
! [V_24Y] :
( c_24__type__13623___24t(V_24Y)
<=> t(V_24Y,c_24__type__13623) ) ).
fof('$tdef_$_type_38914',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38914___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38914___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_44224',axiom,
! [V_24Y] :
( c_24__type__44224___24t(V_24Y)
<=> t(V_24Y,c_24__type__44224) ) ).
fof('$tdef_$_type_65612',axiom,
! [V_24Y] :
( c_24__type__65612___24t(V_24Y)
<=> t(V_24Y,c_24__type__65612) ) ).
fof('$tdef_$_type_2743',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2743___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2743___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_177963',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__177963___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__177963___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_38527',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38527___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38527___24a1(V_24X1)) ) ).
fof('$tdef_$_type_41913',axiom,
! [V_24Y] :
( c_24__type__41913___24t(V_24Y)
<=> t(V_24Y,c_24__type__41913) ) ).
fof('$tdef_$_type_53494',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__53494___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__53494___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_105042',axiom,
! [V_24Y] :
( c_24__type__105042___24t(V_24Y)
<=> t(V_24Y,c_24__type__105042) ) ).
fof('$tdef_$_type_50242',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__50242___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__50242___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_7900',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7900___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7900___24a1(V_24X1)) ) ).
fof('$tdef_$_type_186600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186600___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_215',axiom,
! [V_24X1,V_24Y] :
( c_24__type__215___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__215___24a1(V_24X1)) ) ).
fof('$tdef_$_type_186309',axiom,
! [V_24Y] :
( c_24__type__186309___24t(V_24Y)
<=> t(V_24Y,c_24__type__186309) ) ).
fof('$tdef_$_type_6454',axiom,
! [V_24Y] :
( c_24__type__6454___24t(V_24Y)
<=> t(V_24Y,c_24__type__6454) ) ).
fof('$tdef_$_type_1091',axiom,
! [V_24Y] :
( c_24__type__1091___24t(V_24Y)
<=> t(V_24Y,c_24__type__1091) ) ).
fof('$tdef_$_type_38256',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38256___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38256___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_186218',axiom,
! [V_24Y] :
( c_24__type__186218___24t(V_24Y)
<=> t(V_24Y,c_24__type__186218) ) ).
fof('$tdef_$_type_185692',axiom,
! [V_24X1,V_24Y] :
( c_24__type__185692___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__185692___24a1(V_24X1)) ) ).
fof('$tdef_$_type_176833',axiom,
! [V_24Y] :
( c_24__type__176833___24t(V_24Y)
<=> t(V_24Y,c_24__type__176833) ) ).
fof('$tdef_$_type_21011',axiom,
! [V_24Y] :
( c_24__type__21011___24t(V_24Y)
<=> t(V_24Y,c_24__type__21011) ) ).
fof('$tdef_$_type_54754',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__54754___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__54754___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('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_69691',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__69691___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__69691___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2588',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2588___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2588___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2576',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2576___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2576___24a1(V_24X1)) ) ).
fof('$tdef_$_type_66045',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__66045___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__66045___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_40113',axiom,
! [V_24Y] :
( c_24__type__40113___24t(V_24Y)
<=> t(V_24Y,c_24__type__40113) ) ).
fof('$tdef_$_type_52873',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__52873___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__52873___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_55107',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__55107___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__55107___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_42134',axiom,
! [V_24Y] :
( c_24__type__42134___24t(V_24Y)
<=> t(V_24Y,c_24__type__42134) ) ).
fof('$tdef_$_type_177611',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177611___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177611___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_759',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__759___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__759___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22634',axiom,
! [V_24Y] :
( c_24__type__22634___24t(V_24Y)
<=> t(V_24Y,c_24__type__22634) ) ).
fof('$tdef_$_type_949',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__949___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__949___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_40352',axiom,
! [V_24Y] :
( c_24__type__40352___24t(V_24Y)
<=> t(V_24Y,c_24__type__40352) ) ).
fof('$tdef_$_type_29128',axiom,
! [V_24Y] :
( c_24__type__29128___24t(V_24Y)
<=> t(V_24Y,c_24__type__29128) ) ).
fof('$tdef_$_type_25394',axiom,
! [V_24Y] :
( c_24__type__25394___24t(V_24Y)
<=> t(V_24Y,c_24__type__25394) ) ).
fof('$tdef_$_type_1095',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1095___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1095___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_74',axiom,
! [V_24Y] :
( c_24__type__74___24t(V_24Y)
<=> t(V_24Y,c_24__type__74) ) ).
fof('$tdef_$_type_38642',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38642___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38642___24a1(V_24X1)) ) ).
fof('$tdef_$_type_105126',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__105126___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__105126___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_177125',axiom,
! [V_24Y] :
( c_24__type__177125___24t(V_24Y)
<=> t(V_24Y,c_24__type__177125) ) ).
fof('$tdef_$_type_25186',axiom,
! [V_24Y] :
( c_24__type__25186___24t(V_24Y)
<=> t(V_24Y,c_24__type__25186) ) ).
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_$_type_6765',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6765___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6765___24a1(V_24X1)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_2545',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2545___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2545___24a1(V_24X1)) ) ).
fof('$tdef_$_type_186863',axiom,
! [V_24Y] :
( c_24__type__186863___24t(V_24Y)
<=> t(V_24Y,c_24__type__186863) ) ).
fof('$tdef_$_type_6475',axiom,
! [V_24Y] :
( c_24__type__6475___24t(V_24Y)
<=> t(V_24Y,c_24__type__6475) ) ).
fof('$tdef_$_type_185899',axiom,
! [V_24Y] :
( c_24__type__185899___24t(V_24Y)
<=> t(V_24Y,c_24__type__185899) ) ).
fof('$tdef_$_type_44101',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44101___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44101___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_40068',axiom,
! [V_24Y] :
( c_24__type__40068___24t(V_24Y)
<=> t(V_24Y,c_24__type__40068) ) ).
fof('$tdef_$_type_6452',axiom,
! [V_24Y] :
( c_24__type__6452___24t(V_24Y)
<=> t(V_24Y,c_24__type__6452) ) ).
fof('$tdef_$_type_22817',axiom,
! [V_24Y] :
( c_24__type__22817___24t(V_24Y)
<=> t(V_24Y,c_24__type__22817) ) ).
fof('$tdef_$_type_10433',axiom,
! [V_24Y] :
( c_24__type__10433___24t(V_24Y)
<=> t(V_24Y,c_24__type__10433) ) ).
fof('$tdef_$_type_186064',axiom,
! [V_24X1,V_24Y] :
( c_24__type__186064___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__186064___24a1(V_24X1)) ) ).
fof('$tdef_$_type_105072',axiom,
! [V_24Y] :
( c_24__type__105072___24t(V_24Y)
<=> t(V_24Y,c_24__type__105072) ) ).
fof('$tdef_$_type_42109',axiom,
! [V_24Y] :
( c_24__type__42109___24t(V_24Y)
<=> t(V_24Y,c_24__type__42109) ) ).
fof('$tdef_$_type_65663',axiom,
! [V_24Y] :
( c_24__type__65663___24t(V_24Y)
<=> t(V_24Y,c_24__type__65663) ) ).
fof('$tdef_$_type_22641',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22641___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22641___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_186399',axiom,
! [V_24Y] :
( c_24__type__186399___24t(V_24Y)
<=> t(V_24Y,c_24__type__186399) ) ).
fof('$tdef_$_type_5565',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__5565___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__5565___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_178117',axiom,
! [V_24Y] :
( c_24__type__178117___24t(V_24Y)
<=> t(V_24Y,c_24__type__178117) ) ).
fof('$tdef_$_type_176669',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__176669___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__176669___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_177021',axiom,
! [V_24Y] :
( c_24__type__177021___24t(V_24Y)
<=> t(V_24Y,c_24__type__177021) ) ).
fof('$tdef_$_type_177574',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177574___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177574___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__6841___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__6841___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_2606',axiom,
! [V_24Y] :
( c_24__type__2606___24t(V_24Y)
<=> t(V_24Y,c_24__type__2606) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31189',axiom,
! [V_24Y] :
( c_24__type__31189___24t(V_24Y)
<=> t(V_24Y,c_24__type__31189) ) ).
fof('$tdef_$_type_186836',axiom,
! [V_24Y] :
( c_24__type__186836___24t(V_24Y)
<=> t(V_24Y,c_24__type__186836) ) ).
fof('$tdef_$_type_107211',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__107211___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__107211___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_69754',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__69754___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__69754___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_68826',axiom,
! [V_24Y] :
( c_24__type__68826___24t(V_24Y)
<=> t(V_24Y,c_24__type__68826) ) ).
fof('$tdef_$_type_176660',axiom,
! [V_24Y] :
( c_24__type__176660___24t(V_24Y)
<=> t(V_24Y,c_24__type__176660) ) ).
fof('$tdef_$_type_686',axiom,
! [V_24X1,V_24Y] :
( c_24__type__686___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__686___24a1(V_24X1)) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_44604',axiom,
! [V_24Y] :
( c_24__type__44604___24t(V_24Y)
<=> t(V_24Y,c_24__type__44604) ) ).
fof('$tdef_$_type_44208',axiom,
! [V_24Y] :
( c_24__type__44208___24t(V_24Y)
<=> t(V_24Y,c_24__type__44208) ) ).
fof('$tdef_$_type_49204',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__49204___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__49204___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_38897',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38897___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38897___24a1(V_24X1)) ) ).
fof('$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_44205',axiom,
! [V_24Y] :
( c_24__type__44205___24t(V_24Y)
<=> t(V_24Y,c_24__type__44205) ) ).
fof('$tdef_$_type_8059',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8059___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8059___24a1(V_24X1)) ) ).
fof('$tdef_$_type_177598',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177598___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177598___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2726',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2726___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2726___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6614',axiom,
! [V_24Y] :
( c_24__type__6614___24t(V_24Y)
<=> t(V_24Y,c_24__type__6614) ) ).
fof('$tdef_$_type_6757',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6757___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6757___24a1(V_24X1)) ) ).
fof('$tdef_$_type_42140',axiom,
! [V_24Y] :
( c_24__type__42140___24t(V_24Y)
<=> t(V_24Y,c_24__type__42140) ) ).
fof('$tdef_$_type_42330',axiom,
! [V_24Y] :
( c_24__type__42330___24t(V_24Y)
<=> t(V_24Y,c_24__type__42330) ) ).
fof('$tdef_$_type_2619',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2619___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2619___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_62',axiom,
! [V_24Y] :
( c_24__type__62___24t(V_24Y)
<=> t(V_24Y,c_24__type__62) ) ).
fof('$tdef_$_type_42124',axiom,
! [V_24Y] :
( c_24__type__42124___24t(V_24Y)
<=> t(V_24Y,c_24__type__42124) ) ).
fof('$tdef_$_type_10379',axiom,
! [V_24Y] :
( c_24__type__10379___24t(V_24Y)
<=> t(V_24Y,c_24__type__10379) ) ).
fof('$tdef_$_type_142',axiom,
! [V_24Y] :
( c_24__type__142___24t(V_24Y)
<=> t(V_24Y,c_24__type__142) ) ).
fof('$tdef_$_type_515',axiom,
! [V_24Y] :
( c_24__type__515___24t(V_24Y)
<=> t(V_24Y,c_24__type__515) ) ).
fof('$tdef_$_type_925',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__925___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__925___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_69871',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__69871___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__69871___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_40214',axiom,
! [V_24X1,V_24Y] :
( c_24__type__40214___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__40214___24a1(V_24X1)) ) ).
fof('$tdef_$_type_11202',axiom,
! [V_24Y] :
( c_24__type__11202___24t(V_24Y)
<=> t(V_24Y,c_24__type__11202) ) ).
fof('$tdef_$_type_44094',axiom,
! [V_24Y] :
( c_24__type__44094___24t(V_24Y)
<=> t(V_24Y,c_24__type__44094) ) ).
fof('$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_69260',axiom,
! [V_24Y] :
( c_24__type__69260___24t(V_24Y)
<=> t(V_24Y,c_24__type__69260) ) ).
fof('$tdef_$_type_95',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__95___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__95___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_107896',axiom,
! [V_24Y] :
( c_24__type__107896___24t(V_24Y)
<=> t(V_24Y,c_24__type__107896) ) ).
fof('$tdef_$_type_38659',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38659___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38659___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_119',axiom,
! [V_24Y] :
( c_24__type__119___24t(V_24Y)
<=> t(V_24Y,c_24__type__119) ) ).
fof('$tdef_$_type_176762',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__176762___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__176762___24a2(V_24X1,V_24X2)) ) ).
fof('$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_681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__681___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__681___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_2494',axiom,
! [V_24Y] :
( c_24__type__2494___24t(V_24Y)
<=> t(V_24Y,c_24__type__2494) ) ).
fof('$tdef_$_type_46750',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46750___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46750___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_24136',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24136___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24136___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10544',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__10544___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__10544___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_44047',axiom,
! [V_24X1,V_24Y] :
( c_24__type__44047___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__44047___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25197',axiom,
! [V_24Y] :
( c_24__type__25197___24t(V_24Y)
<=> t(V_24Y,c_24__type__25197) ) ).
fof('$tdef_$_type_177593',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__177593___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__177593___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2195',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2195___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2195___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24856',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24856___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24856___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38',axiom,
! [V_24Y] :
( c_24__type__38___24t(V_24Y)
<=> t(V_24Y,c_24__type__38) ) ).
fof('$tdef_$_type_44294',axiom,
! [V_24Y] :
( c_24__type__44294___24t(V_24Y)
<=> t(V_24Y,c_24__type__44294) ) ).
fof('$tdef_$_type_220',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__220___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__220___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_53920',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__53920___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__53920___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_QuicksortComplexity.monads.Monad',axiom,
! [V_24Y] :
( cQuicksortComplexity_2emonads_2eMonad___24t(V_24Y)
<=> t(V_24Y,cQuicksortComplexity_2emonads_2eMonad) ) ).
fof('$tdef_$_type_69265',axiom,
! [V_24Y] :
( c_24__type__69265___24t(V_24Y)
<=> t(V_24Y,c_24__type__69265) ) ).
fof('$tdef_$_type_24141',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24141___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24141___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11324',axiom,
! [V_24Y] :
( c_24__type__11324___24t(V_24Y)
<=> t(V_24Y,c_24__type__11324) ) ).
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_$_type_22829',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22829___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22829___24a1(V_24X1)) ) ).
fof('$tdef_$_type_70279',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70279___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70279___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6487',axiom,
! [V_24Y] :
( c_24__type__6487___24t(V_24Y)
<=> t(V_24Y,c_24__type__6487) ) ).
fof('$tdef_$_type_43960',axiom,
! [V_24Y] :
( c_24__type__43960___24t(V_24Y)
<=> t(V_24Y,c_24__type__43960) ) ).
fof('$tdef_$_type_11320',axiom,
! [V_24Y] :
( c_24__type__11320___24t(V_24Y)
<=> t(V_24Y,c_24__type__11320) ) ).
fof('$tdef_$_type_28549',axiom,
! [V_24Y] :
( c_24__type__28549___24t(V_24Y)
<=> t(V_24Y,c_24__type__28549) ) ).
fof('$tdef_$_type_42087',axiom,
! [V_24Y] :
( c_24__type__42087___24t(V_24Y)
<=> t(V_24Y,c_24__type__42087) ) ).
fof('$tdef_$_type_48189',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__48189___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__48189___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_24835',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24835___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24835___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_55143',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__55143___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__55143___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_50565',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__50565___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__50565___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_185700',axiom,
! [V_24Y] :
( c_24__type__185700___24t(V_24Y)
<=> t(V_24Y,c_24__type__185700) ) ).
fof('$tdef_$_type_102',axiom,
! [V_24X1,V_24Y] :
( c_24__type__102___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__102___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38556',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__38556___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__38556___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_186510',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186510___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186510___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_49550',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__49550___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__49550___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_53707',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__53707___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__53707___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_38532',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__38532___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__38532___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_186487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186487___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_71051',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__71051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__71051___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_44321',axiom,
! [V_24Y] :
( c_24__type__44321___24t(V_24Y)
<=> t(V_24Y,c_24__type__44321) ) ).
fof('$tdef_$_type_34750',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34750___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34750___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_185961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__185961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__185961___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_39532',axiom,
! [V_24Y] :
( c_24__type__39532___24t(V_24Y)
<=> t(V_24Y,c_24__type__39532) ) ).
fof('$tdef_$_type_2188',axiom,
! [V_24Y] :
( c_24__type__2188___24t(V_24Y)
<=> t(V_24Y,c_24__type__2188) ) ).
fof('$tdef_$_type_51903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__51903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__51903___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_42451',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__42451___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__42451___24a2(V_24X1,V_24X2)) ) ).
fof('$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_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_177004',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__177004___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__177004___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_7908',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7908___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7908___24a1(V_24X1)) ) ).
fof('$tdef_$_type_68787',axiom,
! [V_24Y] :
( c_24__type__68787___24t(V_24Y)
<=> t(V_24Y,c_24__type__68787) ) ).
fof('$tdef_$_type_186394',axiom,
! [V_24Y] :
( c_24__type__186394___24t(V_24Y)
<=> t(V_24Y,c_24__type__186394) ) ).
fof('$tdef_$_type_479',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__479___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__479___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_70336',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__70336___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__70336___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7888',axiom,
! [V_24Y] :
( c_24__type__7888___24t(V_24Y)
<=> t(V_24Y,c_24__type__7888) ) ).
fof('$tdef_$_type_43988',axiom,
! [V_24Y] :
( c_24__type__43988___24t(V_24Y)
<=> t(V_24Y,c_24__type__43988) ) ).
fof('$tdef_$_type_199',axiom,
! [V_24Y] :
( c_24__type__199___24t(V_24Y)
<=> t(V_24Y,c_24__type__199) ) ).
fof('$tdef_$_type_10397',axiom,
! [V_24Y] :
( c_24__type__10397___24t(V_24Y)
<=> t(V_24Y,c_24__type__10397) ) ).
fof('$tdef_$_type_186701',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__186701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__186701___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29133',axiom,
! [V_24X1,V_24Y] :
( c_24__type__29133___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__29133___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_705',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__705___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__705___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_106961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__106961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__106961___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_46649',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__46649___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__46649___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_39840',axiom,
! [V_24Y] :
( c_24__type__39840___24t(V_24Y)
<=> t(V_24Y,c_24__type__39840) ) ).
fof('$tdef_$_type_108384',axiom,
! [V_24Y] :
( c_24__type__108384___24t(V_24Y)
<=> t(V_24Y,c_24__type__108384) ) ).
fof('$tdef_$_type_2168',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2168___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2168___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_105193',axiom,
! [V_24Y] :
( c_24__type__105193___24t(V_24Y)
<=> t(V_24Y,c_24__type__105193) ) ).
fof('$tdef_$_type_23683',axiom,
! [V_24Y] :
( c_24__type__23683___24t(V_24Y)
<=> t(V_24Y,c_24__type__23683) ) ).
fof('$tdef_$_type_39870',axiom,
! [V_24X1,V_24Y] :
( c_24__type__39870___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__39870___24a1(V_24X1)) ) ).
fof('$tdef_$_type_10449',axiom,
! [V_24Y] :
( c_24__type__10449___24t(V_24Y)
<=> t(V_24Y,c_24__type__10449) ) ).
fof('$tdef_$_type_66395',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__66395___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__66395___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_6810',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__6810___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__6810___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_107572',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__107572___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__107572___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('_HAMMER_GOAL',conjecture,
( cm = cn
=> ( cQuicksortComplexity_2eutil_2eext__eq___24a4(cA,cQuicksortComplexity_2emonads_2emon___24a2(cM,cB),cf,cg)
=> cQuicksortComplexity_2emonads_2ebind___24a5(cM,cA,cB,cm,cf) = cQuicksortComplexity_2emonads_2ebind___24a5(cM,cA,cB,cn,cg) ) ) ).
%------------------------------------------------------------------------------